Using the Fluctuation Theorem (FT), we give a first-principles derivation of Boltzmann’s postulate of equal a priori probability
in phase space for the microcanonical ensemble. Using a corollary of the Fluctuation Theorem, namely the Second Law Inequality, we show that if the initial distribution differs from the uniform distribution over the energy hypersurface, then under very wide and commonly satisfied conditions, the initial distribution will relax to that uniform distribution. This result is somewhat analogous to the Boltzmann H-theorem but unlike that theorem, applies to dense fluids as well as dilute gases and also permits a nonmonotonic relaxation to equilibrium. We also prove that in ergodic systems the uniform (microcanonical) distribution is the only stationary, dissipationless distribution for the constant energy ensemble.
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa.de:bsz:15-qucosa-190362 |
| Date | 03 December 2015 |
| Creators | Evans, Denis J., Searles, Debra J., Williams, Stephen R. |
| Contributors | Australian National University, Research School of Chemistry, Griffith University, School of Biomolecular and Physical Sciences, Universität Leipzig, Fakultät für Physik und Geowissenschaften |
| Publisher | Universitätsbibliothek Leipzig |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | doc-type:article |
| Format | application/pdf |
| Source | Diffusion fundamentals 11 (2009) 57, S. 1-8 |
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