Efficiency fluctuations in cyclic machines

TL;DR

This paper analyzes the efficiency fluctuations of isothermal cyclic machines, deriving a universal probability distribution and revealing conditions for optimal and reversible efficiencies based on coupling strength.

Contribution

It provides a general derivation of efficiency distribution functions and identifies universal bounds and conditions for maximum and reversible efficiencies.

Findings

Macroscopic efficiency equals the most likely efficiency.

Universal efficiency bounds depend only on thermodynamic forces.

Tight coupling is necessary for near-reversible efficiency.

Abstract

We study the statistics of the efficiency in a class of isothermal cyclic machines with realistic coupling between the internal degrees of freedom. We derive, under fairly general assumptions, the probability distribution function for the efficiency. We find that the macroscopic efficiency is always equal to the most likely efficiency, and it lies in an interval whose boundaries are universal as they only depend on the input and output thermodynamic forces, and not on the details of the machine. The machine achieves the upper boundary of such an interval only in the limit of tight coupling. Furthermore, we find that the tight coupling limit is a necessary, yet not sufficient, condition for the engine to perform close to the reversible efficiency. The reversible efficiency is the least likely regardless of the coupling strength, in agreement with previous studies. By using a large deviation formalism we derive a fluctuation relation for the efficiency which holds for any number of internal degrees of freedom in the system.