Thermodynamics and optimal protocols of multidimensional quadratic Brownian systems

TL;DR

This paper develops a geometric framework for analyzing and optimizing finite-time thermodynamic processes in multidimensional quadratic Brownian systems, providing explicit formulas and principles for minimal dissipation protocols.

Contribution

It introduces a geometric approach using the Bures-Wasserstein metric to characterize dissipation and derive optimal protocols in multidimensional quadratic overdamped systems.

Findings

Explicit formulas for heat, work, and dissipation in terms of covariance matrix evolution

Identification of the Bures-Wasserstein metric as a natural measure of dissipation

Application of geometric principles to partial control scenarios

Abstract

We characterize finite-time thermodynamic processes of multidimensional quadratic overdamped systems. Analytic expressions are provided for heat, work, and dissipation for any evolution of the system covariance matrix. The Bures-Wasserstein metric between covariance matrices naturally emerges as the local quantifier of dissipation. General principles of how to apply these geometric tools to identify optimal protocols are discussed. Focusing on the relevant slow-driving limit, we show how these results can be used to analyze cases in which the experimental control over the system is partial.