2003/12/18 by Constantino Tsallis · 3 citations
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Boltzmann constant #Boltzmann distribution #Complex Systems and Time Series Analysis #Ergodicity #H-theorem #Hamiltonian (control theory) #Mathematics #Maximum entropy thermodynamics #Metastability #Physics #Quantum #Quantum mechanics #Statistical Mechanics and Entropy #Statistical mechanics #Statistical physics #Thermal equilibrium #cond-mat.stat-mech
paper · pdf · doi:10.1016/j.physa.2004.03.072
Invited paper at the Second Sardinian International Conference on "News and Expectations in Thermostatistics" held in Villasimius (Cagliari)- Italy in 21-28 September 2003. 12 pages including 2 figures
arxiv created 2003/12/18 · openalex publication_date 2004/04/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Statistical mechanics can only be ultimately justified in terms of microscopic dynamics (classical, quantum, relativistic, or any other). It is known that Boltzmann-Gibbs statistics is based on the hypothesis of exponential sensitivity to the initial conditions, mixing and ergodicity in Gibbs Γ-space. What are the corresponding hypothesis for nonextensive statistical mechanics? A scenario for answering such question is advanced, which naturally includes the \it a priori determination of the entropic index q, as well as its cause and manifestations, for say many-body Hamiltonian systems, in (i) sensitivity to the initial conditions in Gibbs Γ-space, (ii) relaxation of macroscopic quantities towards their values in anomalous stationary states that differ from the usual thermal equilibrium (e.g., in some classes of metastable or quasi-stationary states), and (iii) energy distribution in the Γ-space for the same anomalous stationary states.