Markovian Approximation for the Nos\'e--Hoover method and H-theorem
Statistical Mechanics
2009-11-13 v1
Abstract
A Langevin equation with state-dependent random force is considered. When the Helmholtz free energy is a nonincreasing function of time (the H-theorem), a generalized Einstein relation is obtained. A stochastic process of the Nos\'e--Hoover method is discussed on the basis of the Markovian approximation. It is found that the generalized Einstein relation holds for the Fokker--Planck equation associated with the stochastic Nos\'e--Hoover equation. The present result indicates that the Nos\'e--Hoover dynamics coarse-grained with time satisfies the H-theorem and therefore works as a heat bath.
Cite
@article{arxiv.0807.1406,
title = {Markovian Approximation for the Nos\'e--Hoover method and H-theorem},
author = {Hiroshi Watanabe},
journal= {arXiv preprint arXiv:0807.1406},
year = {2009}
}
Comments
7 pages, no figures, submitted to J. Phys. Soc. Jpn