Anomalous Brownian Refrigerator

TL;DR

This paper analyzes a Brownian particle in a harmonic potential operating as a stochastic refrigerator, heater, or heat engine depending on cycle parameters, revealing complex fluctuation behaviors and non-universal efficiency distributions.

Contribution

It provides a comprehensive analytical study of a Brownian refrigerator that can also function as a heater or heat engine, highlighting fluctuation effects and non-universality.

Findings

System can act as a refrigerator, heater, or heat engine depending on parameters.

Efficiency and COP fluctuations have power-law tails with non-universal exponents.

Operation as an engine is unreliable with non-trivial fluctuation dominance.

Abstract

We present a detailed study of a Brownian particle driven by Carnot-type refrigerating protocol operating between two thermal baths. Both the underdamped as well as the overdamped limits are investigated. The particle is in a harmonic potential with time-periodic strength that drives the particle cyclically between the baths. Each cycle consists of two isothermal steps at different temperatures and two adiabatic steps connecting them. Besides working as a stochastic refrigerator, it is shown analytically that in the quasistatic regime the system can also act as stochastic heater, depending on the bath temperatures. Interestingly, in non-quasistatic regime, our system can even work as a stochastic heat engine for certain range of cycle time and bath temperatures. We show that the operation of this engine is not reliable. The fluctuations of stochastic efficiency/coefficient of performance (COP) dominate their mean values. Their distributions show power law tails, however the exponents are not universal. Our study reveals that microscopic machines are not the microscopic equivalent of the macroscopic machines that we come across in our daily life. We find that there is no one to one correspondence between the performance of our system under engine protocol and its reverse.