Thermodynamics from first principles: Correlations and nonextensivity

S. N. Saadatmand, Tim Gould, E. G. Cavalcanti, J. A. Vaccaro
2020 Physical review. E  
The standard formulation of thermostatistics, being based on the Boltzmann-Gibbs distribution and logarithmic Shannon entropy, describes idealized uncorrelated systems with extensive energies and short-range interactions. In this Rapid Communication, we use the fundamental principles of ergodicity (via Liouville's theorem), the self-similarity of correlations, and the existence of the thermodynamic limit to derive generalized forms of the equilibrium distribution for long-range-interacting
more » ... ms. Significantly, our formalism provides a justification for the well-studied nonextensive thermostatistics characterized by the Tsallis distribution, which it includes as a special case. We also give the complementary maximum entropy derivation of the same distributions by constrained maximization of the Gibbs-Shannon entropy. The consistency between the ergodic and maximum entropy approaches clarifies the use of the latter in the study of correlations and nonextensive thermodynamics.
doi:10.1103/physreve.101.060101 pmid:32688595 fatcat:kmzknxpbvzdc5aowa4bifc6r2e