2019-03-05T23:10:23Z http://export.arxiv.org/oai2

oai:arXiv.org:1810.09584 2019-01-15 physics:cond-mat physics:physics

1810.09584\'Edgar Rold\'anMon, 22 Oct 2018 22:41:50 GMT401kbDSun, 13 Jan 2019 11:17:09 GMT669kbDRaphael Chetrite, Shamik Gupta, Izaak Neri and \'Edgar Rold\'ancond-mat.stat-mech physics.bio-ph physics.data-an7 pages, 2 figuresEPL 124,60006 (2018)10.1209/0295-5075/124/60006http://arxiv.org/licenses/nonexclusive-distrib/1.0/ 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.