2006/03/06 by Gavin E. Crooks · 68 citations
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Boltzmann distribution #Canonical ensemble #Complex Systems and Time Series Analysis #Entropy (arrow of time) #Equilibrium thermodynamics #Mathematics #Monte Carlo method #Non-equilibrium thermodynamics #Physics #Principle of maximum entropy #Probability distribution #Statistical Mechanics and Entropy #Statistical physics #Statistics #Thermodynamic equilibrium #Thermodynamics #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.75.041119
published in Physical Review E 75(4), 041119 (American Physical Society) · 4 pages
arxiv created 2006/03/06 · openalex publication_date 2007/04/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
What is the best description that we can construct of a thermodynamic system that is not in equilibrium, given only one, or a few, extra parameters over and above those needed for a description of the same system at equilibrium? Here, we argue the most appropriate additional parameter is the nonequilibrium entropy of the system. Moreover, we should not attempt to estimate the probability distribution of the system directly, but rather the metaprobability (or hyperensemble) that the system is described by a particular probability distribution. The result is an entropic distribution with two parameters, one a nonequilibrium temperature, and the other a measure of distance from equilibrium. This dispersion parameter smoothly interpolates between certainty of a canonical distribution at equilibrium and great uncertainty as to the probability distribution as we move away from equilibrium. We deduce that, in general, large, rare fluctuations become far more common as we move away from equilibrium.