Stochastic thermodynamic engines under time-varying temperature profile

TL;DR

This paper investigates the power output and efficiency limits of overdamped stochastic thermodynamic engines operating with periodically varying temperature profiles, extending beyond traditional fixed-temperature heat bath models.

Contribution

It derives explicit bounds on power and efficiency for engines with arbitrary periodic temperature profiles, considering physical constraints on potential gradients.

Findings

Derived bounds on power output

Derived bounds on efficiency

Highlighting importance of potential gradient constraints

Abstract

In the present paper, we study the power output and efficiency of overdamped stochastic thermodynamic engines that are in contact with a heat bath having a temperature that varies periodically with time. This is in contrast to most of the existing literature that considers the Carnot paradigm of alternating contact with heat baths having different fixed temperatures, hot and cold. Specifically, we consider a periodic and bounded but otherwise arbitrary temperature profile and derive explicit bounds on the power and efficiency achievable by a suitable controlling potential that couples the thermodynamic engine to the external world. Standing assumptions in our analysis are bounds on the norm of the gradient of effective potentials -- in the absence of any such constraint, the physically questionable conclusion of arbitrarily large power can be drawn.