2005/10/07 by R. Silva, J. A. S. Lima · 40 citations
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Classical mechanics #Complex Systems and Time Series Analysis #Distribution function #Entropy (arrow of time) #Limit (mathematics) #Mathematical analysis #Mathematics #Physics #Power law #Quantum mechanics #Second law of thermodynamics #Statistical Mechanics and Entropy #Statistical physics #Theoretical physics #Theory of relativity #Tsallis entropy #astro-ph #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.72.057101
published in Physical Review E 72(5), 057101 (American Physical Society) · Accepted for publication in PRE
arxiv created 2005/10/07 · openalex publication_date 2005/11/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A proof of the relativistic theorem by including nonextensive effects is given. As it happens in the nonrelativistic limit, the molecular chaos hypothesis advanced by Boltzmann does not remain valid, and the second law of thermodynamics combined with a duality transformation implies that the parameter lies on the interval [0,2]. It is also proven that the collisional equilibrium states (null entropy source term) are described by the relativistic power law extension of the exponential Juttner distribution which reduces, in the nonrelativistic domain, to the Tsallis power law function. As a simple illustration of the basic approach, we derive the relativistic nonextensive equilibrium distribution for a dilute charged gas under the action of an electromagnetic field . Such results reduce to the standard ones in the extensive limit, thereby showing that the nonextensive entropic framework can be harmonized with the space-time ideas contained in the special relativity theory.