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Related Experiment Video

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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

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Published on: December 4, 2017

Relativity, nonextensivity, and extended power law distributions.

R Silva¹, J A S Lima

¹Observatório Nacional, Rua Gal. José Cristino 77, 20921-400 Rio de Janeiro, Rio de Janeiro, Brazil and Universidade do Estado do Rio Grande do Norte, 59610-210, Mossoró, RN, Brazil.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|December 31, 2005

Summary

This study proves a relativistic theorem incorporating nonextensive effects, showing Boltzmann's molecular chaos hypothesis is invalid. Relativistic nonextensive equilibrium states are described by a power law distribution, harmonizing with special relativity.

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Area of Science:

Relativistic statistical mechanics
Nonextensive thermodynamics

Background:

Boltzmann's molecular chaos hypothesis is a cornerstone of classical statistical mechanics.
The Juttner distribution describes relativistic Maxwell-Boltzmann statistics.

Purpose of the Study:

To prove a relativistic theorem by incorporating nonextensive effects.
To investigate the validity of the molecular chaos hypothesis in a relativistic nonextensive framework.
To derive the equilibrium distribution for a relativistic nonextensive system.

Main Methods:

Inclusion of nonextensive effects into relativistic statistical mechanics.
Application of the second law of thermodynamics and duality transformation.
Derivation of relativistic nonextensive equilibrium distribution.

Main Results:

The molecular chaos hypothesis is shown to be invalid in the relativistic nonextensive limit.
The parameter characterizing nonextensivity is constrained to the interval [0,2].
Collisional equilibrium states are described by a relativistic power law extension of the Juttner distribution, reducing to the Tsallis power law in the nonrelativistic limit.

Conclusions:

The nonextensive entropic framework is compatible with special relativity.
The derived relativistic nonextensive equilibrium distribution generalizes standard results.