Entropic Fluctuations in Statistical Mechanics I. Classical Dynamical Systems

TL;DR

This paper presents a general, model-independent mathematical framework for understanding fluctuation theorems in non-equilibrium statistical mechanics, with potential extensions to quantum systems and various examples.

Contribution

It introduces a minimal, conceptual approach to fluctuation theorems within dynamical systems theory, applicable across classical and quantum contexts.

Findings

Unified mathematical structure for fluctuation theorems

Extension to quantum statistical mechanics outlined

Examples include thermostated and chaotic systems

Abstract

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.