• DOI:10.1103/PHYSREVE.101.060101
• Corpus ID: 195791360

Thermodynamics from first principles: Correlations and nonextensivity.

@article{Saadatmand2019ThermodynamicsFF,
  title={Thermodynamics from first principles: Correlations and nonextensivity.},
  author={S. N. Saadatmand and Tim Gould and Eric G. Cavalcanti and Joan A. Vaccaro},
  journal={Physical review. E},
  year={2019},
  volume={101 6-1},
  pages={
          060101
        }
}

• S. N. Saadatmand, T. Gould, +1 author J. Vaccaro
• Published 3 July 2019
• Physics
• 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 systems. 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.