2002/07/31 by P. H. Chavanis, Pierre-Henri Chavanis · 3 citations
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Canonical ensemble #Classical mechanics #Cosmology and Gravitation Theories #Gravitation #Gravitational collapse #Instability #Isobaric process #Isothermal process #Mathematics #Mechanics #Monte Carlo method #Physics #Polytropic process #SPHERES #Statistical Mechanics and Entropy #Statistical physics #Theoretical physics #Thermodynamics #astro-ph
paper · pdf · doi:10.1051/0004-6361:20021779
published as Astron.Astrophys. 401 (2003) 15 · Submitted to A&A
openalex publication_date 2003/03/17 · arxiv created 2003/05/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We complete previous investigations on the thermodynamics of self-gravitating systems by studying the grand canonical, grand microcanonical and isobaric ensembles. We also discuss the stability of polytropic spheres in connexion with a generalized thermodynamical approach proposed by Tsallis. We determine in each case the onset of gravitational instability by analytical methods and graphical constructions in the Milne plane. We also discuss the relation between dynamical and thermodynamical stability of stellar systems and gaseous spheres. Our study provides an aesthetic and simple approach to this otherwise complicated subject.