Large Fluctuations of the Macroscopic Current in Diffusive Systems: A Confirmation of the Additivity Principle

TL;DR

This paper confirms the additivity principle in a simple energy transport model, showing it accurately predicts current fluctuations and profiles in nonequilibrium systems, including Gaussian and exponential regimes, consistent with fluctuation theorems.

Contribution

The study provides simulation-based validation of the additivity principle for current fluctuations in a general energy transport model, including detailed fluctuation regimes and profile invariance.

Findings

Current distribution exhibits Gaussian and exponential tails.

Optimal temperature profiles are invariant under current inversion.

Finite-time joint fluctuations are well described by the additivity functional.

Abstract

Most systems, when pushed out of equilibrium, respond by building up currents of locally-conserved observables. Understanding how microscopic dynamics determines the averages and fluctuations of these currents is one of the main open problems in nonequilibrium statistical physics. The additivity principle is a theoretical proposal that allows to compute the current distribution in many one-dimensional nonequilibrium systems. Using simulations, we confirm this conjecture in a simple and general model of energy transport, both in the presence of a temperature gradient and in canonical equilibrium. In particular, we show that the current distribution displays a Gaussian regime for small current fluctuations, as prescribed by the central limit theorem, and non-Gaussian (exponential) tails for large current deviations, obeying in all cases the Gallavotti-Cohen fluctuation theorem. In order to facilitate a given current fluctuation, the system adopts a well-defined temperature profile different from that of the steady state, and in accordance with the additivity hypothesis predictions. System statistics during a large current fluctuation is independent of the sign of the current, which implies that the optimal profile (as well as higher-order profiles and spatial correlations) are invariant upon currenst inversion. We also demonstrate that finite-time joint fluctuations of the current and the profile are well described by the additivity functional. These results confirm the additivity hypothesis as a general and powerful tool to compute current distributions in many nonequilibrium systems.