Gibbsian dynamics and the generalized Langevin equation
Probability
2023-01-10 v2
Abstract
We study the statistically invariant structures of the nonlinear generalized Langevin equation (GLE) with a power-law memory kernel. For a broad class of memory kernels, including those in the subdiffusive regime, we construct solutions of the GLE using a Gibbsian framework, which does not rely on existing Markovian approximations. Moreover, we provide conditions on the decay of the memory to ensure uniqueness of statistically steady states, generalizing previous known results for the GLE under particular kernels as a sum of exponentials.
Keywords
Cite
@article{arxiv.2111.04187,
title = {Gibbsian dynamics and the generalized Langevin equation},
author = {David P. Herzog and Jonathan C. Mattingly and Hung D. Nguyen},
journal= {arXiv preprint arXiv:2111.04187},
year = {2023}
}