ARTICLE
Econo-physics: A Perspective of Matching TwoSciences
Yuri YEGOROV
Institute for Advanced Studies, Stumpergasse 56, A-1060, Vienna, Austria, and University ofVienna, Department of Industry and Energy, Brünner Strasse, 72, A-1210, Vienna, Austria. E-mail: [email protected]
AbstractThe present article marks some potentially fruitful dimensions of economic research basedon principles of economic theory but using more analogies with physics. Molecularstructure of society with its different states, principles generating spontaneous orderdifferent from “invisible hand”, social analogies of the concepts of temperature and pressurein physics are investigated. Some analogies between phase transitions in physics andtransition between different social regimes can reveal the areas of stability of liberal regimesas well as possibility of spontaneous emergence of different social orders. A possibility toexpand neoclassical economics to capture Marxism and nationalism in a formalmathematical framework is also discussed.Keywords: economic structures, origin of order, econo-physics, socio-physics.
1. Introduction
This article is methodological. It focuses on economic and social questions that are
rarely touched by economic theorists despite their obvious importance for our
understanding of economic processes in the world. No fully formalized model will be
proposed here. Instead, the focus will be on interaction between economic elements and
emergence of structures. These ideas have been successfully elaborated in natural
science by physicists. That is why it makes sense to look for some analogies between
physical and economic concepts, and then to find ways of employing principles of
modelling from physcis into economic science.
The term “econophysics” is already used in narrow sense, to describe models of
financial markets using some ideas from physics (see Mantegna and Stanley, 2000).
However, the cross-fertilization between these two sciences allows for a wider treatment.
That is why here we will use another word “econo-physics” (and sometimes “socio-
physics”), following the paper by Aruka and Mimkes (2006) in order to escape
Evol. Inst. Econ. Rev. 4(1): 143–170 (2007)
JEL: B41, B51, B52, F02, P25.
misunderstanding in terminology. While the word “socio-physics” was not commonly
accepted among scientists that work in this field, there exist fundamental contribution to
this field from such authors as Haken (1977) and Weidlich (2002).
1.1 Motivation
The main goal of this paper is to describe directions of fruitful explorations, based on
past positive experience of physics and taking into account specific economic
assumptions. There is no criticism here about microeconomic preferences, but more
about little explored directions in economic science. The other goals of this article are:
a) to put some of the ideas into a language more common for economists (thus, not to
escape utility function, etc);
b) to describe different social organizations and ideologies of society (nationalism,
Marxism) in a mathematical framework that naturally extends classical economics;
c) to discuss multiplicity of social order-generating principles;
d) to discuss phases and phase transition in society.
Physics is a science about structures, their emergence and transformation. All the
nature has different level of organizations, and macro properties can be derived on the
basis of micro elements and interactions between them. Economics seems to move a
similar path, since agents are considered as fundamental elements, like atoms in physics.
However, economics at present is linear science in a sense that it puts an individual at the
absolute level and does not consider endogeneous emergence of structures of
individuals. Clearly, the primitives may be not individual agents but firms (in industrial
organization) or countries (in macroeconomics). However, little is done to understand
what kind of interactions bring individuals to the further level of organization (firms,
countries, etc). Physics has great experience of building links between micro and macro
levels. Statistical physics is the branch of physics that derives the changes of macro
states of matter through micro parameters. The theory of waves in continuous media
focuses on the link between micro and macro levels but in different research field. There
the local interaction between small subsets (neighbourhoods) leads to emergence of
complex dynamics in space and time. Physical chemistry studies the transformation of
properties of matter when coupling occurs at the level of (elementary) atoms that can
form different types of molecules. Finally, nuclear physics is about transformations
inside atoms changing their structure.
Clearly, not all of these transitions from micro to different macro levels can be
successfully implemented in economics. For example, changing internal structure of
atom would mean, if we employ the analogy between atom and economic agent, the
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change of agent’s nature. It may be of biological or psychological origin, but typically
economics consider individuals as stable over time. This change, for example evolution
of preferences with ageing, can be an interesting economic question, but it will not be
elaborated here. There also exist some problems with application of mathematically rich
theory of waves to economics. The problem is that there are too few observations
confirming existence of economic processes with deterministic cyclical origin. But while
economics is unlikely to give very rich field for mathematical models of regular wave
structures with deterministic nature, there still exist some works in this direction. That is
why analogies with statistical mechanics and physical chemistry might find easier
application in economic models. And this paper will concentrate more on these issues.
Section 2 is oriented on the necessity of common language of economics and physics
in order to deal with the phenomena of molecular structure of society. Section 3 is
devoted to origins of social order, that are complementary to market forces. Section 4
introduces thermodynamic concepts for society (analogies of temperature and pressure)
and describes several social types (solid, liquid and gas) that depend on combination of
these parameters. The role of altruism in preferences is discussed in Section 5. This goes
in line with new concepts elaborated in the book of Bowles (2003). Moreover, adding
altruism into preferences allows to describe not only liberal society (like neoclassical
economics does) but also societies of Marxist and nationalist types. Altruistic
preferences bring more solid grounding to emergence of social structures. Existing types
of equilibria developed by non-cooperative game theory are rather weak and unstable,
while even small altruistic element can make them more robust. An example is provided.
Section 6 deals with potential applications.
1.2 Link with modern paradigms in sciences
The agenda presented in abstract is unusual for a paper in economic theory. An important
aspect is related to heterogeneity and structure. While it is true that physicists also
consider the world to be formed of a large number of elementary objects (atoms from the
time from Aristotle to Newton, and elementary particles or quarks at later stage), these
particles are interacting not equally with each other, since this interaction depends on
distance and since they are located in different points in space at any time moment.
Clusters of particles form different structures starting from molecules and ending with
crystals. This gives self-evolving patterns, which at one level of abstraction can be
described as wave motion and at the other level as phase transition.
My agenda would be not in putting in doubt some mutually recognized principles of
economic science but rather to focus the attention on its limitation in conceptual sense.
Econo-physics: A Perspective of Matching Two Sciences
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That is why I want to keep all these assumptions about utility and rationality, but to
consider also some other conditions (acting as external forces). Different sections would
deal with some philosophical and methodological aspects of creating models in
economics.
1.3 Related literature
The ideas of unified science, including economics and physics, have been expressed
more than a century ago. The 120-year old ideas of Serhij Podolinsky to combine
Marxism with ecology have been rejected by Marxists. Proposal for unified science was
expressed by Otto Neurath in 1920s.1) Economics should include physical aspects of
human ecology, study of cultural, social, ethical influences on production and
consumption (see Krishan et al. (1995)).
This agenda became critically important in the last 3 decades of the 20th century,
when ecologists realized the danger of combining the reality of exhaustible resources
with the continuing growth of population and production. The necessity of ecological
economics was formulated by Goodwin. He proves the existence of substantial set of
questions, which are addressed to real economic problems and located on the frontier of
traditional economic science, and tries to study questions on the intersection of different
sciences. He says that “if the study of economics is to be of value to society it must stress
the aspects of economic behaviour that matter the most”.2) A number of critical areas of
economic thought have been left by mainstream economists on the margin. He argues
that while the relevant agenda was formulated by classics of economics in the past, some
priorities have been shifted later. For example, Adam Smith put similar value to the
concepts of wealth, morality and nation, but currently the last two concepts are out of
interest of mainstream economics. Similarly, von Thünen in 1826 pioneered the research
of spatial economic structures, which later became a part of regional science, but this
field is left out of major economic textbooks in microeconomics.
Ecological economics, although inspired by ecological degradation and ideas of
sustainable development, is not a science of ecology, but also addresses the questions of
evolution of purely economic systems (see ch. 8 in Faber et al. (1996)). The authors use
a parallel between physics, theoretical biology and economics and try to classify what
processes are predictable and non-predictable in all these sciences. Physical systems
exhibit the highest degree of predictability, due to lower complexity, partly in
deterministic and partly in stochastic terms. This was the major reason of successful
Y. YEGOROV
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1) See the summary of “The history of future” by J. Martinez-Alier and K. Schluppman there.2) See introduction to the book by Krishan et al. (1995)
development of mathematical tools describing dynamical systems in physics. Economics
also exhibit phenomena, which are completely predictable, and establishing of market
equilibria is one of such phenomena. However, economics does not use all available
techniques from physics to explain other classes of processes that are also predictable.
The difficulty of economic modelling can be easier understood on the basis of statement
of theoretical biology about “fundamental unpredictability of genotypic evolution”, in
contrast to phenotypic evolution. The economic analogy of genotype is innovation.
While evolutionary path after innovation occurs can be predicted, the moment of
innovation cannot.
Here the issues of non-predictability and evolution will not be substantially
elaborated. Instead, more attention will be paid to structures and mechanisms of their
emergence and survival under changing conditions. This already represents wide
direction of research, and little analytical work was done here by economists so far.
A nice exception is the book of Bowles (2003), where he suggests evolutionary theory
of institutions. Non-market social interactions represent one of key points of his
research. He studies co-evolution of individual preferences and structures of markets
using dynamic models. This agenda differs substantially from one delivered by classical
microeconomics, but it allows to explain much more historical episodes and empirical
puzzles.
In the article by Aruka and Mimkes (2006) different areas of influence of physical
ideas on social sciences and economics are discussed. The importance of considering
heterogeneous interacting agents is stressed. While agents’ heterogeneity is sometimes
present in economic models,3) most of classical economic papers deal with homogeneous
individualistic agents. Such an approach is easier from methodological perspectives,
because it allows to build self-consistent economic theory based on rationality principles,
while heterogeneous assumption often requires the shift to bounded rationality.
Following the principles of homogeneity and full rationality limits the possibility of
modelling real social phenomena (like wealth distribution) and broadens the gap between
theoretical and empirical economics.
The role of synergetics (see Haken (1977)) in understanding social dynamics is
important. There are two levels: micro and macro. Macrodynamic evolution is
dominated by few key variables, named order-parameters. Macro states of a social
system are described in probabilistic terms. The central equation of evolution for the
probability distribution over the macro variables is called Master equation (see Weidlich
Econo-physics: A Perspective of Matching Two Sciences
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3) In fact, WEHIA conferences by definition deal with this type of agents.
(2002, 2006)).
The main claim of the work by Bowles and Gintis (2005) is that “other-regarding
preferences such as altruism and reciprocity are essential” for understanding why
humans are cooperative. At the first glance, cooperation often takes place even if the
preferences are self-regarding (like in almost all research of economics). However, these
theories are not sufficient to explain all evidence. For example, reciprocal altruism
provide some explanation of cooperation among dyads, but not in larger groups and
when future interactions are unlikely.
Kara-Murza (2002) writes that Thomas Gobbs has developed the myth about man as
egoistic and individualistic atom. These “atomic” ideas emerge every time when ruling
groups want to impose liberal economics in the society. Emergence of industry and
market economy required the freedom of a man from conservative political, economical
and cultural structures. The ideas of atomism and rationality allow solving two
ideological tasks of rising bourgeoisie: to legitimate new political order and new
economic order.
Skirbekk (2003) analyses the negative influence of the presently dominant liberal
ideology on social moral, growing instability of family and argue about the missed
positive elements of traditional cultures and ideologies that went to decline in the end of
the 20th century.
Emergence of structures (large groups, countries) resembles emergence of molecules
or crystals from atoms. In physics, this requires the field of interaction. The standard
assumptions of economic theory (self-regarding preferences, non-convexities) do not
allow for emergence of such structures. Thus they are either considered as given (firm,
state) or not considered at all. The papers of Yegorov (2001b, 2005a) study the
emergence of such groups on the assumption of non-convex technology that makes it
optimal for group members to keep group growing in a dynamic sense until it reaches its
optimal size. Also, the conditions of country emergence are considered. It is shown that a
territory of certain size becomes an optimal structure for its inhabitants (assumed to be
homogeneous) when we move from micro to macro level and consider the balance
between benefits from harvesting certain territory and the costs to protect its border and
to maintain centralized structure that needs communication with all points (regions) for
efficient management.
As will be claimed later, both spatial structures in economics (location heterogeneity
plus transport cost) and scale economies play important roles as origins of order in
society. Some ideas of the author in both of these areas can be taken from Yegorov
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(1998, 2001ab, 2005ab).
2. Working Out Common Language between Economics and Physics
The tragedy of contemporary science is an increased specialization, leading to
impossibility of general public to understand science. This property was mentioned by
Kuhn (1970). That is why one cannot use the language of most sophisticated concepts
inside physics and economics. In order to be understandable to more scientists, it is
better to use relatively simple concepts from both sciences and to find link across them.
Only simple concepts from physics such as “particles”, “state of matter”, “field”,
“energy”, which are studied in school, will be employed here. Economic concepts of
similar simplicity would be employed as analogy. I am fully aware that complete
analogy is impossible, but even incomplete analogy can be powerful. Below I introduce
several concepts that can be used as approximate translations from language of “physics”
to “economics” and visa versa.
Elements
The elements in physics are “particles”, “atoms”, while in economics the analogy is
played by “agents”. Clearly, there is a difference since particles cannot think, while
agents obey laws of behaviour different from particles. But the analogy can be exploited
when we are doing aggregation and consider nonlinear interactions between elements.
Simple structures
In physics “molecules” represent a relatively stable union of a small number of atoms.
Similar structures also exist in economics; for example, family or small business.
Complex structures
In physics complex structures emerge on macro level. In statistical physics, the micro-
state is a set of many particles with their coordinates and velocities (which is never
completely observed). The parameters of macro-state (temperature, pressure) can be
measured. Physics knows how to interrelate macroparameters with distribution of micro-
parameters. Economics is addressing similar models when it talks about aggregation,
from micro to macro level.4) Economy, state or global society are examples of complex
structures in economics.
Interaction
In physics, particles interact via the field. All fields are usually declining with distance
according to a particular inverse power law. The coordinates of particles make them
naturally asymmetric with respect to field. Depending on initial conditions, different
Econo-physics: A Perspective of Matching Two Sciences
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4) See the papers of Hildenbrandt.
structures can emerge. For example, gravity force has created a system of planets. On
micro-level, molecules are stable structures of the field generated by particles. It is
worthwhile mentioning that nonlinearity and heterogeneity are responsible for
emergence of most structures. In economics, interaction is usually modelled as linear:
agents contribute their endowments to the market, and take other products from there,
according to their preferences. The only nonlinearity can come from utility, but as it is
ordinal, this nonlinearity does not play a crucial role. Nevertheless, markets exhibit self-
organizing property.5) Non-linear element of interaction among agents is given by
externalities. The potential of externalities in building stable structures in economics is
still under-exploited, and one of the goals of present work is to attract attention to this
problem.
Characteristics of elements
In physics, particles are characterized by their coordinates, velocities and energies. Due
to Heisenberg inequality from quantum mechanics, the first two parameters cannot be
measured exactly on micro level. On the other hand, energy can be defined and
measured. Economic science may also have a type of Heisenberg inequality, because
some microeconomic parameters (like utility) are not observable directly. This is an
interesting question, however it is not developed yet. In economics, an analogy of
coordinates and velocities can be given by dynamic pattern of consumption bundle,
while “wealth” (or income) is an analogy of energy. The latter can be easier observed.
Thus, macroeconomic state should depend on wealth distribution of agents, which is
measurable in reality. The role of wealth distribution for the stability of social structures
will be discussed later.
Characteristics of structures
Structures in physics can be characterized by their total energy, mass, entropy, type of
micro-order (crystal or gas, for example). In economics, macroeconomics deals with
country’s GDP, interest rate, growth rate, etc. The parameters characterizing type of
order (see section 3) are usually not studied by economics, although they represent an
important macro characteristic of society.
2.1 Molecular structure of society
Classical microeconomics and industrial organization consider the number of firms as
given. Thus, they view firms like mechanics views atoms, but do not allow for an
analogy of chemical reactions. In real business, firms may split, join together, be born
and die.
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5) In the sense that they generate equilibrium under certain assumptions (see Arrow-Debreu theory).
Molecules of firms can form chains with local interaction. This is similar to a structure
of polymer. The idea of “polymer society” is represented in the studies of network
economics, especially the part related to emergence of random networks with short-scale
or long scale links.6)
Structures can be imposed (by state) or self-organized (emergence of small firms of
Italian type, with about 10 workers, mostly relatives; or agricultural cooperatives). The
influence of state on economy is studied by economics of public sector (see the book of
Stiglitz (1988) as an example). Self-organization of structures can occur on the basis of
mixed utility (see mathematical model subsequently). Physical analogy: forced order or
crystallization in external field vs. spontaneously emerging clusters.
Different particles of physical substance have different energy, and stable distribution
of their velocities in gas can be an analogy to stable distribution of wealth in particular
societies. This question of wealth distribution deserves special attention and will be
briefly elaborated later.
3. Equilibrium, Structure and Order in Economics
The concept of equilibrium plays the major role in theoretical economics. The principle
of equilibrium was brought to economics from mechanics. Equilibrium world was
neither scientific nor logical conclusion. Equilibrium in economics was not a discovered
law. Contrary, the search for economic laws was based on beliefs in equilibrium. All
economics (political economy) starting from Adam Smith, neglects all sources of
disequilibrium (see Kara-Murza (2002), pp. 124–125).
3.1 Why structure is important?
When we look at structures in natural sciences (physics, chemistry, biology), we find that
structure is some composition of elements which is relatively stable under some range of
external parameters and thus can be observed. For example, some chemical elements are
observed on earth in natural conditions, while other need some special laboratory
conditions. Species and populations are biological structures, also composed of elements.
When they die, they are decomposed back to sub-elements. In social sciences, structures
include some composition of elementary agents: firms, clubs, countries, mankind.
Neoclassical economics does not pay much attention to these structures. However, even
its father, Adam Smith stressed the importance of states and nations as objects of study
of economics. Neoclassical economics exploits another idea of Smith, “invisible hand”,
Econo-physics: A Perspective of Matching Two Sciences
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6) See Stocker et al. (2000); there are also many unpublished drafts presented at conferences and
seminars.
which brings spontaneous order by market forces. Despite the relative success of this
idea for explaining spontaneous order, it is clear that it is incomplete.
3.2 Structures and transition in Russia
Application of ideas from neoclassical economics with welfare theorems to transition in
Russia in 1992 was not a successful experiment. Only in 1999 J. Stiglitz has recognized
that this type of transition was a mistake for Russia. Many structures have been
destroyed during transition of 1990s. It was clear that changing environment should
destroy some of the old order, but it is not clear how new order can emerge from chaos.
Global shocks on Earth have led to death of some populations (dinosaurs). But they are
not replaced immediately by new types of species. When a biological object dies, it
dissolves into molecules, which give rise to emergence of some low-structured life
(bacterias). It takes long time for evolution, for life of higher complexity to emerge. If
the higher level of economy (high-tech industry) is dead during transition in a particular
country (Russia), elements (capital and labour) become free. But capital in a form of
constructions may become obsolete, while labour can find itself facing the only
possibility to start individual activity or small business. It takes some time for high-level
firms to organize on these ruins, and the only possibility is takeover by transnational
companies. However, in 1990s capital was not flowing freely in Russia, and one reason
behind that was described by Parshev (2001). I will not focus now more on transition.
The goal was to show that study of emergence of structures is crucial and should be hot
topic for modern economics which wants to explain processes in real but not imaginary
world of abstract spaces that some part of modern economic theory does.
3.3 Origins of order in society
It is important to formulate this philosophical question about origins of social order.
While it is clear that its substantial investigation in one isolated article is impossible, it
still makes sense to suggest some working hypothesis.
There exists at least three main forces generating spontaneous order in economy. The
first one is well known from microeconomic textbooks. It is linked with market forces
caused by diminishing returns and competition (they are responsible for the effect of
Adam Smith’s “invisible hand”).
The second force comes from studies in regional science and economic geography
(see, for example, Beckmann and Thisse (1986)). This force may bring complementary
properties to those derived by non-spatial economic theory. For example, monopolistic
competition of Chamberlin (1933) reveals the existence of spatial areas around a firm
when they act as local monopolists and compete only through edge consumer.
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Monopolistic competition with product differentiation (see, for example, Fujita,
Krugman and Venables (1999)) rely on completely different case (methodological and
topological), where consumers have access to all variety of commodities. Spatial forces
based on transport cost and local interaction become responsible for geographical,
location effect, which are always present and cannot be fully controlled by rational
decisions. Some spatial effects are elaborated by Yegorov (2005b).
The third self-organizing principle is based on nonlinear interaction of elements (when
the whole is not exactly sum of its parts). Without trying to present sufficient literature
survey on this topic, I will just mention two important publications: Arthur (1994) and
Durlauf and Young (2001). This principle summarizes the self-organizing role of
externalities. They can bring the difference between social outcome and individual
preferences (like in segregation model of T. Schelling). They often lead to multiplicity of
equilibria, also in dynamic sense.
Role of space
Space works as an element imposing heterogeneity (at least, with respect to distance),
and thus bringing nonlinearity to interaction of a priori identical elements.7) But space
also works as a stabilizing factor. For example, the IRS technology in a spaceless context
gives rise to a firm of infinite size. With transport costs and topology of real geographical
space, optimal cooperation extends to a particular spatial limit (see Yegorov (1998,
2001a)).
Analogy with different sciences
This duality between market and spatial forces is similar to one argument of social
scientists about the role of biology and environment in human beings. Most likely,
humans are not fully predetermined by genetics. Maugli’s example shows that an
important part of individual formation depends on the environment. However, it would
be too far-fetched to expect that everything depends on environment and has no relation
to genetics and biology. Economists (except for regional scientists) mostly ignore the
spatial forces. Another extreme view (complete geographic predetermination) is also
unlikely to be true.
Econo-physics: A Perspective of Matching Two Sciences
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7) Hence, agents equal in skills become unequal just due to location difference. This contrasts an
approach of urban economics where at equilibrium such agents have a possibility to change location
but are indifferent to do it. Frictions and historical factors might make this inequality persistent (like
people got used to less productive land and not all migrate to the region where they would have higher
productivity.)
It makes sense to describe the mechanism of self-organization of spatial structures in
economics. Geographical forces are considered as “gravity” by some economists, with
complete copying of inverse power8) Newton’s law, and this has no microeconomic
justification. But it is possible to build a simple model describing an emergence of a
country of optimal size (Yegorov, 2005a) based on the principles of optimization,
transport costs and Euclidean geometry applied to continuous space.
Order-generating principles
It makes sense to end this discussion with a potentially incomplete list of principles that
generate order.
1. A common idea (religion, nation) can be responsible for non-market grouping of
large number of people. Historically such groups had leaders accepted by all. This
leads to society of crystal type, since agents sacrifice some part of individual
preferences in favour of joint preferences of the society (nonlinearity).
2. Consider a community of farmers-landowners. When land slots are fixed by law
(inheritance, etc), there no room for conflicts. Endogeneous cooperation can emerge
in sharing machines, due to scale economies.9) Here we have mixed effect of spatial
economics and nonlinearity.
3. The balance between increasing returns to scale and transport cost in the
environment of consumers spread over space can lead to emergence of optimal
spatial structures, which are vulnerable to the change of external parameters, like
world price for energy or transport cost; see Yegorov (1998, 2005a).
4. Invisible hand is also responsible for emergence of order, and this is done by
neoclassical microeconomics. However, some equilibria are not robust or
dynamically unstable, and thus they are not considered in dynamic framework.
4. Role of Analogies of Temperature and Pressure in Society
Thermodynamics is one of branches of physics that is formally close to economic theory.
Contrary to many “open branches” of physics that are not formalized axiomatically and
develop together with new empirical findings, thermodynamics is deduced from a set of
axioms and thus formally resembles the building of contemporary economic theory.
Y. YEGOROV
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8) Newton’s law has inverse first power for potential, and inverse second for a force; economists more
often use inverse first power.9) This case was observed in 1920s in Soviet Union, after revolution and before collectivisation,
which has not been endogeneous formation of cooperatives but too rapid process influenced by
external force.
However, there is an important difference in one property of studied processes.
Thermodynamics studies irreversible processes. They are different from those in Newton
mechanics, because at macro level (and thermodynamics formally deals with the
properties of large groups of molecules, although a formal link between micro and macro
levels is studied by statistical physics) time in physics becomes irreversible.
For microeconomic theory this question is irrelevant, since it typically abstracts from
dynamic processes. However, even if it would do dynamics (like macroeconomic growth
models, for example), the principle of equilibrium would put important limits to the set
of studied questions. In thermodynamics and statistical physics only a class of adiabatic
processes (infinitely slow) is reversible.
But the main goal of this section is different: it is related to finding the analogies
between some macro variables in thermodynamics and in social science.
4.1 Analogies
In physics, temperature T represents one of the parameters responsible for different states
of matter as well as phase transitions between them.10) Temperature of gas is related to
the average energy of molecules. The increase of temperature leads to the transition from
solid state to liquid, and later to gas and plasma.
The second parameter is pressure p. If temperature is kept constant, the decline of
pressure works in a way similar to temperature increase.
The thermodynamic state of gas in a fixed volume V is described by the law of Boyle-
Mariott: pV�Tc, where c is constant for fixed mass and chemical composition: c�Rm/m .
The average kinetic energy, K, of molecules in gas is much higher than potential energy
of interaction, ∏: K/∏��1. For liquid, they are of similar order, while for solid state the
relation is reversed: K/∏��1.
Low temperature and high pressure create crystals with long-scale order. High
temperature and low pressure create gas with no order, practically chaotic motion. Liquid
is an intermediate stage, while liquid polymer is a particular case of rather complex chain
structure.
Now consider social analogies. Temperature is an analogy of economic wealth w,
while inverse pressure is an analogy of economic freedom, f.11) The increase of wealth
and individual freedom should lead dictatorship to democracy through a chain of
Econo-physics: A Perspective of Matching Two Sciences
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10) In fact, this is a general philosophical law of transformation of quantitative change into qualitative
change, discovered by Hegel.11) While it is difficult to propose quantitative formula for economic freedom, it is clear that one is
higher in democratic society than under dictatorship.
intermediate states. There is an analogy between dictatorship and solid state, and
between democracy and gas. For dictatorship, the ratio of individual energy to social
energy (measured for example, as the share of freely disposable income in per capita
GDP) is low, while for democracy it is high. Another prediction based on physical
analogy is that democracies should be richer societies than dictatorships.
4.2 Solid, liquid and gas-type societies
In nature we have a variety of different chemical substances with a common property: to
be sequentially in solid, liquid and gas states depending on temperature and pressure.
The trip of “Voyager” towards giants of the Solar system has discovered different
substances on different planets to be in states different from those on the Earth. This is a
collective interaction of identical elements, that gives rise to different states under
different external conditions. Although the similar theory of society is currently absent,
economic models involve representative agents which to some extent are analogies of
atoms or molecules.12) We observe societies (also in historical retrospect) with different
level of individual freedom. In dictatorships we have low level of individual activity in
comparison to social; these are “solid” societies. Fully liberal societies (where the role of
state can be asymptotically neglected) have unrestricted individual activity, and all
equilibria (at least in neoclassical economic models) emerge under this assumption.
The intermediate case corresponds to “liquid society”. In physics, liquid is
characterised with low-distance order and long-distance disorder. Models based on local
interaction satisfy this property. This is also similar to economics of networks, which is
now becoming increasingly popular. Liquid society may contain spontaneously emerging
chains of polymers.13) It usually takes place in moderately rich societies with some
degree of individual freedom. Strong state and little individual wealth prevents this state
from emergence. Mafia, at least in the sense of unofficial power different from state,
usually do not emerge in very poor and very rich society, and when state is extremely
strong.
Interaction between agents of different types can be neutral, positive or negative. In
the paper by Aruka and Mimkes (2006) six real structures of agent interaction are
introduced: segregation, aggression, partnership, hierarchy, democracy and global
Y. YEGOROV
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12) The economic concept of agents does not specify whether agent can be given by individual,
household, firm, etc. Usually it assumes that agents are identical, which suggests that individuals are
considered. It is also problematic to talk about unique utility for a group of agents. That is why
economic individuals resemble atoms in physics, while household–molecules.13) Examples of these polymer structures contain mafias and clans.
structure. Classical economics deals more with either no interaction (everybody
maximizes own utility, gas-type society) or negative interaction (an attempt to gain at the
expense of partner is common in games considered by economists). It is important to
mention that a theory of positive interaction (altruism) is also finding its way among new
trends of economic theory (see Bowles, 2003).
5. Extensions of Neoclassical Economics: Mathematical Formalization
5.1 Post-Liberal Economics: Necessity to build a link between main
fundamental ideologies
Globalisation process sets forward a problem of coexistence in the world with
different ideologies. In order to understand how multiplicities of social structures can
coexist, interact and transform into each other, it is necessary to have common language
for expression of global states of economy. Especially this was important before
transition. How was it possible to talk rationally about it, if there was no economic
language to describe transition path (it started in one society and had to end in another)?
Contribution to political science is also on agenda. This section aims to introduce some
mathematical elements of formalization of the problem.
Bowles and Gintis (2005) show that it is difficult to sustain cooperation in n-person
public good games, like food-sharing, co-insurance, common defence, information
sharing, by means of standard tit-for-tat and other reciprocal strategies. The
contemporary study of human behaviour has documented a large class of social
behaviours inexplicable in terms of reciprocal altruism. Laboratory and field experiments
show that other-regarding preferences cause robust cooperative behaviour, even in
anonymous setting. These finding put the investigation of non self-regarding preferences
into the agenda. Almost all microeconomic textbooks (with a nice exception of Bowles
2003) exclude them from consideration.
The link between a dominant economic theory (neoclassical economics) with the
ideology of liberalism is obvious, but is not discussed by economists. While Marxism
was the major ideology for substantial part of the world during several decades of the
20th century, there was no attempt to translate its paradigms into mathematical language
and to compare them with those from neoclassical economics. Here it is important to
make a distinction between works of K. Marx and Marxism as one of important
ideologies. In its practical implementation (Soviet Union, Eastern European countries,
China) it lead to low income dispersion and caring about the utility of the poorest
members of the society. This section aims to suggest a direction in mathematical
Econo-physics: A Perspective of Matching Two Sciences
– 157 –
economics, along which such a link can be done.
5.2 Preferences
Despite significant ideological difference with neoclassical economics (and not less with
Marxist or other alternative), I will follow the formal canons of neoclassics and start with
assumptions and mathematical formulations.
In order to cross the natural border of neoclassical economics and to build a formal
link with formal economics, describing alternative social structures (nationalism,
Marxism), it makes sense to extend individualistic utility function, in order to capture
some altruism, or care about social utility. The social welfare functions are studied in
public economics and normally include a wide spectrum of utilities formally captured by
the formula
(1)
where a�[0,1]. In the limit case, a�1, we get utilitarian social indifference curve:
. Without special justification at the moment, we will consider this
social utility to correspond to nationalist society. Consider as an alternative Rawlsian
social indifference curve, formally given by the wealth of the poorest member of society:
Usoc|a�0�miniU0,i. This concept is very close to Marxian paradigm, since in this case
equalization of income of all members of society brings the highest social welfare. The
basic difference of nationalist society from Marxist society is that wealth inequality in
nationalist state does not generate envy, and all agents are better off if some members of
their nation become richer. The next step is a formal link between individualistic and
social theories. Let us make formal assumptions.14)
Assumption 1
Individual utility in a nationalist society is a weighted sum of own utility plus the sum of
utilities of all members of the nation:
(2)U U Ui i i
j
� �0 0, , .β∑
U Usoc a i
i
| ,� �1 0∑
U Usoc ia
i
a
� 0
1
,
/
,∑
Y. YEGOROV
– 158 –
14) These assumptions assume some level of altruism which is also studied by economists. We do not
focus the attention here on the extent of this altruism (family level, nation level or global level). Every
level can generate some structures of different order, and we focus on a country level only in order to
use minimal mathematical complexity.
Assumption 2
Individual utility in Marxist society is given by another weighted sum:
(3)
Corollary 1
Both nationalist and Marxist societies, in contrast to liberal individualistic society,
assume some level of altruism, since b�0.
Corollary 2
These utilities allow for some (nonlinear) interaction between members of the society,
which normally15) gives rise to spontaneous emergence of some state-type structures,
which can become a separate subject of action and not necessarily act in line with the
preferences of all society members. On the other hand, liberal principle, under certain
condition16) considers state as something external, destroying Pareto optimality which
spontaneously emerges on liberal market.
Corollary 3
The distribution of wealth matters for both nationalist and Marxist societies, while it
does not matter for liberal society, because the latter has no nonlinearities in market
interactions. This issue will be studied further.
This is only the first step of mathematical formalization. It is based on existing
concept of social utility (see Stiglitz, 1988), introduction of second dimension in
individual preferences (idea of McClintock (1978)) and coexistence of three main
ideologies (liberalism, nationalism and Marxism).
We can see that neoclassical economics based on liberal principles is an asymptotic
limit of nationalist or Marxist society, for b→0. It shows also why altruism is not
included in neoclassical agenda: it gives rise to spontaneous emergence of state-type
structures through preferences. But historically one can deal with existing state. One can
remember how aggressively the state was destroyed in the former Soviet Union: before
1990 it controlled the production of almost all output, while in 1999 the state controlled
less than 20% of GDP, which was an overshooting not only with respect to EU countries
(with about 50%) but also USA (with about 30%).
5.3 Scale economies and externality effects
The emergence of stable structures in physics occurs through potential of interaction.
U U Ui ij
j� �0 0, ,min .β
Econo-physics: A Perspective of Matching Two Sciences
– 159 –
15) This is a result of synergetics.16) No externalities, perfect information, etc — see Stiglitz (1988) for details.
Generally, the energy of the system is not equal to sum of energies of separate parts but
is given by:
(4)
The difference represents interaction. In economic language, it is externality. Economic
models are mostly linear, i.e. they ignore interaction potential. The theory of firm in its
part related to its spontaneous emergence, is not a part of modern economic theory. But it
is clear that externality effects play role here.
Externalities for labour
Consider a production function with labour being the only input: Y�f(L). Since labour is
not infinitely divisible, consider self-employment as a firm with minimal quantity of
labour. If technology is such that joint productivity of 2 workers is higher than sum of
their productivities if they work separately, Y(2)�2Y(1), we have positive externality, or
increasing returns to scale (IRS) effect to labour input in technology, and thus a potential
for cooperation. As is shown in Yegorov (2001b, 2005a), the distribution of output for
this technology is not obvious, and there may be contradictions between individual and
group goals if we base conclusions on standard microeconomic principles. Modern game
theory focuses too much on the bargaining problem. It makes sense to consider the case
when bargaining would not emerge at all, i.e. individual optimisation will coincide with
group optimisation. But if preferences are altruistic (of type (2)), there might be some
range of parameters b so that there is no contradiction.
Externalities for capital
Now consider a technology with capital K as unique input. Assume that agents’
individual wealth, W, is an upper limit for capital that they can use for investment.
Consider technology Y�g(K), with g of IRS-DRS type. Then, at some level of K�K*,
the average capital productivity Y/K is maximized. If the total capital in society with N
agents is KN, then it is socially optimal to split it into M firms, each of size K*�KN/M.
Now consider individual investment decisions. For low W, several agents need to
cooperate to start a firm with K*. In a rich society individual may own a firm.17) If wealth
grows, less cooperation is required, and society becomes more atomised. This is
completely in line with the discussion about the role of temperature in society provided
above.
E system E Ei
i
( ) ( ).� � interaction∑
Y. YEGOROV
– 160 –
17) This is more applicable for agriculture, with small farms, and necessity to cooperate for poorer
people.
5.4 Local cooperation leading to emergence of ethnic group
The role of altruism in preferences is important for many reasons. Some of them have
been discussed in the book of Bolwes (2003). Here an example is provided. It has two
goals: a) to demonstrate that altruism can bring more stability to the concept of equilibria
and to lead to more robust structures, b) to explain possible mechanism of emergence of
ethnic group.
The idea of the model is based on the stylised fact about cooperation inside local
communities, along to their suspicion to a stranger. The border of a community may be
different: some people put it on a broad family, some on nation, there also exist
internationalists, with altruistic attitude towards all human beings. It is clear that
altruistic component plays an important role in such formations, as well as the link
between nation and particular area on geographic map. The goal of this model is to
propose a procedure leading to an emergence of such structures.
Consider uniformly populated landscape, where agents can be put on a lattice (in
discrete model) or occupy the space with a uniform population density. Two-
dimensionality and geographical relief are not very important at this stage. Thus, it is
assumed that agents live on a line, each occupying a particular location x. Geographic
dimension is not a unique dimension in this model. Assume also cultural difference
(language, habits, traditions, religion), measured by a function h(x), which is assumed to
be slowly varying with spatial coordinate: |h�(x)|��1.
Local interaction and altruism
In order to model interaction, we assume that initially agents are playing prisoner’s
dilemma game with their neighbours. The payoffs are given by the matrix18) (Table 1):
This game has bad (not efficient) Nash equilibrium (1, 1) in a standard framework of
preferences.
Now assume that both agents value not only their utility Ui, but utility of their partner
as well (Table 2):
Table 1. Game for U
L R
U (3, 3) (0, 4)
D (4, 0) (1, 1)
Econo-physics: A Perspective of Matching Two Sciences
– 161 –
18) The payoffs are chosen just for illustration
V1�U1�aU2,V2�U2�aU1, (5)
where a�(0,1) — coefficient of altruism. The new game for V is given by the following
table of payoffs. Depending on a , we can get a shift to more efficient equilibrium UL.
We need a�1/3 to have such a shift.
Radius of cooperation
Let us assume that the level of altruism depends negatively on total distance between any
pair of agents,19) d�d12�mDx�Dh. This can be a combination of geographical and
cultural distances. Historically, people did not move a lot,20) and geographical proximity
implied cultural and religious proximity. Suppose that a�1/(1�d ). Then for d�(0,∞)
we have a�(0,1). We immediately arrive to spatial pattern of cooperation. In our game
people with distance d�d*�2 would select efficient equilibrium. Translation into
normal language would mean that “local communities play games cooperatively across
them, but may be noncooperative with strangers”. This behaviour can be easily observed
in some modern cultures that have kept traditions (Greece or Japan, for example).
So far, we have explained why an agent would treat his local community better than
strangers. But we have not explained, how nations, with much higher radius of territorial
distance (R��d*), would form a cluster of cooperation. We need to describe the
mechanism of spatial propagation of local interaction, which at the same time ends at
some border. Such borders are usually determined by either language or religious
Y. YEGOROV
– 162 –
19) Here m�0 is a parameter, which can be used for setting different weights for geographical and
cultural differences.20) In the sense that a small fraction of population migrated on long distances during their lifetime.
Only recently overall migration increased significantly.
Table 2. Game for V
L R
U (3(1�a), 3(1�a) ) (4a , 4)
D (4, 4a) (1+a , 1+a)
differences.21)
Travellers
Now assume that agents can travel, but their frequency of travel declines with distance
exponentially. In other words, his probability to play a game with an agent at the
geographical distance x is P(x)�le�l ,x. Such a specification satisfies the necessary
condition for probability distribution: ∫0
∞P(x)dx�1. At the same time we will consider
factor m to be a small parameter: m��1. In other words, agents almost neglect
geographical distance and look only at cultural. Still, we cannot take geography out of
the model, since it defines the pattern of travel. We also assume that initially agents were
grown in a cooperative neighbourhood and got used to it when they became adults and
started to travel. Finally, we assume that agents cannot measure cultural difference
before interaction but can observe it through response. They can adapt their behaviour in
two ways: a) they reverse cooperative to non-cooperative behaviour, if the payoff (in V!)
becomes smaller than for alternative strategy; b) they travel less frequently to the
direction where they have observed non-cooperative behaviour.
Propagation of cooperation in space
Without focusing on initial emergence of cultures and languages, we will consider spatial
heterogeneity, characterized by function h(x), as given. Clearly, it has areas of slow
variation (dialects, for example) and sharp borders, where transition occurs over small
geographical distance Dx. Define the area with no sharp differences in culture as pre-
nation area. As people increased their mobility (and this happened historically with the
development of transportation), parameter l declined. Agents started to cooperate in a
broader neighbourhood, and they did not learn to reverse their behaviour unless they
lived close to cultural border, and had high fraction of communications with different
culture, which has resulted in suboptimality of cooperative behaviour. By learning to
move there less frequently, they managed not to reverse initial strategy of cooperation,
which finally has covered all pre-nation area. This is how nations could have formed.
Econo-physics: A Perspective of Matching Two Sciences
– 163 –
21) Holland and Belgium represent a good example. Belgium is not homogeneous, with Flemish
(almost Dutch) language spoken on the North and French in the South. At the same time, it is
religiously more unique, since the border between Catholic and Protestant religions approximately
coincides with the border between two countries. This shows more important role of religion in
comparison with language, in defining historical borders of a country. However, often the difference
of only one factor is sufficient for separations. We can observe a variety of languages and religions
inside one country for former empires, which worked as an external force to put together communities
that would segregate otherwise.
6. Applications
The goal of this section is to describe the directions where this philosophy of research
can be applied. It is impossible to predict now all fruitful applications, but it makes sense
to mention some of them. Some elaboration is done with the concept of wealth
distribution and stability conditions for liberal society. The final subsection tries to bring
some structure and interlinks between areas of research.
6.1 Where these models can be useful?
Here the short agenda of interesting directions of future research is listed. It is believed
that these social processes can be properly described by the methods discussed in this
article. However, further elaboration can take substantial effort and time, and thus could
be an agenda for future research.
1. Analytical description of transition process. The transition from centralized to
market economy in the former Soviet Union started in 1992 with “shock therapy”.
In the press it was argumented by welfare theorems from neoclassical economics
about efficiency of emerging market equilibrium. However, the concepts of that
theory were not applicable not only because lack of knowledge, lack of
institutions, incomplete and asymmetric information (especially in the case of
privatisation), but also because the transition itself is a disequilibrium process
(and fast, shock, non-adiabatic transition especially) by definition, and the western
economic school has never developed such disequilibrium theory. The use of
some tools from physics allows to do this in principle, and although it is too late
to apply results practically, this could be an important contribution to our
understanding of modelling real economic processes.
2. Explaining historical paths of different social formations.
3. Understanding the stability of different regimes and seeing economic reasons
behind it (a self-reinforcing loop: poor society tends to be a dictatorship which
keeps it poor) and their right to exist.
4. Studying the role of state in economy and its link to level of freedom and
richness.
6.2 The role of wealth distribution
It is possible to predict the crucial difference between Marxism and nationalism, arising
from the effect of wealth distribution. Empirically we know that nationalist or religious
societies are much more tolerant to wealth inequality than those based on Marxist
Y. YEGOROV
– 164 –
principles. But the structure of formulae in Assumptions 1,2 give exactly the same
predictions. Suppose that wealth is distributed not equally but there is no way for
costless redistribution. Then such redistribution would mean some decline of the second
term in utility function of each member. For some members, non necessarily rich, but of
middle class, this decline will overweight potential personal gain. Thus, a majority
interested in such redistribution will not emerge. Consider now Marxist society. For it,
any deviation from equality brings negative utility to each member. Suppose, for
simplicity, that there are two levels of wealth: low w (fraction a) and high w (fraction
1�a), where a�(0,1) but most likely to be closer to 1. Then the utility of poor is
Up�U0(w)(1�b), while the utility of rich is Ur�U0(W)�bU0(w). For b high enough,
even richer people would be personally interested in full equalization. Alternatively, for
low b two classes will emerge, with all consequences predicted by Marxists. In the case
of general distributions it is likely that low inequalities will not generate antagonism is
either society, while for higher level, nationalist society is more tolerant and stable than
Marxist.
6.3 The conditions of stability of liberal society
While it is difficult to criticize the principles of liberal society (freedom, equality,
brotherhood), its realization is often far from proclaimed principles.22) Usually liberal
society self-reinforce the initial difference in endowments and skills among agents.23)
The main reasons involve asymmetric access to credit (the rich can get it always and at
lower interest rate than the poor) and more destabilizing effect of random shocks on
households close to subsistence level. Thus, liberal principles does not guarantee “honest
outcome” when every worker gets wage according to his productivity, and everybody
can be an entrepreneur, with outcome depending on skills only.
The natural political principle of liberal society is the majority voting scheme, with the
main focus on median voter. Now let us turn to the physical principle of phase transitions
described before. Suppose that the initially high role of state in relatively poor country
was forcefully diminished, like it happened in Russia in 1990s. The liberalization has
caused wealth polarization.24) If Marxist ideology had not been rapidly abandoned, this
could have lead to emergence of classes with their struggle. The main ideological
Econo-physics: A Perspective of Matching Two Sciences
– 165 –
22) As well as realized societies based on Marxist principles.23) The polarization across peasants initially endowed with almost equal slots of land after Russian
revolution of 1917, by the year 1930.24) I am not mentioning the increased role of mafia as another natural consequence of the decline of
state role.
competition was between nationalist and liberal idea. Consider the conditions for liberal
paradigm to win this competition. The median voter was objectively worse off
economically.25) With a monthly average income of about 100 USD and almost western
prices (despite huge temporal variation of nominal average income in Russia between
1993–1999, the PPP adjusted income did not change much.) At such income level, gain
from less pressure (more freedom) did not compensate for economic loss, and the
composition of these two parameters naturally corresponded to “solid” or “liquid”, but
not “gas” state. The richer 10% were naturally supporting “gas” (liberal) state, but they
needed to use some manipulation of public opinion with mass media, to form an illusion
of social agreement on liberal state. On the other hand, the increase of nationalistic ideas
and the role of religion worked towards higher popularity of nationalist (solid) state
among medium voters. Since “solid” and “gas” state cannot coexist (while solid and
liquid can), some liquid (better to say, polymer) structures have started to emerge in
business. They can be formally studied by economics of networks.
6.4 Link with research on structural economics, science of transition and
political science
In order not to get lost in the variety of fundamental cornerstones of future econo-physic
theory and variety of its applications, it makes sense to impose some preliminary
structure.
Structural economics
Structural economics is one of the corner stones of this new theory. It studies self-
emergence of structures in a form of spontaneously united group of agents, or network
(with or without topology of interlinks). Space is an important but not unique factor of
self-organization (Yegorov, 2001a), which also comes from nonlinear interaction of
initially identical elements (for example, through production function, locally having
IRS; see Yegorov (2001b, 2005a).
Economics of transition
To study economics of transition theoretically, one needs a formal link between different
regimes first. The proposed utility function and the analogies of phase transitions in
physics represent one possibility to build such models. Modelling transition is a
fundamentally difficult task. While transition in a narrow sense (as shift of capital and
labour to new sectors during industrialization) can follow an optimal path, transition of
Big Bang type is unpredictable in details in principle. In the chapter 8 of Faber et al.
Y. YEGOROV
– 166 –
25) By observations, only about 10 % of population had economic gain from transition, although the
majority recognize the gain in individual freedom previously suppressed by state.
(1996) the model of Big Bang, describing the behaviour of universe in the first few
seconds after its emergence, is discussed. It is fundamentally unpredictable process, as
even some fundamental physical constants could take different asymptotic values
depending on the path of the process. Transition from post-communist to market
economies included simultaneous shift in ideologies, changing of legal structure,
privatisation, mostly on the background of hyperinflation. There have been many
unpredictable novelties, and the complexity is likely to be of higher order, than simple
multiplicity of equilibria. It could also involve a sequence of unforcastable structural
changes along the path of convergence to new equilibria. While it is generally
impossible to describe this process mathematically as a deterministic path, the
application of some evolutionary concepts is important in understanding its structure.
The concept of self-emergence of structures and their stability is as important as the
concepts of “genotype” and “ecological niche” in theoretical biology. But obtaining
unified mathematical model, that is able to describe the social system dynamics both is
non-liberal and liberal framework, which was discussed above, is of crucial importance
before any practical modelling takes place.
Political science
The emergence of stable structures and studying the limits of their stability can give
some insights for policy makers. If a particular state is natural, no external reforms can
change its structure in the long run. “Heating” society involves both the decline of the
state role together with wealth increase (external aid). For example, decline of state’s
role without significant increase of wealth of median voter, cannot assure a foundation
for a stable democratic society. And the example of Russia (where an attempt to
compensate the lack of aid by excess destruction of state, which did not finally succeed
in establishing stable irreversible democracy), in contrast with Eastern and Central
European countries,26) is a good illustration.
6.5 About social diffusion, vertical and horizontal
Let us start from physics. Diffusion is the process of penetration of elements of one
nature into the media of different nature. For example, two gases were separated and
now they are in contact. Molecules of one of them will penetrate into the other. The
process of diffusion is described by diffusion equation, which shows that the total
amount of penetrated molecules and the average distance of penetration grow over time
but non-linearly. The situation with liquids is different. If we have a mixture of different
liquids with different densities, their location is ordered with time. This principle is used
Econo-physics: A Perspective of Matching Two Sciences
– 167 –
26) I mean mostly Hungary, Poland, Czech Republic.
in rectification columns to separate oil into fractions. If we mix oil with water, it will
occupy the upper part of the volume in gravity field. The reason that prevents diffusion
in the case of liquid is related to the interaction field between the molecules of the same
type: other molecules do not allow one molecule to escape, we have some kind of
collective phenomenon.
Can we find interesting analogies in social life? Yes. Let personal wealth be an
analogy of individual energy, while the interaction forces are represented by some formal
and informal laws (traditions, collective rules, etc). If these forces are weak, we have
liberal society (an analogy of gas), but if they are strong, we have a traditional society. In
traditional societies it is difficult to make an action without mental self-reference to the
opinion of collective, while in liberal societies individuals are independent on this
opinion.
Consider the process of mobility across social classes. In traditional society, a person
without proper genealogy could not become an aristocrat, independently on the level of
his wealth. This was the reason of bourgeois revolutions, which improved social status of
the “third class”. In modern liberal societies, entry to another social group is more easy,
but we also have some “closed societies”, a ticket to which cannot by bought. The
described case is an example of vertical social diffusion, which is more easy in gas-type
(liberal) society and more difficult in liquid-type (traditional) society.
Another example is related to horizontal diffusion, and it can be easier explained using
military example. In the time of the Second World war the fronts separating two armies
were well defined in space, and penetration (diffusion) was a difficult task, at least at
mass level. Now, in the epoque of terrorist attacks, such diffusions play an increasing
role in the strategy of a conflict. The previous society was more of liquid type, with more
control over actions of each individual, while now societies are more liberal, and this
control became less. Gas-type diffusion in modern societies became easier for
individuals. The examples considered above show how the analogies between physics
and social life can be used for studying particular questions of social organization and
movement.
7. Conclusive Remarks
The method of introducing physical methodology into economic modelling with keeping
most of economic assumptions allows to describe much richer class of socio-economic
phenomena. In particular, it is possible to deal with emergence of different structures and
study different social orders by common mathematical tools. This paper only sets up
Y. YEGOROV
– 168 –
some potentially fruitful directions of research.
It is shown that market force in not a unique interaction between economic agents.
Non-market interaction include deviation from self-regarding preferences that can
explain the emergence of stable structures (like groups, nations and countries).
Moreover, movement along these lines allow to explain the societies based on alternative
ideologies (Marxism and nationalism).
Spatial forces represent another self-organizing social principle that is complementary
to “invisible hand”. This explains the importance of regional science and urban
economics. Scale economies can also lead to endogeneous group formation. In
combination with transport costs they give rise to a wide range of stable heterogeneous
structures in space.
The analogy between different phases of matter (solid, liquid, gas) and social orders
with different levels of economic freedom is presented. It allows to provide a wider view
on possible socio-economic structures and the order parameters (social analogies of
temperature and pressure from physics) that are responsible for phase transitions
between them.
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