Dissipation and the relaxation to equilibrium

Evans, Denis J., Searles, Debra J. and Williams, Stephen R. (2009) Dissipation and the relaxation to equilibrium. Journal of Statistical Mechanics-Theory and Experiment, 7: P07029.1-P07029.11. doi:10.1088/1742-5468/2009/07/P07029

Author Evans, Denis J.
Searles, Debra J.
Williams, Stephen R.
Title Dissipation and the relaxation to equilibrium
Journal name Journal of Statistical Mechanics-Theory and Experiment   Check publisher's open access policy
ISSN 1742-5468
Publication date 2009-07-01
Sub-type Article (original research)
DOI 10.1088/1742-5468/2009/07/P07029
Issue 7
Start page P07029.1
End page P07029.11
Total pages 11
Place of publication Bristol, United Kingdom
Publisher Institute of Physics Publishing
Language eng
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.
Keyword Rigorous results in statistical mechanics
Molecular dynamics
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Non-UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Chemistry and Molecular Biosciences
Australian Institute for Bioengineering and Nanotechnology Publications
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Citation counts: TR Web of Science Citation Count  Cited 24 times in Thomson Reuters Web of Science Article | Citations
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