2014/10/31 by Leandro Beraldo e Silva, Marcos Lima, M. Lima +3
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Boltzmann distribution #Boltzmann equation #Classical mechanics #Complex Systems and Time Series Analysis #Cosmology and Gravitation Theories #Distribution (mathematics) #Distribution function #Function (biology) #Mathematical analysis #Mathematics #Mixing (physics) #Physics #Quantum mechanics #Relaxation (psychology) #Statistical Mechanics and Entropy #Statistical mechanics #Statistical physics #astro-ph.GA #cond-mat.stat-mech
paper · pdf · doi:10.1103/physrevd.90.123004
published as PRD 90:123004 (2014) · Minor changes; Published in PRD
openalex publication_date 2014/12/03 · arxiv created 2014/12/04 · arxiv updated 2014/12/05 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We propose an association between the phase-space mixing level of a self-gravitating system and the indistinguishability of its constituents (stars or dark matter particles). This represents a refinement in the study of systems exhibiting incomplete violent relaxation. Within a combinatorial analysis similar to that of Lynden-Bell, we make use of this association to obtain a distribution function that deviates from the Maxwell-Boltzmann distribution, increasing its slope for high energies. Considering the smallness of the occupation numbers for large distances from the center of the system, we apply a correction to Stirling's approximation which increases the distribution slope also for low energies. The distribution function thus obtained presents some resemblance to the ``S'' shape of distributions associated with cuspy density profiles (as compared to the distribution function obtained from the Einasto profile), although it is not quite able to produce sharp cusps. We also argue how the association between mixing level and indistinguishability can provide a physical meaning to the assumption of particle-permutation symmetry in the N-particle distribution function, when it is used to derive the one-particle Vlasov equation, which raises doubts about the validity of this equation during violent relaxation.