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arXiv · 1810.09584

Martingale theory for housekeeping heat

Raphael Chetrite·Shamik Gupta·Izaak Neri·Édgar Roldán
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Abstract

The housekeeping heat is the energy exchanged between a system and its environment in a nonequilibrium process that results from the violation of detailed balance. We describe fluctuations of the housekeeping heat in mesoscopic systems using the theory of martingales, a mathematical framework widely used in probability theory and finance. We show that the exponentiated housekeeping heat (in units of $k_{\rm B}T$, with $k_{\rm B}$ the Boltzmann constant and $T$ the temperature) of a Markovian nonequilibrium process under arbitrary time-dependent driving is a martingale process. From this result, we derive universal equalities and inequalities for the statistics of stopping-times and suprema of the housekeeping heat. We test our results with numerical simulations of a system driven out of equilibrium and described by Langevin dynamics.

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BibTeXRIS

Raphael Chetrite, Shamik Gupta, Izaak Neri, Édgar Roldán. 2018-10-22. Martingale theory for housekeeping heat. https://doi.org/10.1209/0295-5075%2F124%2F60006

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