A quantum dynamical framework for Brownian heat engines

TL;DR

This paper introduces a quantum dynamical framework for analyzing microscopic Brownian heat engines, providing exact results on efficiency, dissipation effects, and finite-time corrections, with broad applicability in quantum thermodynamics.

Contribution

It develops a self-contained quantum formalism for Brownian heat engines, enabling detailed analysis of dissipation, finite-time effects, and efficiency optimization in quantum regimes.

Findings

Exact analytical results on decoupling and recoupling dynamics.

Derived thermodynamic complementarity relations.

Computed efficiencies at maximum power for various engines.

Abstract

We present a self contained formalism modelled after the Brownian motion of a quantum harmonic oscillator for describing the performance of microscopic Brownian heat engines like Carnot, Stirling and Otto engines. Our theory, besides reproducing the standard thermodynamics results in the steady state enables permits us to study the role dissipation plays in determining the efficiency of Brownian heat engines under actual laboratory conditions. In particular, we analyse in detail the dynamics associated with decoupling a system in equilibrium with one bath and recoupling it to another bath and obtain exact analytical results which are shown to have significant ramifications on the efficiencies of engines involving such a step. We also develop a simple yet powerful technique for computing corrections to the steady state results arising from finite operation time and use it to arrive at the thermodynamic complementarity relations for various operating conditions and also to compute the efficiencies of the three engines cited above at maximum power. Some of the methods and techniques and exactly solvable models presented here are interesting in their own right and, in our opinion, would find useful applications in other contexts as well.