Multiplicative Langevin equation to reproduce long-time properties of nonequilibrium Brownian motion

Atsumasa Seya, Tatsuya Aoyagi, Masato Itami, Yohei Nakayama, Naoko Nakagawa

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


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.

Original languageEnglish
Article number013201
JournalJournal of Statistical Mechanics: Theory and Experiment
Issue number1
Publication statusPublished - 2020


  • Brownian motion
  • heat conduction
  • large deviations in non-equilibrium systems
  • numerical simulations

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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