Statistical Mechanics of Unbound Two Dimensional Self-Gravitating Systems

We study, using both theory and molecular dynamics simulations, the relaxation dynamics of a microcanonical two dimensional self-gravitating system. After a sufficiently large time, a gravitational cluster of N particles relaxes to the Maxwell-Boltzmann distribution. The time to reach the thermodyna...

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Bibliographic Details
Published in:arXiv.org 2010-04
Main Authors: Teles, Tarcísio N, Levin, Yan, Pakter, Renato, Rizzato, Felipe B
Format: Article
Language:English
Subjects:
Boltzmann distribution
Gravitation
Mathematical analysis
Molecular dynamics
Statistical mechanics
Thermodynamic equilibrium
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Summary:We study, using both theory and molecular dynamics simulations, the relaxation dynamics of a microcanonical two dimensional self-gravitating system. After a sufficiently large time, a gravitational cluster of N particles relaxes to the Maxwell-Boltzmann distribution. The time to reach the thermodynamic equilibrium, however, scales with the number of particles. In the thermodynamic limit, \(N\to\infty\) at fixed total mass, equilibrium state is never reached and the system becomes trapped in a non-ergodic stationary state. An analytical theory is presented which allows us to quantitatively described this final stationary state, without any adjustable parameters.
ISSN:2331-8422
DOI:10.48550/arxiv.1004.0247