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Entropy fluctuation theorems in driven open systems: Application to electron counting statistics

Massimiliano Esposito*, Upendra Harbola, and Shaul Mukamel

  • Department of Chemistry, University of California, Irvine, California 92697, USA

  • *Also at Center for Nonlinear Phenomena and Complex Systems, Universite Libre de Bruxelles, Code Postal 231, Campus Plaine, B-1050 Brussels, Belgium.
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Phys. Rev. E 76, 031132 – Published 26 September, 2007

DOI: https://doi.org/10.1103/PhysRevE.76.031132

Abstract

The total entropy production generated by the dynamics of an externally driven systems exchanging energy and matter with multiple reservoirs and described by a master equation is expressed as the sum of three contributions, each corresponding to a distinct mechanism for bringing the system out of equilibrium: Nonequilibrium initial conditions, external driving, and breaking of detailed balance. We derive three integral fluctuation theorems (FTs) for these contributions and show that they lead to the following universal inequality: An arbitrary nonequilibrium transformation always produces a change in the total entropy production greater than or equal to the one produced if the transformation is done very slowly (adiabatically). Previously derived fluctuation theorems can be recovered as special cases. We show how these FTs can be experimentally tested by performing the counting statistics of the electrons crossing a single level quantum dot coupled to two reservoirs with externally varying chemical potentials. The entropy probability distributions are simulated for driving protocols ranging from the adiabatic to the sudden switching limit.

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Outline

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Phys. Rev. E 76, 031132– Published 26 September, 2007
  • Received 30 April 2007

© 2007 American Physical Society

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