A Differential Fluctuation Theorem†

A quantitative description of the violation of the second law of thermodynamics in relatively small classical systems and over short time scales comes from the fluctuation-dissipation theorem. It has been well established both theoretically and experimentally, the validity of the fluctuation theorem to small scale systems that are disturbed from their initial equilibrium states. Some experimental studies in the past have also explored the validity of the fluctuation theorem to nonequilibrium steady states at long time scales in the asymptotic limit. To this end, a theoretical and/or purely numerical model of the integral fluctuation theorem has been presented. An approximate general expression for the dissipation function has been derived for accelerated colloidal systems trapped/confined in power-law traps. Thereafter, a colloidal particle trapped in a harmonic potential (generated by an accelerating one-dimensional optical trap) and undergoing Brownian motion has been considered for the numerical study. A toy model of a quartic potential trap in addition to the harmonic trap has also been considered for the numerical study. The results presented herein show that the integral fluctuation theorem applies not only to equilibrium steady state distributions but also to nonequilibrium steady state distributions of colloidal systems in accelerated frames of reference over long time scales.

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Stochastic approach and fluctuation theorem for charge transport in diodes

Physical Review E ◽

10.1103/physreve.97.052138 ◽

2018 ◽

Vol 97 (5) ◽

Cited By ~ 4

Author(s):

Jiayin Gu ◽

Pierre Gaspard

Keyword(s):

Charge Transport ◽

Stochastic Approach ◽

Fluctuation Theorem

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On the analysis of the integral fluctuation theorem for accelerated colloidal systems in the long-time limit

10.21203/rs.3.rs-591486/v1 ◽

2021 ◽

Author(s):

Yash Lokare

Keyword(s):

Steady State ◽

Time Scales ◽

Numerical Study ◽

Quantitative Description ◽

Experimental Studies ◽

Fluctuation Theorem ◽

Nonequilibrium Steady States ◽

Small Scale ◽

Colloidal Systems ◽

Long Time

Abstract A quantitative description of the violation of the second law of thermodynamics in relatively small classical systems and over short time scales comes from the fluctuation-dissipation theorem. It has been well established both theoretically and experimentally, the validity of the fluctuation theorem to small scale systems that are disturbed from their initial equilibrium states. Some experimental studies in the past have also explored the validity of the fluctuation theorem to nonequilibrium steady states at long time scales in the asymptotic limit. To this end, a theoretical and/or purely numerical model of the integral fluctuation theorem has been presented. An approximate general expression for the dissipation function has been derived for accelerated colloidal systems trapped/confined in power-law traps. Thereafter, a colloidal particle trapped in a harmonic potential (generated by an accelerating one-dimensional optical trap) and undergoing Brownian motion has been considered for the numerical study. A toy model of a quartic potential trap in addition to the harmonic trap has also been considered for the numerical study. The results presented herein show that the integral fluctuation theorem applies not only to equilibrium steady state distributions but also to nonequilibrium steady state distributions of colloidal systems in accelerated frames of reference over long time scales.

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