On the use of stochastic differential geometry for non-equilibrium thermodynamics modeling and control

TL;DR

This paper explores how stochastic differential geometry, especially the Eells-Elworthy-Malliavin construction, can be used to model and optimize non-equilibrium thermodynamic processes in small systems.

Contribution

It introduces a geometric framework for stochastic thermodynamics and applies it to formulate and interpret optimal control problems in finite-time thermodynamic transitions.

Findings

Geometric concepts clarify stochastic thermodynamics modeling.

The Eells-Elworthy-Malliavin construction provides a transparent control formulation.

Recent results on optimal thermodynamic control are evaluated and interpreted.

Abstract

We discuss the relevance of geometric concepts in the theory of stochastic differential equations for applications to the theory of non-equilibrium thermodynamics of small systems. In particular, we show how the Eells-Elworthy-Malliavin covariant construction of the Wiener process on a Riemann manifold provides a physically transparent formulation of optimal control problems of finite-time thermodynamic transitions. Based on this formulation, we turn to an evaluative discussion of recent results on optimal thermodynamic control and their interpretation.