What is a Fluctuation Theorem?

TL;DR

This book offers a comprehensive review of Fluctuation Relations and Theorems in nonequilibrium statistical mechanics, emphasizing their theoretical foundations, universal symmetry properties, and applications to chaotic dynamics.

Contribution

It provides a unified probabilistic framework for Fluctuation Relations applicable to both deterministic and stochastic systems, including new insights into chaotic dynamics.

Findings

Universal fluctuation relation for time-reversal invariant systems

General formulation of Fluctuation Theorems for various dynamical systems

Application of the framework to concrete physical models

Abstract

This book provides a modern review of Fluctuation Relations and Fluctuation Theorems in nonequilibrium statistical mechanics. It focuses on the pioneering perspectives of Gallavotti and Cohen, according to which a fluctuation theorem describes the statistics of the deviations of entropy production from its expected value. For time-reversal invariant systems, these fluctuations obey a universal (i.e., model-independent) symmetry called the fluctuation relation. The probabilistic framework introduced in the first part of the book allows for a very general formulation of Fluctuation Relations and Theorems for both deterministic and stochastic dynamical systems. The authors further explore models of physical interest, illustrating this framework by concrete applications. The second part of the book focuses on chaotic dynamics. The formulation of two general Fluctuation Theorems, followed by the detailed study of a concrete example, provides the reader with an understanding of both the theoretical and practical aspects of the subject.