# The Entropy Production of Ornstein-Uhlenbeck Active Particles: a path integral method for correlations

## TL;DR

This paper introduces a path integral approach to calculate entropy production in active Ornstein-Uhlenbeck particles, clarifying previous ambiguities and providing explicit formulas for different noise conditions.

## Contribution

It presents a novel path integral method for entropy production in AOUP, resolving contradictions and avoiding assumptions about variable parity.

## Key findings

- Explicit formulas for entropy production in various AOUP scenarios
- Clarification of the role of auxiliary variables in entropy calculations
- Agreement with previous mesoscopic approaches

## Abstract

By employing a path integral formulation, we obtain the entropy production rate for a system of active Ornstein-Uhlenbeck particles (AOUP) both in the presence and in the absence of thermal noise. The present treatment clarifies some contraddictions concerning the definition of the entropy production rate in the AOUP model, recently appeared in the literature. We derive explicit formulas for three different cases: overdamped Brownian particle, AOUP with and without thermal noise. In addition, we show that it is not necessary to introduce additional hypotheses concerning the parity of auxiliary variables under time reversal transformation. Our results agree with those based on a previous mesoscopic approach.