Fluctuations in Nonequilibrium Statistical Mechanics: Models, Mathematical Theory, Physical Mechanisms

TL;DR

This paper reviews the theoretical and mathematical understanding of fluctuations in nonequilibrium systems, highlighting models, physical mechanisms, and the growth of the field with recent developments and applications.

Contribution

It provides a comprehensive analysis of models, mathematical results, and physical mechanisms underlying fluctuation relations in nonequilibrium statistical mechanics.

Findings

Analysis of theoretical models and their assumptions

Discussion of rigorous mathematical results

Identification of physical mechanisms behind fluctuation relations

Abstract

The fluctuations in nonequilibrium systems are under intense theoretical and experimental investigation. Topical ``fluctuation relations'' describe symmetries of the statistical properties of certain observables, in a variety of models and phenomena. They have been derived in deterministic and, later, in stochastic frameworks. Other results first obtained for stochastic processes, and later considered in deterministic dynamics, describe the temporal evolution of fluctuations. The field has grown beyond expectation: research works and different perspectives are proposed at an ever faster pace. Indeed, understanding fluctuations is important for the emerging theory of nonequilibrium phenomena, as well as for applications, such as those of nanotechnological and biophysical interest. However, the links among the different approaches and the limitations of these approaches are not fully understood. We focus on these issues, providing: a) analysis of the theoretical models; b) discussion of the rigorous mathematical results; c) identification of the physical mechanisms underlying the validity of the theoretical predictions, for a wide range of phenomena.