Skip to Main content Skip to Navigation
Journal articles

Statistical mechanics of self-gravitating systems: Mixing as a criterion for indistinguishability

Abstract : 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.
Document type :
Journal articles
Complete list of metadatas

Cited literature [16 references]  Display  Hide  Download
Contributor : Jérôme Perez <>
Submitted on : Sunday, April 12, 2015 - 11:22:21 AM
Last modification on : Sunday, November 1, 2020 - 11:06:01 AM
Long-term archiving on: : Tuesday, April 18, 2017 - 4:44:13 PM


Phys. Rev. D 90, 123004, 2014....
Files produced by the author(s)




Leandro Beraldo, Marcos Lima, Laerte Sodré, Jérôme Perez. Statistical mechanics of self-gravitating systems: Mixing as a criterion for indistinguishability. Physical Review D, American Physical Society, 2014, 90 (12), pp.123004. ⟨10.1103/PhysRevD.90.123004⟩. ⟨hal-01141375⟩



Record views


Files downloads