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Statistical mechanics in the context of special relativity. II
1Dipartimento di Fisica, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy. giorgio.kaniadakis@polito.it
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 26, 2005
Summary
Special relativity generalizes classical physics using light speed. This study introduces a relativistic entropy, creating a consistent statistical theory that aligns with experimental power-law distributions.
Area of Science:
- Theoretical Physics
- Statistical Mechanics
- Relativistic Physics
Background:
- Classical physics laws are generalized by special relativity.
- Lorentz transformations impact physical observables and theoretical frameworks.
- The Boltzmann-Gibbs-Shannon entropy is a cornerstone of classical statistical mechanics.
Purpose of the Study:
- To introduce a one-parameter generalization of Boltzmann-Gibbs-Shannon entropy based on Lorentz transformations.
- To develop a self-consistent relativistic statistical theory.
- To derive a relativistic distribution function and explore its properties.
Main Methods:
- Generalizing classical statistical mechanics using principles of special relativity.
- Applying Lorentz transformations to derive a relativistic entropy.
- Constructing a relativistic distribution function and a generalized kinetic theory.
Main Results:
- A novel relativistic entropy is derived, generalizing the Boltzmann-Gibbs-Shannon entropy.
- A coherent relativistic statistical theory is established, consistent with classical statistical theory in the limit.
- The derived distribution function exhibits power-law tails, matching experimental observations.
Conclusions:
- The developed relativistic statistical mechanics provides a consistent framework for high-energy physics.
- The theory recovers classical statistical mechanics in the non-relativistic limit.
- The findings support the application of this framework to systems exhibiting power-law behavior.
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