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<identifier>oai:arXiv.org:1810.09584</identifier>
<datestamp>2019-01-15</datestamp>
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<arXivRaw xmlns="http://arxiv.org/OAI/arXivRaw/" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://arxiv.org/OAI/arXivRaw/ http://arxiv.org/OAI/arXivRaw.xsd">
<id>1810.09584</id><submitter>\'Edgar Rold\'an</submitter><version version="v1"><date>Mon, 22 Oct 2018 22:41:50 GMT</date><size>401kb</size><source_type>D</source_type></version><version version="v2"><date>Sun, 13 Jan 2019 11:17:09 GMT</date><size>669kb</size><source_type>D</source_type></version><title>Martingale theory for housekeeping heat</title><authors>Raphael Chetrite, Shamik Gupta, Izaak Neri and \'Edgar Rold\'an</authors><categories>cond-mat.stat-mech physics.bio-ph physics.data-an</categories><comments>7 pages, 2 figures</comments><journal-ref>EPL 124,60006 (2018)</journal-ref><doi>10.1209/0295-5075/124/60006</doi><license>http://arxiv.org/licenses/nonexclusive-distrib/1.0/</license><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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