Random paths and current fluctuations in nonequilibrium statistical mechanics

TL;DR

This paper reviews recent progress in nonequilibrium statistical mechanics, focusing on the statistics of random paths and current fluctuations, and their relation to microscopic dynamics and chaos.

Contribution

It provides a comprehensive overview of how current fluctuations relate to microscopic properties in classical, stochastic, and quantum systems, highlighting recent theoretical advances.

Findings

Relationships between transport coefficients and microscopic chaos

Connections between entropy production and fluctuations

Results across classical, stochastic, and quantum systems

Abstract

An overview is given of recent advances in nonequilibrium statistical mechanics about the statistics of random paths and current fluctuations. Although statistics is carried out in space for equilibrium statistical mechanics, statistics is considered in time or spacetime for nonequilibrium systems. In this approach, relationships have been established between nonequilibrium properties such as the transport coefficients, the thermodynamic entropy production, or the affinities, and quantities characterizing the microscopic Hamiltonian dynamics and the chaos or fluctuations it may generate. This overview presents results for classical systems in the escape-rate formalism, stochastic processes, and open quantum systems.