Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2003-12-18
Physics
Condensed Matter
Statistical Mechanics
Invited paper at the Second Sardinian International Conference on "News and Expectations in Thermostatistics" held in Villasim
Scientific paper
10.1016/j.physa.2004.03.072
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 $\Gamma$-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 $\Gamma$-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 $\Gamma$-space for the same anomalous stationary states.
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