Homogenization for a Class of Generalized Langevin Equations with an Application to Thermophoresis

Soon Hoe Lim, Jan Wehr

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


We study a class of systems whose dynamics are described by generalized Langevin equations with state-dependent coefficients. We find that in the limit, in which all the characteristic time scales vanish at the same rate, the position variable of the system converges to a homogenized process, described by an equation containing additional drift terms induced by the noise. The convergence results are obtained using the main result in Hottovy et al. (Commun Math Phys 336(3):1259–1283, 2015), whose version is proven here under a weaker spectral assumption on the damping matrix. We apply our results to study thermophoresis of a Brownian particle in a non-equilibrium heat bath.

Original languageEnglish (US)
Pages (from-to)656-691
Number of pages36
JournalJournal of Statistical Physics
Issue number3
StatePublished - Feb 15 2019


  • Generalized Langevin equation
  • Multiscale analysis
  • Noise-induced drift
  • Small mass limit
  • Thermophoresis

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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