On typicality in nonequilibrium steady states

Evans, Denis J., Williams, Stephen R., Searles, Debra J. and Rondoni, Lamberto (2016) On typicality in nonequilibrium steady states. Journal of Statistical Physics, 164 4: 842-857. doi:10.1007/s10955-016-1563-3

Author Evans, Denis J.
Williams, Stephen R.
Searles, Debra J.
Rondoni, Lamberto
Title On typicality in nonequilibrium steady states
Journal name Journal of Statistical Physics   Check publisher's open access policy
ISSN 0022-4715
Publication date 2016-08-01
Year available 2016
Sub-type Article (original research)
DOI 10.1007/s10955-016-1563-3
Open Access Status Not Open Access
Volume 164
Issue 4
Start page 842
End page 857
Total pages 16
Place of publication New York, NY United States
Publisher Springer New York
Collection year 2017
Language eng
Formatted abstract
From the statistical mechanical viewpoint, relaxation of macroscopic systems and response theory rest on a notion of typicality, according to which the behavior of single macroscopic objects is given by appropriate ensembles: ensemble averages of observable quantities represent the measurements performed on single objects, because “almost all” objects share the same fate. In the case of non-dissipative dynamics and relaxation toward equilibrium states, “almost all” is referred to invariant probability distributions that are absolutely continuous with respect to the Lebesgue measure. In other words, the collection of initial micro-states (single systems) that do not follow the ensemble is supposed to constitute a set of vanishing, phase space volume. This approach is problematic in the case of dissipative dynamics and relaxation to nonequilibrium steady states, because the relevant invariant distributions attribute probability 1 to sets of zero volume, while evolution commonly begins in equilibrium states, i.e., in sets of full phase space volume. We consider the relaxation of classical, thermostatted particle systems to nonequilibrium steady states. We show that the dynamical condition known as  ΩT-mixing is necessary and sufficient for relaxation of ensemble averages to steady state values. Moreover, we find that the condition known as weak T-mixing applied to smooth observables is sufficient for ensemble relaxation to be independent of the initial ensemble. Lastly, we show that weak T-mixing provides a notion of typicality for dissipative dynamics that is based on the (non-invariant) Lebesgue measure, and that we call physical ergodicity.
Keyword Ergodicity
Necessary conditions
Transient states
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status UQ

Version Filter Type
Citation counts: TR Web of Science Citation Count  Cited 0 times in Thomson Reuters Web of Science Article
Scopus Citation Count Cited 0 times in Scopus Article
Google Scholar Search Google Scholar
Created: Fri, 05 Aug 2016, 10:37:28 EST by Mrs Louise Nimwegen on behalf of Aust Institute for Bioengineering & Nanotechnology