2003/11/19 by Jan Naudts · 1 citation
Economics, Econometrics and Finance · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Complex Systems and Time Series Analysis #Statistical Mechanics and Entropy #cond-mat.stat-mech
paper · pdf · doi:10.1016/j.physa.2004.03.074
published as Physica A340, 32-40 (2004) · Invited talk at Next2003, uses Elsevier LaTeX macros
arxiv created 2003/11/19 · openalex publication_date 2004/04/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The equipartition theorem states that inverse temperature equals the log-derivative of the density of states. This relation can be generalized by introducing a proportionality factor involving an increasing positive function phi(x). It is shown that this assumption leads to an equilibrium distribution of the Boltzmann-Gibbs form with the exponential function replaced by a deformed exponential function. In this way one obtains a formalism of generalized thermostatistics introduced previously by the author. It is shown that Tsallis' thermostatistics, with a slight modification, is the most obvious example of this formalism and corresponds with the choice phi(x)=xq.