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.