Thermodynamics of a two-dimensionnal unbounded self-gravitating system

Jérôme Perez and Jean-Jacques Aly
june, 1999
Publication type:
Paper in peer-reviewed journals
Physical Review E, vol. 60, pp. 5185
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.
    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 },
    volume={60 },