quantum maxwell s demon in quantum szilard cycle -...

Hui Dong & C. P. SunHui Dong & C. P. Sun

http://power.itp.ac.cn/~suncp/quantum.htmhttp://power.itp.ac.cn/~suncp/quantum.htm

Institute of Theoretical Physics, CASInstitute of Theoretical Physics, CAS

Quantum MaxwellQuantum Maxwell’’s Demon in s Demon in Quantum Szilard CycleQuantum Szilard Cycle

ContentsContents

1. 1. MaxwellMaxwell’’s Demon in Historys Demon in History

2. 2. LandauerLandauer’’s Principles Principle

3. Quantum Model3. Quantum Model

4. Thermodynamic Cycle4. Thermodynamic Cycle

5. Results5. Results

6. Conclusions6. Conclusions

MaxwellMaxwell’’s Demon in Historys Demon in History

J. C. Maxwell1871

It is impossible to convert heat completely into work in a cycliIt is impossible to convert heat completely into work in a cyclic c process.process.

The Second Law of Thermodynamics (SLoT) by KelvinThe Second Law of Thermodynamics (SLoT) by Kelvin：：

MaxwellMaxwell’’s Demons Demon ColdCold HotHot

Single molecule versionSingle molecule version

Leo Szilard1929

(a)(a) (b)(b)

LL

RR

(d)(d) (c)(c)

Total work extracted:Total work extracted:

?

L. Szilard, Z. Phys. 53, 840 (1929).L. Szilard, Z. Phys. 53, 840 (1929).

ContentsContents







LandauerLandauer’’s Principle(1)s Principle(1)

Erasing one bit information from the memory in computing processErasing one bit information from the memory in computing process

would would

inevitably accompany an increasing entropy inevitably accompany an increasing entropy ln2ln2 in the environment.in the environment.

(a) (b)

L

R

(d) (c)

?

0

1

P=1/2 P=1/2 ““00””P=1/2 P=1/2 ““11””

MD joins in the cycleMD joins in the cycle

R.Landauer, IBM J.Res.Dev.R.Landauer, IBM J.Res.Dev.55, 183(1961); , 183(1961); C.H. Bennett, Int.J.Theor.Phys. 21, 905(1982)C.H. Bennett, Int.J.Theor.Phys. 21, 905(1982)

LandauerLandauer’’s Principle(2)s Principle(2)

Information Erasing:Information Erasing:

Work disspated:Work disspated:

SystemSystem’’s Bath temperatures Bath temperature

Total work extracted:Total work extracted:

The second law of Thermodynamics is saved!The second law of Thermodynamics is saved!

Contents







Quantum Model (I)Quantum Model (I)

ChamberChamber PotentialPotential

Finite size Finite size L L effecteffect

Effective inverse temperatureEffective inverse temperature

General setup:General setup:

Quantum Model (II)Quantum Model (II)

EigenEigen--system in the potential:system in the potential:

0 L 0 Ll

RRLL

Quantum Model (III)Quantum Model (III)

MDMD’’s temperature:s temperature:

Quantum coherence:Quantum coherence:

Effective population:Effective population:

Effective inverse temperature:Effective inverse temperature:







ContentsContents

Thermodynamic CycleThermodynamic Cycle

InsertionInsertion MeasurementMeasurement

=

ExpansionExpansion

=

RemovingRemoving

Step 1: InsertionStep 1: Insertion

Prob. of finding molecule on the leftProb. of finding molecule on the left

Work done:Work done:

FiniteFinite--Size EffectSize Effect

Step 2: MeasurementStep 2: Measurement

CNOT:CNOT:

L L : no change : no change R R : flip: flip

MDMD’’s Logics LogicWrong informationWrong information

Finite temperature Finite temperature TTDD Precision of measurementPrecision of measurement

Ideal measurementIdeal measurement

Maximum information obtainedMaximum information obtained

No information obtainedNo information obtained

Worst measurementWorst measurement

Finite TemperatureFinite Temperature

Step 3: Controlled ExpansionStep 3: Controlled Expansion

MD moves piston according to the memory:MD moves piston according to the memory:

The process is done isothermally.The process is done isothermally.

Step 4: RemovingStep 4: Removing

Removing piston from potential:Removing piston from potential:

The process is also done isothermally.The process is also done isothermally.

Return to the initial stateReturn to the initial state

MD factorized outMD factorized out

MD releases heat to its bathMD releases heat to its bath


2. 2. LandauerLandauer’’s Principals Principal





ContentsContents

Total Work Extracted (I)Total Work Extracted (I)

compensates change of MDcompensates change of MD’’s entropys entropy

Work to flip MDWork to flip MD’’s memory in the measurement s memory in the measurement

Critical value for positive work:Critical value for positive work:

Total Work Extracted (II)Total Work Extracted (II)

Maximum work :Maximum work :

EfficiencyEfficiency

SLoT is saved:SLoT is saved:

Two LimitsTwo Limits

Ideal measurement :Ideal measurement :

Worst measurement :Worst measurement :

Different OrdersDifferent Orders Different ResultsDifferent Results


2. 2. LandauerLandauer’’ss

PrincipalPrincipal





ContentsContents

ConclusionsConclusions

A Quantum model is constructed and whole thermodynamic cycle iA Quantum model is constructed and whole thermodynamic cycle is established.s established.

e.g. Removing process e.g. Removing process

Efficiency is evaluated to prove the validity of Efficiency is evaluated to prove the validity of SLoTSLoT..

Quantum feature in the cycleQuantum feature in the cycle

e.g. Quantum coherence helps to low down effective tee.g. Quantum coherence helps to low down effective temperaturemperature

Finite size effect persists, even for high temFinite size effect persists, even for high temperature. perature.

TheThe methods can be utilized to analyze other cycle with MD.methods can be utilized to analyze other cycle with MD.

quantum maxwell s demon in quantum szilard cycle -...

Documents