Skip to Main content Skip to Navigation
New interface
Journal articles

Thermodynamics of a two-dimensionnal unbounded self-gravitating system

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.
Document type :
Journal articles
Complete list of metadata
Contributor : Aurélien Arnoux Connect in order to contact the contributor
Submitted on : Friday, June 20, 2014 - 1:24:16 PM
Last modification on : Wednesday, May 11, 2022 - 12:06:05 PM




Jérôme Perez, Jean-Jacques Aly. Thermodynamics of a two-dimensionnal unbounded self-gravitating system. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 1999, 60, pp.5185. ⟨10.1103/PhysRevE.60.5185⟩. ⟨hal-01010745⟩



Record views