2016/05/01 by Domagoj Kuić, Domagoj Kuic
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Bayesian inference #Bayesian probability #Binary entropy function #Entropy (arrow of time) #Frequentist inference #H-theorem #Mathematics #Maximum entropy thermodynamics #Physics #Principle of maximum entropy #Statistical Mechanics and Entropy #Statistical mechanics #Statistical physics #Statistics #Thermodynamics #cond-mat.stat-mech #stochastic dynamics and bifurcation
paper · pdf · doi:10.1140/epjb/e2016-70175-6
published as Eur. Phys. J. B (2016) 89: 124 · 15 pages, revtex4; The final publication is available at Springer via http://dx.doi.org/10.1140/epjb/e2016-70175-6
openalex publication_date 2016/05/01 · arxiv created 2016/05/27 · arxiv updated 2016/05/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In this paper an alternative approach to statistical mechanics based on the maximum information entropy principle (MaxEnt) is examined, specifically its close relation with the Gibbs method of ensembles. It is shown that the MaxEnt formalism is the logical extension of the Gibbs formalism of equilibrium statistical mechanics that is entirely independent of the frequentist interpretation of probabilities only as factual (i.e. experimentally verifiable) properties of the real world. Furthermore, we show that, consistently with the law of large numbers, the relative frequencies of the ensemble of systems prepared under identical conditions (i.e. identical constraints) actually correspond to the MaxEnt probabilites in the limit of a large number of systems in the ensemble. This result implies that the probabilities in statistical mechanics can be interpreted, independently of the frequency interpretation, on the basis of the maximum information entropy principle.