Out-of-equilibrium fluctuations in stochastic long-range interacting systems

TL;DR

This paper investigates out-of-equilibrium work fluctuations in stochastic long-range interacting systems, revealing scaling symmetries, validating fluctuation theorems, and demonstrating the mean-field approximation's effectiveness for large systems.

Contribution

It provides the first analysis of work fluctuations in such systems, connecting fluctuation theorems with mean-field theory and extending to non-equilibrium steady states.

Findings

Work distributions exhibit symmetry and scaling properties.

Crooks fluctuation theorem accurately predicts free-energy density.

Distribution tails decay exponentially with different rates.

Abstract

For a many-particle system with long-range interactions and evolving under stochastic dynamics, we study for the first time the out-of-equilibrium fluctuations of the work done on the system by a time-dependent external force. For equilibrium initial conditions, the work distributions for a given protocol of variation of the force in time and the corresponding time-reversed protocol exhibit a remarkable scaling and a symmetry when expressed in terms of the average and the standard deviation of the work. The distributions of the work per particle predict, by virtue of the Crooks fluctuation theorem, the equilibrium free-energy density of the system. For a large number $N$ of particles, the latter is in excellent agreement with the value computed by considering the Langevin dynamics of a single particle in a self-consistent mean field generated by its interaction with other particles. The agreement highlights the effective mean-field nature of the original many-particle dynamics for large $N$. For initial conditions in non-equilibrium steady states (NESSs), we study the distribution of a quantity similar to dissipated work that satisfies the non-equilibrium generalization of the Clausius inequality, namely, the Hatano-Sasa equality, for transitions between NESSs. Besides illustrating the validity of the equality, we show that the distribution has exponential tails that decay differently on the left and on the right.