Dynamical and thermodynamical stability of isothermal distributions in the HMF model

2010/07/28 by Pierre-Henri Chavanis, Chavanis, Pierre-Henri
Environmental Science · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Climate variability and models #FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech) #Statistical Mechanics and Entropy #cond-mat.stat-mech

paper · pdf · doi:10.48550/arxiv.1007.4916

arxiv created 2010/07/28 · openalex publication_date 2010/07/28 · arxiv updated 2010/07/29 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28

Abstract

We provide a new derivation of the conditions of dynamical and thermodynamical stability of homogeneous and inhomogeneous isothermal distributions in the Hamiltonian Mean Field (HMF) model. This proof completes the original thermodynamical approach of Inagaki [Prog. Theor. Phys. 90, 557 (1993)]. Our formalism, based on variational principles, is simple and the method can be applied to more general situations. For example, it can be used to settle the dynamical stability of polytropic distributions with respect to the Vlasov equation [Chavanis & Campa, arXiv:1001.2109]. For isothermal distributions, the calculations can be performed fully analytically, providing therefore a clear illustration of the method.

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