Underdamped Active Brownian Heat Engine

TL;DR

This paper investigates underdamped active Brownian heat engines, exploring how effective temperature concepts apply to non-equilibrium reservoirs and their impact on engine efficiency, especially under specific conditions relating to noise and friction.

Contribution

It introduces a framework for understanding thermodynamic properties of active Brownian engines with underdamped particles, highlighting conditions for defining effective temperature and efficiency bounds.

Findings

Effective temperature can be defined when noise and friction are proportional.

Engine efficiency bounds are established based on the effective temperature.

Parameter regimes exist where the effective temperature concept applies even without fluctuation-dissipation proportionality.

Abstract

Active Brownian engines rectify energy from reservoirs composed of self-propelling non-equilibrium molecules into work. We consider a class of such engines based on an underdamped Brownian particle trapped in a power-law potential. The energy they transform has thermodynamic properties of heat only if the non-equilibrium reservoir can be assigned a suitable effective temperature consistent with the second law and thus yielding an upper bound on the engine efficiency. The effective temperature exists if the total force exerted on the particle by the bath is not correlated with the particle position. In general, this occurs if the noise autocorrelation function and the friction kernel are proportional as in the fluctuation-dissipation theorem. But even if the proportionality is broken, the effective temperature can be defined in restricted, fine-tuned, parameter regimes, as we demonstrate on a specific example with harmonic potential.