Geometry of finite-time thermodynamic cycles with anisotropic thermal fluctuations

TL;DR

This paper presents a geometric framework for understanding energy harvesting in anisotropic thermodynamic cycles using stochastic models like the Brownian gyrator, highlighting fundamental limits on power and efficiency.

Contribution

It introduces a geometric control perspective on finite-time thermodynamic cycles with anisotropic fluctuations, extending analysis beyond linear response and equilibrium.

Findings

Energy harvesting modeled as a controlled trajectory on the thermodynamic manifold

Dissipation and work are expressed as path integrals of the controlled process

Fundamental power and efficiency limits relate to an isoperimetric problem

Abstract

In contrast to the classical concept of a Carnot engine that alternates contact between heat baths of different temperatures, naturally occurring processes usually harvest energy from anisotropy, being exposed simultaneously to chemical and thermal fluctuations of different intensities. In these cases, the enabling mechanism responsible for transduction of energy is typically the presence of a non-equilibrium steady state (NESS). A suitable stochastic model for such a phenomenon is the Brownian gyrator -- a two-degree of freedom stochastically driven system that exchanges energy and heat with the environment. In the context of such a model we present, from a stochastic control perspective, a geometric view of the energy harvesting mechanism that entails a forced periodic trajectory of the system state on the thermodynamic manifold. Dissipation and work output are expressed accordingly as path integrals of a controlled process, and fundamental limitations on power and efficiency are expressed in geometric terms via a relationship to an isoperimetric problem. The theory is presented for high-order systems far from equilibrium and beyond the linear response regime.