Harvesting energy from a periodic heat bath

TL;DR

This paper investigates the maximum power and efficiency of thermodynamic processes with periodically varying heat bath temperatures using stochastic thermodynamics, analyzing both overdamped and underdamped models with derived optimal control strategies.

Contribution

It introduces a framework for analyzing heat engines with periodic temperature variations within stochastic thermodynamics, deriving approximate formulas for optimal performance.

Findings

Derived and validated formulas for maximum power and efficiency.

Identified properties of optimal periodic control strategies.

Compared overdamped and underdamped models in thermodynamic cycles.

Abstract

The context of the present paper is stochastic thermodynamics - an approach to nonequilibrium thermodynamics rooted within the broader framework of stochastic control. In contrast to the classical paradigm of Carnot engines, we herein propose to consider thermodynamic processes with periodic continuously varying temperature of a heat bath and study questions of maximal power and efficiency for two idealized cases, overdamped (first-order) and underdamped (second-order) stochastic models. We highlight properties of optimal periodic control, derive and numerically validate approximate formulae for the optimal performance (power and efficiency).