Martingale theory for housekeeping heat
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...
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| Veröffentlicht in: | Europhysics letters 2018-12, Vol.124 (6), p.60006 |
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| container_title | Europhysics letters |
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| creator | Chétrite, Raphaël Gupta, Shamik Neri, Izaak Roldán, Édgar |
| description | 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 kBT, with kB 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. |
| doi_str_mv | 10.1209/0295-5075/124/60006 |
| format | Article |
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| source | IOP Publishing Journals |
| subjects | 05.40.Ca 05.70.Ln Condensed Matter Heat exchange Martingales Mathematical Physics Mathematics Physics Probability Probability theory Statistical Mechanics Statistical tests Temperature dependence |
| title | Martingale theory for housekeeping heat |
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