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TwitterA&A 432, 117-138 (2005)
DOI: 10.1051/0004-6361:20041114
On the lifetime of metastable states in self-gravitating systems
P. H. ChavanisLaboratoire 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)
Abstract
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 2002b, [arXiv:astroph/0205426]; Chavanis & Rieutord 2003, 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