Finite-Time Thermodynamics of Fluctuations in Microscopic Heat Engines

TL;DR

This paper develops a finite-time thermodynamics framework for fluctuations in microscopic heat engines, enabling the optimization of dissipation and fluctuations in cyclic processes.

Contribution

It introduces a universal formalism for fluctuations in driven microscopic heat engines and identifies optimal protocols to minimize dissipation and fluctuations simultaneously.

Findings

Universal formalism for fluctuations in slow-driving regime

Identification of optimal protocols for dissipation minimization

Improved dissipation and fluctuation performance in experiments

Abstract

Fluctuations of thermodynamic quantities become non-negligible and play an important role when the system size is small. We develop finite-time thermodynamics of fluctuations in microscopic heat engines whose environmental temperature and mechanical parameter are driven periodically in time. Within the slow-driving regime, this formalism universally holds in a coarse-grained time scale whose resolution is much longer than the correlation time of the fluctuations, and is shown to be consistent with the relation analogous to the fluctuation-dissipation relation. Employing a geometric argument, a scenario to simultaneously minimize both the average and fluctuation of the dissipation in the Carnot cycle is identified. For this simultaneous optimization, the existence of a zero eigenvalue of the singular metric for the scale invariant equilibrium state is found to be essential. Furthermore, we demonstrate that our optimized protocol can improve the dissipation and its fluctuation over the current experiment.