Hamiltonian and Brownian systems with long-range interactions: I Statistical equilibrium states and correlation functions

Pierre-Henri Chavanis

Physica A: Statistical Mechanics and its Applications, 2006, vol. 361, issue 1, 55-80

Abstract: We discuss the equilibrium statistical mechanics of systems with long-range interactions. We contrast the microcanonical description of an isolated Hamiltonian system from the canonical description of a stochastically forced Brownian system. We show that the mean-field approximation is exact in a proper thermodynamic limit N→+∞. The one-point equilibrium distribution function is solution of an integrodifferential equation obtained from a static BBGKY-like hierarchy. It also optimizes a thermodynamical potential (entropy or free energy) under appropriate constraints. In the case of attractive potentials of interaction, we show the existence of a critical temperature Tc separating a homogeneous phase (T⩾Tc) from a clustered phase (T⩽Tc). The homogeneous phase becomes unstable for TKeywords: Long-range interactions; Mean-field theory; Hamiltonian systems; Brownian systems (search for similar items in EconPapers)
Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:361:y:2006:i:1:p:55-80

DOI: 10.1016/j.physa.2005.06.087

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