Phase transitions in large deviations of reset processes

TL;DR

This paper investigates the large deviation behavior of additive quantities in stochastic reset processes, revealing conditions for phase transitions and demonstrating their occurrence in simple models, with broader implications for compound stochastic processes.

Contribution

It introduces a mapping from reset processes to the Poland-Scheraga model, deriving conditions for phase transitions in large deviations and illustrating these with random walk examples.

Findings

Conditions for first-order and continuous phase transitions identified

Non-analyticities in large deviation functions can arise from subleading terms

Results applicable to a broad class of reset and compound stochastic processes

Abstract

We study the large deviations of additive quantities, such as energy or current, in stochastic processes with intermittent reset. Via a mapping from a discrete-time reset process to the Poland-Scheraga model for DNA denaturation, we derive conditions for observing first-order or continuous dynamical phase transitions in the fluctuations of such quantities and confirm these conditions on simple random walk examples. These results apply to reset Markov processes, but also show more generally that subleading terms in generating functions can lead to non-analyticities in large deviation functions of 'compound processes' or 'random evolutions' switching stochastically between two or more subprocesses.