Conservation of Fractional Mean Energy in Dissipative Gases

2022/10/11 by Keisuke Fujii, Fujii, Keisuke
Engineering · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Cosmology and Gravitation Theories #FOS: Physical sciences #Phase Equilibria and Thermodynamics #Plasma Physics (physics.plasm-ph) #Statistical Mechanics (cond-mat.stat-mech)

paper · pdf · doi:10.48550/arxiv.2210.06193

openalex publication_date 2022/10/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

I show a nontrivial functional giving a conservation quantity in the collisional energy cascade of dissipative Maxwell gases: a fractional-calculus extension of the mean energy. The conservation of this quantity directly leads the power-law energy tail that is stationary during the temporal evolution. In the thermal limit, this quantity naturally reduces to the standard mean energy. This conservation law and its extension to particles with other interactions are demonstrated with a Monte-Carlo simulation for inelastic gases.

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