Self-propulsion symmetries determine entropy production of active particles with hidden states

TL;DR

This paper develops a perturbative method to calculate the entropy production rate in active particles with hidden states, revealing how symmetries like parity and reversibility influence entropy generation.

Contribution

It introduces a novel framework for computing partial entropy production in systems with unobserved degrees of freedom, highlighting the role of symmetry properties.

Findings

Entropy production appears at sixth order in self-propulsion velocity.

Parity and time-reversal symmetries determine the partial entropy production.

Application to asymmetric telegraph process and stochastic resetting demonstrates the framework's effectiveness.

Abstract

Entropy production distinguishes equilibrium from non-equilibrium. Calculating the entropy production rate (EPR) is challenging in systems where some degrees of freedom cannot be observed. Here we introduce a perturbative framework to calculate the ``partial EPR'' of a canonical hidden-state system, a generic self-propelled active particle with hidden self-propulsion. We find that the parity symmetry, P, and (time-)reversibility, T, of the hidden variable determine partial entropy production. Non-trivial entropy production appears at least at sixth order in the self-propulsion velocity. We apply our framework to two processes which break P- and T-symmetries respectively: an asymmetric telegraph process and diffusion with stochastic resetting.