@article{972957ffbe994aba9c8c0be233742ec4,

title = "Homogenization for a Class of Generalized Langevin Equations with an Application to Thermophoresis",

abstract = "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.",

keywords = "Generalized Langevin equation, Multiscale analysis, Noise-induced drift, Small mass limit, Thermophoresis",

author = "Lim, {Soon Hoe} and Jan Wehr",

note = "Funding Information: The authors were partially supported by NSF grant DMS-1615045. S. Lim is grateful for the support provided by the Michael Tabor Fellowship from the Program in Applied Mathematics at the University of Arizona during the academic year 2017-2018. The authors learned the method of introducing additional variables to eliminate the memory term from E. Vanden-Eijnden. They would like to thank Maciej Lewenstein for insightful discussion on the GLEs and one of the referees for the constructive comments. Funding Information: Acknowledgements The authors were partially supported by NSF grant DMS-1615045. S. Lim is grateful for the support provided by the Michael Tabor Fellowship from the Program in Applied Mathematics at the University of Arizona during the academic year 2017-2018. The authors learned the method of introducing additional variables to eliminate the memory term from E. Vanden-Eijnden. They would like to thank Maciej Lewenstein for insightful discussion on the GLEs and one of the referees for the constructive comments.",

year = "2019",

month = feb,

day = "15",

doi = "10.1007/s10955-018-2192-9",

language = "English (US)",

volume = "174",

pages = "656--691",

journal = "Journal of Statistical Physics",

issn = "0022-4715",

publisher = "Springer New York",

number = "3",

}