Single Particle Stochastic Heat Engine

TL;DR

This paper analyzes a single particle stochastic heat engine with a harmonic potential, revealing how fluctuations dominate efficiency and how system parameters influence engine performance, challenging universal efficiency relations.

Contribution

It provides an analytical and numerical study of a Brownian particle heat engine, highlighting fluctuation effects and the absence of universal efficiency relations.

Findings

Efficiency fluctuations dominate mean values.

Engine operates only above a critical temperature difference.

No universal efficiency relation at maximum power.

Abstract

We have performed an extensive analysis of a single particle stochastic heat engine constructed by manipulating a Brownian particle in a time dependent harmonic potential. The cycle consists of two isothermal steps at different temperatures and two adiabatic steps similar to that of a Carnot engine. The engine shows qualitative differences in inertial and overdamped regimes. All the thermodynamic quantities, including efficiency, exhibit strong fluctuations in a time periodic steady state. The fluctuations of stochastic efficiency dominate over the mean values even in the quasistatic regime. Interestingly, our system acts as an engine provided the temperature difference between the two reservoirs is greater than a finite critical value which in turn depends on the cycle time and other system parameters. This is supported by our analytical results carried out in the quasistatic regime. Our system works more reliably as an engine for large cycle times. By studying various model systems we observe that the operational characteristics are model dependent. Our results clearly rules out any universal relation between efficiency at maximum power and temperature of the baths. We have also verified fluctuation relations for heat engines in time periodic steady state.