Equilibrium Distributions in Open and Closed Statistical Systems

2010/01/19 by Ricardo López‐Ruiz, Ricardo Lopez-Ruiz, Jaime Sanudo +5 · 1 citation
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Chaotic Dynamics (nlin.CD) #Complex Systems and Time Series Analysis #FOS: Mathematics #FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech) #Statistical Mechanics and Entropy #Statistics Theory (math.ST) #cond-mat.stat-mech #math.ST #nlin.CD #stat.TH

paper · pdf · doi:10.48550/arxiv.1001.3327

5 pages, 0 figures

arxiv created 2010/01/19 · openalex publication_date 2010/01/19 · arxiv updated 2010/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this communication, the derivation of the Boltzmann-Gibbs and the Maxwellian distributions is presented from a geometrical point of view under the hypothesis of equiprobability. It is shown that both distributions can be obtained by working out the properties of the volume or the surface of the respective geometries delimited in phase space by an additive constraint. That is, the asymptotic equilibrium distributions in the thermodynamic limit are independent of considering open or closed homogeneous statistical systems.

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• Geometrical Derivation of Equilibrium Distributions in some Stochastic Systems

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