Remarks about the thermodynamic limit in selfgravitating systems

Details Remarks about the thermodynamic limit in selfgravitating systems Remarks about the thermodynamic limit in selfgravitating systems

2003-09-15

arxiv.org/abs/astro-ph/0309386v1

Astronomy and Astrophysics

Astrophysics

RevTex 4, 4 pages. Comments about the de Vega and Sanchez discussion with V. Laliena about the applicability of the diluted li

Scientific paper

The present effort addresses the question about the existence of a well-defined thermodynamic limit for the astrophysical systems with the following power law form: to tend the number of particles, N, the total energy, E, and the characteristic linear dimension of the system, L, to infinity, keeping constant E/N^{\Lambda_{E}} and L/N^{\Lambda_{L}}, being \Lambda_{E} and \Lambda_{L} certain scaling exponent constant. This study is carried out for a system constituted by a non-rotating fluid under the influence of its own Newtonian gravitational interaction. The analysis yields that a thermodynamic limit of the above form will only appear when the local pressure depends on the energy density of fluid as $p=\gamma\epsilon$, being $\gamma$ certain constant. Therefore, a thermodynamic limit with a power law form can be only satisfied by a reduced set of models, such as the selfgravitating gas of fermions and the Antonov isothermal model.

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