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Efficiency and Large Deviations in Time-Asymmetric Stochastic Heat Engines

Authors :
Gingrich, Todd R.
Rotskoff, Grant M.
Vaikuntanathan, Suriyanarayanan
Geissler, Phillip L.
Source :
New J. Phys. 16, 102003 (2014)
Publication Year :
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 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.<br />Comment: 10 pages, 3 figures

Details

Database :
arXiv
Journal :
New J. Phys. 16, 102003 (2014)
Publication Type :
Report
Accession number :
edsarx.1409.1561
Document Type :
Working Paper
Full Text :
https://doi.org/10.1088/1367-2630/16/10/102003