Energy harvesting from anisotropic fluctuations

TL;DR

This paper models a heat engine based on the Brownian gyrator, analyzing how anisotropic temperature fields and thermodynamic path geometry influence work extraction and efficiency bounds.

Contribution

It introduces an isoperimetric framework to bound work and efficiency in anisotropic fluctuation-based engines, connecting geometry with thermodynamic performance.

Findings

Derived a universal efficiency bound for cyclic protocols.

Established a limit on traversal speed for positive work extraction.

Linked thermodynamic path geometry to dissipative losses.

Abstract

We consider a rudimentary model for a heat engine, known as the Brownian gyrator, that consists of an overdamped system with two degrees of freedom in an anisotropic temperature field. Whereas the hallmark of the gyrator is a nonequilibrium steady-state curl-carrying probability current that can generate torque, we explore the coupling of this natural gyrating motion with a periodic actuation potential for the purpose of extracting work. We show that path-lengths traversed in the manifold of thermodynamic states, measured in a suitable Riemannian metric, represent dissipative losses, while area integrals of a work-density quantify work being extracted. Thus, the maximal amount of work that can be extracted relates to an isoperimetric problem, trading off area against length of an encircling path. We derive an isoperimetric inequality that provides a universal bound on the efficiency of all cyclic operating protocols, and a bound on how fast a closed path can be traversed before it becomes impossible to extract positive work. The analysis presented provides guiding principles for building autonomous engines that extract work from anistropic fluctuations.