Carnot process with a single particle

TL;DR

This paper analyzes the work and heat statistics of a microscopic Carnot cycle with a single particle, providing insights into efficiency at maximum power in non-equilibrium thermodynamics.

Contribution

It introduces a detailed statistical analysis of work and heat in a single-particle Carnot cycle, combining isothermal and adiabatic processes.

Findings

Derived the joint probability distribution of heat and work.

Calculated the efficiency at maximum power for the microscopic cycle.

Extended classical thermodynamics to single-particle systems.

Abstract

We determine the statistics of work in isothermal volume changes of a classical ideal gas consisting of a single particle. Combining our results with the findings of Lua and Grosberg [J. Chem. Phys. B 109, 6805 (2005)] on adiabatic expansions and compressions we then analyze the joint probability distribution of heat and work for a microscopic, non-equilibrium Carnot cycle and determine its efficiency at maximum power.