Dissipation and the relaxation to equilibrium
Date
2009
Authors
Evans, Denis
Searles, Debra
Williams, Stephen
Journal Title
Journal ISSN
Volume Title
Publisher
Institute of Physics Publishing
Abstract
Using the recently derived dissipation theorem and a corollary of the transient fluctuation theorem (TFT), namely the second-law inequality, we derive the unique time independent, equilibrium phase space distribution function for an ergodic Hamiltonian system in contact with a remote heat bath. We prove under very general conditions that any deviation from this equilibrium distribution breaks the time independence of the distribution. Provided temporal correlations decay, we show that any nonequilibrium distribution that is an even function of the momenta eventually relaxes (not necessarily monotonically) to the equilibrium distribution. Finally we prove that the negative logarithm of the microscopic partition function is equal to the thermodynamic Helmholtz free energy divided by the thermodynamic temperature and Boltzmann's constant. Our results complement and extend the findings of modern ergodic theory and show the importance of dissipation in the process of relaxation towards equilibrium.
Description
Keywords
Keywords: Molecular dynamics; Rigorous results in statistical mechanics
Citation
Collections
Source
Journal of Statistical Mechanics: Theory and Experiment
Type
Journal article
Book Title
Entity type
Access Statement
License Rights
Restricted until
2037-12-31
Downloads
File
Description