# Efficiency and Large Deviations in Time-Asymmetric Stochastic Heat Engines

Gingrich, Todd R, Rotskoff, Grant M, Vaikuntanathan, Suriyanarayanan, Geissler, Phillip L

October 2014
### 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. Commun. 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 (η), based on large deviation statistics of work and heat, that remains very accurate even when P (η) deviates significantly from its large deviation form.

Publication

New Journal of Physics