Unified geometric formalism for dissipation and its fluctuations in finite-time microscopic heat engines

TL;DR

This paper introduces a unified geometric framework that describes both average dissipation and its fluctuations in microscopic heat engines, connecting thermodynamic performance with geometric structures derived from correlation functions.

Contribution

It develops a comprehensive geometric formalism that captures both dissipation and its fluctuations, extending finite-time thermodynamics to stochastic microscopic systems.

Findings

Provides geometric bounds on mean and variance of dissipation

Unifies description of dissipation and fluctuations across stochastic systems

Applicable to Markov processes and Brownian dynamics

Abstract

Microscopic heat engines operate in regimes where thermodynamic quantities fluctuate strongly, making stochastic effects an essential aspect of their performance. However, existing geometric formulations of finite-time thermodynamics primarily characterize average dissipation and do not systematically capture its fluctuations. Here, we develop a unified geometric framework that consistently describes both the mean dissipated availability and its fluctuations. In the linear-response regime, we show that these quantities are governed by metric tensors constructed from equilibrium correlation functions, providing a common geometric structure for dissipation and its fluctuations. This framework yields geometric bounds on both the mean and variance of the dissipated availability, and thereby on the efficiency and its fluctuations. The formalism applies broadly to stochastic systems, including Markov jump processes and overdamped and underdamped Brownian dynamics, establishing a unified geometric description across microscopic heat engines.