What is a Fluctuation Theorem?

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.

Targeted at Ph.D. students and academic researchers in nonequilibrium statistical mechanics, dynamical systems, and stochastic processes,
this book is also a valuable resource for mathematicians and theoretical physicists interested in the mathematical aspects of this growing field. Its accessible presentation of complex ideas makes it an essential read for anyone interested in the recent theoretical advances in the physics of nonequilibrium processes.

Whether you are an experienced researcher or new to the field, this book offers insights and foundational knowledge crucial
for advancing your understanding of applied sciences.

Unifies deterministic and stochastic dynamics, offering accessible Fluctuation Theorems in one framework Provides insight into Fluctuation Theorems and Relations with tools to analyze systems of physical interest Explains complex math and physics clearly, making it key for mastering nonequilibrium statistical mechanics Is a modern review of fluctuation theorems in nonequilibrium statistical mechanics

Autorentext

No**éCuneo**

N. Cuneo received his Ph.D. in Physics from the University of Geneva in 2016. He is an Associate Professor (Maître de Conférences) of Mathematics at Université Paris Cité. His research focuses on mathematical physics, dynamical systems, and large deviation theory.

Vojkan Jaki

V. Jaki received his Ph.D. from California Institute of Technology in 1991 under the supervision of Barry Simon. He is presently a Full Professor of Mathematical Physics at Politecnico di Milano, Milano, Italy. His research interests are in mathematical physics.

Armen Shirikyan

A. Shirikyan received his Ph.D. from Moscow State University in 1995. He has been a Full Professor at CY Cergy Paris University since 2006. He served as department head from 2008 to 2012, director of the master's programme from 2015 to 2019, and is currently director of the CY Institute for Advanced Studies. Shirikyan's research interests are in random dynamical systems and control theory for PDEs.

Claude-Alain Pillet

C.-A. Pillet received his Ph.D. in theoretical physics from ETH-Zürich in 1986. He is a Full Professor of Mathematics at Université de Toulon and Centre de Physique Théorique (CNRS), France. His research interests are in mathematical physics.

Inhalt

Introduction.- Fluctuations Relations and Large Deviations.- Examples.- Two Fluctuation Theorems for Chaotic Maps.- Examples.