%0 Journal Article
%T Thermodynamics of a two-dimensionnal unbounded self-gravitating system
%+ Optimisation et commande (OC)
%A Perez, Jérôme
%A Aly, Jean-Jacques
%< avec comité de lecture
%@ 1539-3755
%J Physical Review E : Statistical, Nonlinear, and Soft Matter Physics
%I American Physical Society
%V 60
%P 5185
%8 1999-06
%D 1999
%R 10.1103/PhysRevE.60.5185Journal articles
%X 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.
%G English
%L hal-01010745
%U https://hal-ensta-paris.archives-ouvertes.fr/hal-01010745
%~ ENSTA
%~ UMA_ENSTA