A large deviation perspective on ratio observables in reset processes: robustness of rate functions

TL;DR

This paper analyzes the large deviation properties of a ratio observable in reset processes, demonstrating the robustness of its rate function across different correlation regimes and comparing it with thermodynamic efficiency rate functions.

Contribution

It introduces a large deviation framework for ratio observables in reset processes and shows the robustness of the rate function shape regardless of correlation types.

Findings

The ratio rate function is differentiable.

The shape of the ratio rate function is robust across reset processes.

Comparison with thermodynamic efficiency rate functions highlights similarities and differences.

Abstract

We study large deviations of a ratio observable in discrete-time reset processes. The ratio takes the form of a current divided by the number of reset steps and as such it is not extensive in time. A large deviation rate function can be derived for this observable via contraction from the joint probability density function of current and number of reset steps. The ratio rate function is differentiable and we argue that its qualitative shape is 'robust', i.e. it is generic for reset processes regardless of whether they have short- or long-range correlations. We discuss similarities and differences with the rate function of the efficiency in stochastic thermodynamics.