# Thermodynamics of a two-dimensionnal unbounded self-gravitating system

june, 1999

Publication type:

Paper in peer-reviewed journals

Journal:

Physical Review E, vol. 60, pp. 5185

HAL:

Abstract:

The thermodynamics of a two-dimensional self-gravitating system occupying the whole plane is considered in the mean-field approximation. First, it is proven that, if the number N of particles and the total energy E are imposed as the only external constraints, then the entropy admits the least upper bound S+(N,E)=2E/N+N ln(eπ2) (in appropriate units). Moreover, there does exist a unique state of maximum entropy, which is characterized by a Maxwellian distribution function with a temperature T=N/2 independent of E. Next, it is shown that, if the total angular momentum J is imposed as a further constraint, the largest possible value of the entropy does not change, and there is no admissible state of maximum entropy, but in the case J=0. Finally, some inequalities satisfied by a class of so-called H functions and related generalized entropies are given.

BibTeX:

@article{Per-Aly-1999, author={Jérôme Perez and Jean-Jacques Aly }, title={Thermodynamics of a two-dimensionnal unbounded self-gravitating system }, doi={10.1103/PhysRevE.60.5185 }, journal={Physical Review E }, year={1999 }, month={6}, volume={60 }, pages={5185}, }