4-Velocity distribution function using Maxwell-Boltzmann's original approach and a new form of the relativistic equation of state

2011/03/16 by Prasad Basu, Basu, Prasad, Soumen Mondal +1
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #Quantum Mechanics and Non-Hermitian Physics #Solar and Stellar Astrophysics (astro-ph.SR) #Statistical Mechanics and Entropy #astro-ph.SR

paper · pdf · doi:10.48550/arxiv.1103.3330

4pages including 3figures

openalex publication_date 2011/03/16 · arxiv created 2011/03/17 · arxiv updated 2015/03/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Following the original approach of Maxwell-Boltzmann(MB), we derive a 4-velocity distribution function for the relativistic ideal gas. This distribution function perfectly reduces to original MB distribution in the non-relativistic limit. We express the relativistic equation of state(EOS), ρ-ρ₀=(γ-1)^-1p, in the two equations: ρ=ρ₀ f(λ), and p=ρ₀ g(λ), where λ is a parameter related to the kinetic energy, hence the temperature, of the gas. In the both extreme limits, they give correct EOS: ρ=3p in the ultra-relativistic, and ρ-ρ₀=3/2p in the non-relativistic regime. Using these equations the adiabatic index γ (=(c_p)/(c_v)) and the sound speed a_s are calculated as a function of λ. They also satisfy the inequalities: 4/3 ≤ γ≤ 5/3 and a_s ≤ (1)/(√(3)) perfectly.

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