Contents Online
Communications in Mathematical Sciences
Volume 16 (2018)
Number 8
Exponential relaxation of the Nosé–Hoover thermostat under Brownian heating
Pages: 2231 – 2260
DOI: https://dx.doi.org/10.4310/CMS.2018.v16.n8.a8
Author
Abstract
We study a stochastic perturbation of the Nosé–Hoover equation (called the Nosé–Hoover equation under Brownian heating) and show that the dynamics converges at a geometric rate to the augmented Gibbs measure in a weighted total variation distance. The joint marginal distribution of the position and momentum of the particles in turn converges exponentially fast in a similar sense to the canonical Boltzmann–Gibbs distribution. The result applies to a general number of particles interacting through a wide class of potential functions, including the usual polynomial type as well as the singular Lennard–Jones variety.
Keywords
Langevin dynamics, Nosé–Hoover equation, Lennard–Jones potential, geometric ergodicity, molecular dynamics simulation, random sampling
2010 Mathematics Subject Classification
37A25, 60H10, 60J22, 65C05, 82C31
Received 24 April 2018
Accepted 22 August 2018
Published 18 April 2019