Fluctuation relations without uniform large deviations

TL;DR

This paper investigates the relationship between fluctuation relations and large deviations in a stochastic particle model, revealing that fluctuation relations can hold even without uniform large deviation properties due to non-exponential tail decay.

Contribution

It demonstrates that fluctuation relations can exist without the probability density exhibiting uniform large deviation behavior, challenging common assumptions.

Findings

Negative tail decays exponentially with time

Positive tail decays slower than exponentially due to long trajectories

Fluctuation relations can hold without uniform large deviation form

Abstract

We study the fluctuations of a stochastic Maxwell-Lorentz particle model driven by an external field to determine the extent to which fluctuation relations are related to large deviations. Focusing on the total entropy production of this model in its steady state, we show that, although the probability density of this quantity globally satisfies (by definition) a fluctuation relation, its negative tail decays exponentially with time, whereas its positive tail decays slower than exponentially with time because of long collision-free trajectories. This provides an example of physical system for which the fluctuation relation does not derive, as commonly thought, from a probability density decaying everywhere exponentially with time or, in other words, from a probability density having a uniform large deviation form.