Thermodynamics of the self-gravitating ring model

Abstract : We present the phase diagram, in both the microcanonical and the canonical ensemble, of the Self-Gravitating-Ring (SGR) model, which describes the motion of equal point masses constrained on a ring and subject to 3D gravitational attraction. If the interaction is regularized at short distances by the introduction of a softening parameter, a global entropy maximum always exists, and thermodynamics is well defined in the mean-field limit. However, ensembles are not equivalent and a phase of negative specific heat in the microcanonical ensemble appears in a wide intermediate energy region, if the softening parameter is small enough. The phase transition changes from second to first order at a tricritical point, whose location is not the same in the two ensembles. All these features make of the SGR model the best prototype of a self-gravitating system in one dimension. In order to obtain the stable stationary mass distribution, we apply a new iterative method, inspired by a previous one used in 2D turbulence, which ensures entropy increase and, hence, convergence towards an equilibrium state.
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Contributor : Thierry Dauxois <>
Submitted on : Tuesday, October 16, 2007 - 9:54:06 PM
Last modification on : Wednesday, August 21, 2019 - 9:02:02 PM

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Takayuki Tatekawa, Freddy Bouchet, Thierry Dauxois, Stefano Ruffo. Thermodynamics of the self-gravitating ring model. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, American Physical Society, 2005, 71 (5), pp.056111. ⟨ensl-00179879⟩

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