Thermodynamics of a stochastic twin elevator

TL;DR

This paper analyzes the non-equilibrium thermodynamics of a single particle with two energy levels, exploring work, heat, and entropy production in classical and quantum heat baths, and deriving efficiency limits and large deviation functions.

Contribution

It provides explicit calculations of thermodynamic quantities and efficiency limits for a stochastic twin elevator model in both classical and quantum regimes.

Findings

Efficiency approaches a limit between 100% and 50% depending on transition rates.

Explicit large deviation functions for heat, work, and internal energy are derived.

Thermodynamic behavior differs between classical and quantum heat baths.

Abstract

We study the non-equilibrium thermodynamics of a single particle with two available energy levels, in contact with a classical (Maxwell-Boltzmann) or quantum (Bose-Einstein) heat bath. The particle can undergo transitions between the levels via thermal activation or deactivation. The energy levels are alternately raised at a given rate regardless of occupation by the particle, maintaining a fixed energy gap equal to epsilon between them. We explicitly calculate the work, heat and entropy production rates. The efficiency in both the classical and the quantum case goes to a limit between 100% and 50% that depends on the relative rates of particle transitions and level elevation. In the classical problem we explicitly find the large deviation functions for heat, work, and internal energy.