Physics – Condensed Matter – Statistical Mechanics
Scientific paper
May 1987
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1987apj...316..497m&link_type=abstract
Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 316, May 15, 1987, p. 497-501. Research supported by the Statens Naturviden
Physics
Condensed Matter
Statistical Mechanics
16
Galactic Evolution, Gravitational Collapse, Statistical Mechanics, Stellar Motions, Computational Astrophysics, Dark Matter, Liouville Theorem, Relaxation (Mechanics)
Scientific paper
Fundamental problems for statistical mechanical theories of violent relaxation that raise doubts about their applicability are examined. Shu's particle approach predicts a most probable final state that may not be accessible from the initial state, since access would require a violation of Liouville's theorem. Furthermore, it is not clear how to treat the initial shuffling in phase space of different types of particles properly in the particle approach. Lynden-Bell's phase-element approach incorporates Liouville's theorem and takes account of initial shuffling, but overestimates the fine-grained phase-space density of stars by many orders of magnitude (this problem can be cirumvented). Both theories lead in the nondegenerate limit to infinite mass isothermal spheres, which is inconsistent with the assumed finite mass of the initial state. A time-scale problem also remains in both theories.
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