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INITIAL MEMORY IN HEAT PRODUCTION
Chulan Kwon, Myongji UniversityJaesung Lee, Kias
Kwangmoo Kim, KiasHyunggyu Park, Kias
The Fifth KIAS Conference on Statistical PhysicsNonequilibrium Statistical Physics of Complex Systems
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I. Introduction5th KIAS Conference-NSPCS12
- path dependent- accumulated incessantly in time
in nonequilibrium steady state (NESS) - Fluctuation theorem
Thermodynamic first law
Steady state FT for entropy production
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I. Introduction
R. van Zon and E. Cohen, PRL 91, 110601 (2003) “Extended fluctuation theorem”
J.D. Noh and J.-M. Park, Phys. Rev. Lett. 108, 240603 (2012)
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U. Seifert, PRL 95, 040602 (2005)M. Esposito and V. den Broeck, PRL 104, 090601 (2010)
should depend on initial distribution.
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II. Equilibration process5th KIAS Conference-NSPCS12
Dissipated power
Injected power
Total heat
Calculate
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II. Equilibration Process
Saddle-point integration near the branch point Not a Gaussian integral!
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II. Equilibration Process5th KIAS Conference-NSPCS12
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II. Equilibration Process
Phase transition in the shape of the heat distribution functionat β=1/2
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III. Dragged Harmonic Potential
Initial distribution
Heat production
Probability densityfunction for heat
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III. Dragged Harmonic Potential
FT for heat holds for flat initial distribution, β=0
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III. Dragged Harmonic Potential
Large deviation form
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LDF is absent in the positive tail for β=0where there is no exponential decay, but a power-decaywhich can be seen from the 1/τ correction in the exponent
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IV. Summary1. For the equilibration process of the Brownian motionthe phase transition takes place in the shape of heat distribution at β=1/2.2. For the dragged harmonic potential the FT for heat holdsfor a flat initial distribution, β=0. The modification of FT depends for on β. 3. The correction to the LDF needs a nontrivial saddle point integration near the branch point that is not a conventionalGaussian integral. Our result may be useful for other casesin which the generating function, the Fourier transform, ofthe distribution function with power-law singularity, as the case of heat and work distribution.
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