a presentation on 'maxwell's demon

8/9/2019 A presentation on 'Maxwell's Demon'

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MAXWELL 'S DEMON

A Look At The Connection betweenThermodynamics And Information Theory

And The Promises It Holds



CONTENTS

The Maxwell¶s Demon-- The µProblem¶?-- The Solution

The Connection With Information Theory-- Landauer¶s Principle

Some Systems of Interest

The Future



THE MAXWELL ¶S DEMON

Maxwell's demon is a thought experiment, firstformulated in 1867 by the Scottish physicist JamesClerk Maxwell, intended to "show that the 2nd Law

of Thermodynamics has only a statistical certainty,"and commonly used for imagining the possibility of violating it.

The concept was named by Lord Kelvin.



THE DEMONIN M AXWELL 'S WORDS «

... if we conceive of a being whose faculties are so sharpened that he can follow every molecule in its course, such a being, whose attributes are as essentially finite as our own, would be able to do what is impossible to us.For we have seen that molecules in a vessel full of air at uniform temperature are moving with velocities by no means uniform, though the mean velocity of any great number of them, arbitrarily selected, is almost exactly uniform.

Now let us suppose that such a vessel is divided into two portions, A and B,by a division in which there is a small hole, and that a being, who can see the individual molecules, opens and closes this hole, so as to allow only the swifter molecules to pass from A to B, and only the slower molecules to pass

from B to A. He will thus, without expenditure of work, raise the temperature of B and lower that of A, in contradiction to the second law of thermodynamics.



THE P ROBLEM -IN ESSENCE « A wall separates two compartmentsfilled with gas, at thermal equilibrium.

A little demon sits by a tiny trapdoor inthe wall.It looks at oncoming gas molecules, and

depending on their speeds it opens or closes the trapdoor.



THE P ROBLEM -IN ESSENCE «The objective of the demon is to eventuallycollect all the molecules faster than averageon one side and the slower ones onthe other side. A temperature gradient with ahot, high pressure gas on one side, and acold, low pressure gas on the other, iscreated. The random kinetic energy of molecules (heat) has been redistributed insuch a way that energy can now beextracted from the system.



THE P ROBLEM -IN ESSENCE «



THE P ROBLEM - VIOLATION OF THE 2ND

LAW OF THERMODYNAMICS

The demon has managed to decrease the entropyof the system, in contradiction to the 2nd Law of Thermodynamics , which states:

³In any cyclic process the total entropy of thephysical systems involved in the process willeither increase or remain the same ´ .

OR

³ A transformation whose only result is to transferheat from a body at a given temperature to a bodyat a higher temperature is impossible . ´ (Clausius¶sstatement).



DOES THE DEMON WIN ? W HAT DOES IT

ENTAIL FOR PHYSICS ?

So, the question that arises is does the Demonsucceed?

The question is unusually important because thefailure of the 2 nd Law entails the possibility of the:Construction of a perpetual motion machinerevolutionising Physics and engineering;

A Revolution in Information Theory, enabling thedevelopment of Reversible Computing Technology(nil or minimal energy wastage and high-accuracycomputation).



THE S OLUTION

T he essence of the solution lies in a more complete

analysis of the system, along with the Demon,aimed to show by calculation that any demonmust generate" more entropy segregating themolecules than it could ever eliminate by themethod described.



THE S OLUTION

One of the most famous responses to thisproblem was suggested in 1929 by LeoSzilard and later by Leon Brillouin. Szilárd

pointed out that a real-life Maxwell's demonwould need to have some means of measuringmolecular speed, and that the act of acquiringinformation would require an expenditure of

energy«



THE S OLUTION

The second law states that the total entropy of an isolated system must increase . Since thedemon and the gas are interacting, we mustconsider the total entropy of the gas and thedemon combined«



THE S OLUTION

For example, if the demon is checkingmolecular positions using a flashlight, theflashlight battery is a low-entropy device, a

chemical reaction waiting to happen. As itsenergy is used up emitting photons (whoseentropy must now be counted as well), thebattery's chemical reaction will proceed and itsentropy will increase, more than offsetting thedecrease in the entropy of the gas.



A C OUNTER TO THE S OLUTION

In 1960, Rolf Landauer raised an exception to this

argument. He realized that certain measuringprocesses need not increase thermodynamicentropy as long as they were thermodynamicallyreversible, and hence would still violate the 2 nd

Law of T hermodynamics .



INFORMATION THEORY TO THE

RESCUE

This is where the Information Theory comes in and saves the day for The 2 nd

Law. Let¶s see how«



LANDAUER ¶S P RINCIPLE

Landauer's Principle , first argued in 1961 by Rolf Landauer of IBM, holds that

"any logically irreversible manipulation of information,such as the erasure of a bit or the merging of twocomputation paths, must be accompanied by acorresponding entropy increase in non-informationbearing degrees of freedom of the informationprocessing apparatus or its environment ".




Due to Landauer¶s Principle, it was realized that thedemon would need to record the measurement and

that this measurement would need to not be erasedto have the entropy of the system lowered.

Hence, as long as the demon stores theinformation, the system works without any increasein entropy.




In 1982, Bennett showed that, however wellprepared, eventually the demon will run out of information storage space and must begin to erasethe information it has previously gathered,immediately incresing the entropy of the system.Bennett calculated the minimum amount of heatenergy required to erase one bit of information,which is known as Landauer·s bound .

B ut, is this increase in entropy sufficient to savethe 2 nd law?



A C OUNTER TO THE S OLUTION :

THE 2ND LAW SAVED

It turned out that the demon was generating more

entropy by discarding information about theparticles than it was eliminating by ushering theparticles into hot and cold chambers.

The 2

nd

Law was saved, as of now.



S OME S YSTEMS OF INTEREST

Real-life versions of Maxwellian demons occur, but all such "real demons" have their entropy-lowering

effects duly balanced by increase of entropyelsewhere.



VORTEX TUBE

A large-scale, commercially-available pneumatic device,called a Ranque-Hilsch Vortex Tube separates hot andcold air. It sorts molecules by exploiting the conservationof angular momentum: hotter molecules are spun to theoutside of the tube while cooler molecules spin in atighter whirl within the tube. Gas from the two differenttemperature whirls may be vented on opposite ends of

the tube. Although this creates a temperature difference,the energy to do so is supplied by the pressure drivingthe gas through the tube.



MIRROR MATTER

If hypothetical mirror matter exists, Zurab Silagadzeproposes that demons can be envisaged, "which can actlike perpetuum mobiles of the second kind: extract heatenergy from only one reservoir, use it to do work and beisolated from the rest of ordinary world. Yet the SecondLaw is not violated because the demons pay their entropy cost in the hidden (mirror) sector of the world by

emitting mirror photons."



NANO-SCALE VIOLATION

B ennett s analysis settled the matter of the Maxwell sDemons in Macroscsopic Sytems, but in Microscopicsystems,there seems to be a certain phenomenon that remains unaccounted for and might be another

Demon .

T his phenomenon is that of Thermal Fluctuations .



T HERMAL FLUCT UAT IONS

Thermal fluctuations are usually extremelysmall at large scales and easily discarded.However, these fluctuations becomepredominant in microscopic systems, andscientists have recently begun to recognize thatthe second law should be amended to accountfor these fluctuations. They can haveobservable consequences in nanomemories:information may be erased by dissipating lessheat than required by Landauer's principle.



THE FUTURE P OSSIBILITIES

Certain avenues of future interest may be:Th e impact of tiny t h ermal fluctuations onnanoparticle-based memory system, especially inmemory erasure. Th e breac h ing of t h e Landauer s

Bound in nano-scale systems could revolutionise t h

ewh ole of computing as it would h erald t h e beginningof t h e Reversible Computing Era.The influence of both thermal and quantumfluctuations on memory erasure might haveimportant consequences for quantum informationprocessing as well (that is, erasure of qubits of information instead of classical bits).



THE FUTURE P OSSIBILITIES

S ince t h is researc h provides insig h t into nanoscalesystems, it could h ave applications in ot h er areas.Ot h er t h an Information T heory wh ere it could leadto a better understanding and amendment of Th eLandauer s Principle and new tec h nology, it s greatestpower might lie in biology , for the organizingentities in living beings - the proteins and certainRNAs - are apparently nothing but microscopic

Maxwell's demons.



B IBLIOGRAPHY

Wikipediahttp://knol.google.com/khttp://eve.physics.ox.ac.uk/Personal/steane/qcomp.

htmlhttp://universe-review.ca/R01-02-z1-information.htm#demon

Arxiv.org

Concepts In thermal Physics- Bundell & Blundell

a presentation on 'maxwell's demon

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