ABSTRACT
This chapter presents the statistical equilibrium states of single-wave–particle system. Indeed these states are generally considered as representative of the typical states of the many-body system and, as such, as typical of the asymptotic states to which the system evolves. The natural ensemble for a self-consistent model of interacting waves and particles is Gibbs’ microcanonical ensemble. While the physical motivation for the microcanonical ensemble was that the microscopic state of the system would visit over a ‘reasonably short’ time lapse a ‘reasonably large’ part of phase space, the physical motivation for describing a system by the canonical ensemble is that it can exchange energy with its surroundings. The thermodynamic treatment of the binary interaction assumes that all particles reach a ‘global’ equilibrium, whereas the thermodynamic treatment of the wave–particle system applies to a reduced system, in which only the faster, more efficient interactions are taken into account.
