Entropic Fluctuations in Statistical Mechanics I. Classical Dynamical Systems

Details Entropic Fluctuations in Statistical Mechanics I. Classical Dynamical Systems Entropic Fluctuations in Statistical Mechanics I. Classical Dynamical Systems

2010-09-16

arxiv.org/abs/1009.3248v2

Nonlinearity 24, 699-763 (2011)

Physics

Mathematical Physics

72 pages, revised version 12/10/2010, to be published in Nonlinearity

Scientific paper

10.1088/0951-7715/24/3/003

Within the abstract framework of dynamical system theory we describe a general approach to the Transient (or Evans-Searles) and Steady State (or Gallavotti-Cohen) Fluctuation Theorems of non-equilibrium statistical mechanics. Our main objective is to display the minimal, model independent mathematical structure at work behind fluctuation theorems. Besides its conceptual simplicity, another advantage of our approach is its natural extension to quantum statistical mechanics which will be presented in a companion paper. We shall discuss several examples including thermostated systems, open Hamiltonian systems, chaotic homeomorphisms of compact metric spaces and Anosov diffeomorphisms.

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