Efficiency statistics at all times: Carnot limit at finite power

TL;DR

This paper analyzes the statistical behavior of efficiency in thermodynamic systems with fluctuating fluxes, revealing unique maxima and the conditions under which Carnot efficiency can be approached at finite power.

Contribution

It introduces a model for efficiency fluctuations incorporating a coupling parameter, elucidating conditions for reaching Carnot efficiency at finite entropy production.

Findings

Efficiency fluctuations have a peculiar distribution with maxima at reverse regimes.

The most probable efficiency decreases over time.

Approaching Carnot efficiency at finite entropy production is possible in a transient regime.

Abstract

We derive the statistics of the efficiency under the assumption that thermodynamic fluxes fluctuate with normal law, parametrizing it in terms of time, macroscopic efficiency, and a coupling parameter $\zeta$. It has a peculiar behavior: No moments, one sub- and one super-Carnot maxima corresponding to reverse operating regimes (engine/pump), the most probable efficiency decreasing in time. The limit $\zeta\to 0$ where the Carnot bound can be saturated gives rise to two extreme situations, one where the machine works at its macroscopic efficiency, with Carnot limit corresponding to no entropy production, and one where for a transient time scaling like $1/\zeta$ microscopic fluctuations are enhanced in such a way that the most probable efficiency approaches Carnot at finite entropy production.