Efficiency and Large Deviations in Time-Asymmetric Stochastic Heat Engines

TL;DR

This paper investigates fluctuations in efficiency of a stochastic heat engine using simulations and large deviation theory, revealing differences from time-symmetric protocols and proposing an accurate finite-time efficiency distribution approximation.

Contribution

It introduces a new approximation for finite-time efficiency distribution based on large deviation statistics, applicable to non-time-symmetric stochastic heat engines.

Findings

Efficiency distributions have a local minimum similar to previous models.

The minimum does not necessarily occur at the reversible Carnot efficiency.

The proposed approximation remains accurate even with significant deviations from large deviation form.

Abstract

In a stochastic heat engine driven by a cyclic non-equilibrium protocol, fluctuations in work and heat give rise to a fluctuating efficiency. Using computer simulations and tools from large deviation theory, we have examined these fluctuations in detail for a model two-state engine. We find in general that the form of efficiency probability distributions is similar to those described by Verley et al. [2014 Nat Comm, 5 4721], in particular featuring a local minimum in the long-time limit. In contrast to the time-symmetric engine protocols studied previously, however, this minimum need not occur at the value characteristic of a reversible Carnot engine. Furthermore, while the local minimum may reside at the global minimum of a large deviation rate function, it does not generally correspond to the least likely efficiency measured over finite time. We introduce a general approximation for the finite-time efficiency distribution, $P(\eta)$, based on large deviation statistics of work and heat, that remains very accurate even when $P(\eta)$ deviates significantly from its large deviation form.