Large deviations of the current in stochastic collisional dynamics

TL;DR

This paper investigates the fluctuations of energy current in deterministic collisional systems by approximating them with stochastic models, analyzing their large deviations, and revealing a non-convex rate functional.

Contribution

It introduces a method to approximate deterministic collisional dynamics with stochastic models and explicitly computes the large deviations rate functional for the energy current.

Findings

Variance of the current is finite and related to conductivity via Green-Kubo.

The empirical current satisfies a large deviations principle.

The rate functional for the current is not strictly convex.

Abstract

We consider a class of deterministic local collisional dynamics, showing how to approximate them by means of stochastic models and then studying the fluctuations of the current of energy. We show first that the variance of the time-integrated current is finite and related to the conductivity by the Green-Kubo relation. Next we show that the law of the empirical average current satisfies a large deviations principle and compute explicitly the rate functional in a suitable scaling limit. We observe that this functional is not strictly convex.