Steady-state heat engines driven by finite reservoirs

TL;DR

This paper analyzes how finite-size reservoirs influence the performance and efficiency of stochastic heat engines, providing new tools for optimizing nanoscale engines under realistic conditions.

Contribution

It introduces a thermodynamic framework for finite reservoirs, deriving effective temperatures and demonstrating potential to surpass classical efficiency bounds.

Findings

Finite reservoirs affect engine power and efficiency.

Efficiency at maximum power can exceed Curzon-Ahlborn bound.

Optimization strategies for nanoscale engines are proposed.

Abstract

We provide a consistent thermodynamic analysis of stochastic thermal engines driven by finite-size reservoirs, which are in turn coupled to infinite-size reservoirs. We consider a cyclic operation mode, where the working medium couples sequentially to hot and cold reservoirs, and a continuous mode with both reservoirs coupled simultaneously. We derive an effective temperature for the finite-size reservoirs determining the entropy production for two-state engines in the sequential coupling scenario, and show that finite-size reservoirs can meaningfully affect the power when compared to infinite-size reservoirs in both sequential and simultaneous coupling scenarios. We also investigate a three-state engine comprising two interacting units and optimize its performance in the presence of a finite reservoir. Notably, we show that the efficiency at maximum power can exceed the Curzon-Ahlborn bound with finite reservoirs. Our work introduces tools to optimize the performance of nanoscale engines under realistic conditions of finite reservoir heat capacity and imperfect thermal isolation.