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Martingale theory for housekeeping heat

Research output: Contribution to journalArticlepeer-review

Raphaël Chétrite, Shamik Gupta, Izaak Neri, Edgar Roldan

Original languageEnglish
Article number60006
Number of pages7
JournalEurophysics Letters
Volume124
DOIs
Accepted/In press7 Dec 2018
PublishedDec 2018

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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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