Beyond Boltzmann-Gibbs statistics: Maximum entropy hyperensemblesout-of-equilibrium
What is the best description that we can construct of athermodynamic system that is not in equilibrium, given only one, or afew, extra parameters over and above those needed for a description ofthe same system at equilibrium? Here, we argue the most appropriateadditional parameter is the non-equilibrium entropy of the system, andthat we should not attempt to estimate the probability distribution ofthe system, but rather the metaprobability (or hyperensemble) that thesystem is described by a particular probability distribution. The resultis an entropic distribution with two parameters, one a non-equilibriumtemperature, and the other a measure of distance from equilibrium. Thisdispersion parameter smoothly interpolates between certainty of acanonical distribution at equilibrium and great uncertainty as to theprobability distribution as we move away from equilibrium. We deducethat, in general, large, rare fluctuations become far more common as wemove away from equilibrium.
- Research Organization:
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
- Sponsoring Organization:
- USDOE Director, Office of Science
- DOE Contract Number:
- DE-AC02-05CH11231
- OSTI ID:
- 919749
- Report Number(s):
- LBNL-59723; PRLTAO; TRN: US0806478
- Journal Information:
- Physical Review Letters, Vol. E75; Related Information: Journal Publication Date: 04/2007; ISSN 0031-9007
- Country of Publication:
- United States
- Language:
- English
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