Statistical mechanics of violent relaxation

Journal Article · Sun Oct 01 00:00:00 EDT 1978 · Astrophys. J.; (United States)

DOI:https://doi.org/10.1086/156470· OSTI ID:6585430

Shu, F H

We reexamine the foundations of Lynden-Bell's statistical mechanical discussion of violent relaxation in collisionless stellar systems. We argue that Lynden-Bell's formulation in terms of a continuum description introduces unnecessary complications, and we consider a more conventional formulation in terms of particles. We then find the exclusion principle discovered by Lynden-Bell to be quantitatively important only at phase densities where two-body encounters are no longer negligible. Since the edynamical basis for the exclusion principle vanishes in such cases anyway, Lynden-Bell statistics always reduces in practice to Maxwell-Boltzmann statistics when applied to stellar systems. Lynden-Bell also found the equilibrium distribution function generally to be a sum of Maxwellians with velocity dispersions dependent on the phase density at star formation. We show that this difficulty vanishes in the particulate description for an encounterless stellar system as long as stars of different masses are initially well mixed in phase space. Our methods also demonstrate the equivalence between Gibbs's formalism which uses the microcanonical ensemble and Boltzmann's formalism which uses a coarse-grained continuum description. In addition, we clarify the concept of irreversible behavior on a macroscopic scale for an encounterless stellar system. Finally, we comment on the use of unusual macroscopic constraints to simulate the effects of incomplete relaxation.

• Research Organization: Astronomy Department, University of California at Berkeley
• OSTI ID: 6585430
• Journal Information: Astrophys. J.; (United States), Vol. 225:1
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
STARS
STATISTICAL MECHANICS
BOLTZMANN STATISTICS
ENTROPY
GRAVITATIONAL FIELDS
LIOUVILLE THEOREM
STAR CLUSTERS
STATISTICAL MODELS
MATHEMATICAL MODELS
MECHANICS
PHYSICAL PROPERTIES
THERMODYNAMIC PROPERTIES
640102* - Astrophysics & Cosmology- Stars & Quasi-Stellar
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