Issue |
A&A
Volume 432, Number 1, March II 2005
|
|
---|---|---|
Page(s) | 117 - 138 | |
Section | Galactic structure, stellar clusters, and populations | |
DOI | https://doi.org/10.1051/0004-6361:20041114 | |
Published online | 22 February 2005 |
On the lifetime of metastable states in self-gravitating systems
Laboratoire de Physique Théorique, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse, France e-mail: chavanis@irsamc.ups-tlse.fr
Received:
17
April
2004
Accepted:
3
November
2004
We discuss the physical basis of the statistical
mechanics of self-gravitating systems. We show the correspondance
between statistical mechanics methods based on the evaluation of
the density of states and partition function and thermodynamical
methods based on the optimization of a thermodynamical potential
(entropy or free energy). We address the question of the
thermodynamic limit of self-gravitating systems, the justification
of the mean-field approximation, the validity of the saddle point
approximation near the transition point, the lifetime of metastable
states and the fluctuations in isothermal spheres. In particular,
we emphasize the tremendously long lifetime of metastable states of
self-gravitating systems which increases exponentially with the
number of particles N except in the vicinity of the critical
point. More specifically, using an adaptation of the Kramers
formula justified by a kinetic theory, we show that the lifetime of
a metastable state scales as in microcanonical
ensemble and
in canonical ensemble, where
and
are the barriers of entropy and free energy
per particle respectively. The physical
caloric curve must take these metastable states (local entropy
maxima) into account. As a result, it becomes multi-valued and
leads to microcanonical phase transitions and “dinosaur's necks”
(Chavanis [CITE], [arXiv:astroph/0205426]; Chavanis & Rieutord [CITE], A&A, 412, 1). The consideration of
metastable states answers the critics raised by D.H.E. Gross
[cond-mat/0307535/0403582].
Key words: gravitation / stellar dynamics / globular clusters: general / methods: miscellaneous
© ESO, 2005
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.