Energetics and performance of a microscopic heat engine based on exact calculations of work and heat distributions

TL;DR

This paper presents an exact analysis of a microscopic two-level heat engine, calculating work, heat, and efficiency distributions, revealing how irreversibility affects its thermodynamic performance.

Contribution

It provides an exact solution for the work and heat distributions of a microscopic heat engine using a two-level system, including the effects of irreversibility.

Findings

Work and heat distributions are exactly calculated.

Irreversibility causes significant deviations from Gaussian work distributions.

The engine's thermodynamic quantities are analytically characterized.

Abstract

We investigate a microscopic motor based on an externally controlled two-level system. One cycle of the motor operation consists of two strokes. Within each stroke, the two-level system is in contact with a given thermal bath and its energy levels are driven with a constant rate. The time evolution of the occupation probabilities of the two states are controlled by one rate equation and represent the system's response with respect to the external driving. We give the exact solution of the rate equation for the limit cycle and discuss the emerging thermodynamics: the work done on the environment, the heat exchanged with the baths, the entropy production, the motor's efficiency, and the power output. Furthermore we introduce an augmented stochastic process which reflects, at a given time, both the occupation probabilities for the two states and the time spent in the individual states during the previous evolution. The exact calculation of the evolution operator for the augmented process allows us to discuss in detail the probability density for the performed work during the limit cycle. In the strongly irreversible regime, the density exhibits important qualitative differences with respect to the more common Gaussian shape in the regime of weak irreversibility.