The unlikely Carnot efficiency

Gatien Verley (), Massimiliano Esposito, Tim Willaert and Christian Van den Broeck
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Gatien Verley: Complex Systems and Statistical Mechanics, University of Luxembourg
Massimiliano Esposito: Complex Systems and Statistical Mechanics, University of Luxembourg
Tim Willaert: Theoretical physics, Hasselt University
Christian Van den Broeck: Theoretical physics, Hasselt University

Nature Communications, 2014, vol. 5, issue 1, 1-5

Abstract: Abstract The efficiency of an heat engine is traditionally defined as the ratio of its average output work over its average input heat. Its highest possible value was discovered by Carnot in 1824 and is a cornerstone concept in thermodynamics. It led to the discovery of the second law and to the definition of the Kelvin temperature scale. Small-scale engines operate in the presence of highly fluctuating input and output energy fluxes. They are therefore much better characterized by fluctuating efficiencies. In this study, using the fluctuation theorem, we identify universal features of efficiency fluctuations. While the standard thermodynamic efficiency is, as expected, the most likely value, we find that the Carnot efficiency is, surprisingly, the least likely in the long time limit. Furthermore, the probability distribution for the efficiency assumes a universal scaling form when operating close-to-equilibrium. We illustrate our results analytically and numerically on two model systems.

Date: 2014
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DOI: 10.1038/ncomms5721

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