Heat fluctuations in a harmonic chain of active particles

TL;DR

This paper investigates heat fluctuations in a one-dimensional harmonic chain of active particles, deriving analytical expressions for heat flow cumulants and validating results with numerical simulations.

Contribution

It introduces a framework to compute heat flow statistics in active particle chains, extending stochastic thermodynamics beyond passive systems.

Findings

Analytical expressions for the moment-generating function of heat flow.

Explicit calculation of scaled cumulants for the chain.

Numerical simulations confirm analytical results for two-particle systems.

Abstract

One of the major challenges in stochastic thermodynamics is to compute the distributions of stochastic observables for small-scale systems for which fluctuations play a significant role. Hitherto much theoretical and experimental research has focused on systems composed of passive Brownian particles. In this paper, we study the heat fluctuations in a system of interacting active particles. Specifically we consider a one-dimensional harmonic chain of $N$ active Ornstein-Uhlenbeck particles, with the chain ends connected to heat baths of different temperatures. We compute the moment-generating function for the heat flow in the steady state. We employ our general framework to explicitly compute the moment-generating function for two example single-particle systems. Further, we analytically obtain the scaled cumulants for the heat flow for the chain. Numerical Langevin simulations confirm the long-time analytical expressions for first and second cumulants for the heat flow for a two-particle chain.