# 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 } }

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…

## One Citation

### Entropy Optimization, Generalized Logarithms, and Duality Relations

- Computer ScienceEntropy
- 2022

The present work analyzes one of the specific structural features of the Sq thermostatistics, according to which the q-logarithm function lnqx≡x1−q−11−q(ln1x=lnx) associated with the SQ entropy is linked, via a duality relation, to theq-exponential function characterizing the maximum-entropy probability distributions.

## References

SHOWING 1-10 OF 88 REFERENCES

### Weakly nonextensive thermostatistics and the Ising model with long-range interactions

- Physics
- 2000

Abstract:We introduce a new nonextensive entropic measure that grows like , where N is the size of the system under consideration. This kind of nonextensivity arises in a natural way in some N-body…

### Fingerprints of nonextensive thermodynamics in a long-range Hamiltonian system

- PhysicsPhysica A: Statistical Mechanics and its Applications
- 2002

### Nonadditive entropy reconciles the area law in quantum systems with classical thermodynamics.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2008

It is shown, for d=1,2 , that the (nonadditive) entropy Sq satisfies the classical thermodynamical prescription for the entropy to be extensive, i.e., Sq proportional variant Ld, and the system critical features are marked by a maximum of the special entropic index q.

### The Nonadditive Entropy Sq and Its Applications in Physics and Elsewhere: Some Remarks

- PhysicsEntropy
- 2011

The nonadditive entropy Sq has been introduced in 1988 focusing on a generalization of Boltzmann–Gibbs (BG) statistical mechanics, and some relevant aspects of this entropy are reviewed and commented on.

### Thermodynamic description of the relaxation of two-dimensional turbulence using Tsallis statistics.

- PhysicsPhysical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
- 1996

Observations make possible the construction of a comprehensive thermodynamic description of two-dimensional turbulence, and the maximization of the generalized entropy with $q=\frac{1}{2}$ for the pure-electron plasma column leads to precisely the same profiles predicted by the restricted minimum enstrophy theory.