Systems with long-range interactions are characterized by a pair potential which decays at large distances as a power law, with an exponent smaller than the space dimension. Examples are gravitational and Coulomb interactions. The thermodynamic and dynamical properties of such systems were poorly understood until a few decades ago. Substantial progress has been made only recently, when it was realized that the lack of additivity induced by long-range interactions does not hinder the development of a fully consistent thermodynamic formalism.
This has, however, important consequences : entropy is no more a convex function of macroscopic extensive parmeters and the set of accessible macroscopic states does not form a convex region in the space of thermodynamic parameters. This is at the origin of ensemble inequivalence, which in turn determines curious thermodynamic properties such as negative specific heat in the microcanonical ensemble. On the other hand, it has been recognized that systems with long-range interactions display universal nonequilibrium features. In particular, long-lived metastable states, also called quasi-stationary states (QSS) may develop, in which the system remains trapped for a long time before relaxing towards thermodynamic equilibrium. Historically, it was with the work of Emden and Chandrasekhar, in the context of astrophysics, that it was realized that, for systems with long-range interactions, the thermodynamic equilibrium itself could not exist. The appearance and meaning of negative temperature was first discussed in a seminal paper by Onsager on point vortices interacting via a long-range logarithmic potential in two-dimensions.
M. Joyce, J. Morand, F. Sicard and P. Viot*, Scaling quasi-stationary states in long-range systems with dissipation, Phys. Rev. Lett., 112, 070602 (2014)
F. Sicard*, Out-of-equilibrium dynamics in infinite one-dimensional self-gravitating systems, Ph.D. Thesis, University Pierre & Marie Curie (2010)
A. Gabrielli, M. Joyce*, B. Marcos and F. Sicard, A dynamical classification of the range of pair interactions, J. Stat. Phys., 141, 970 (2010)
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