Multiplicative Langevin Equation to Reproduce Long-time Properties of Nonequilibrium Brownian Motion

We statistically examine long time sequences of Brownian motion for a nonequilibrium version of the Rayleigh piston model and confirm that the third cumulant of a long-time displacement for the nonequilibrium Brownian motion linearly increases with the observation time interval. We identify a multip...

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Bibliographic Details
Published inarXiv.org
Main Authors Seya, Atsumasa, Aoyagi, Tatsuya, Itami, Masato, Nakayama, Yohei, Nakagawa, Naoko
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 20.09.2019
Subjects
Brownian motion
Coefficient of friction
Conduction heating
Conductive heat transfer
Cylinders
Physics - Statistical Mechanics
Temperature gradients
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Summary:We statistically examine long time sequences of Brownian motion for a nonequilibrium version of the Rayleigh piston model and confirm that the third cumulant of a long-time displacement for the nonequilibrium Brownian motion linearly increases with the observation time interval. We identify a multiplicative Langevin equation that can reproduce the cumulants of the long-time displacement up to at least the third order, as well as its mean, variance and skewness. The identified Langevin equation involves a velocity-dependent friction coefficient that breaks the time-reversibility and may act as a generator of the directionality. Our method to find the Langevin equation is not specific to the Rayleigh piston model but may be applied to a general time sequence in various fields.
ISSN:2331-8422
DOI:10.48550/arxiv.1904.07033