Kinetic equation of finite Hamiltonian systems with integrable mean field

2014 In this paper, we propose a kinetic theory of finite systems, and a new equation for their « microscopic » average behaviour. The equations of particle motion are supposed to be integrable in the mean collective field or/and in an outside given field. The collision time is assumed to be longer than the characteristic orbital time which rules out a local theory of the Fokker-Planck, or Balescu-Lenard type. Two applications of our equation are foreseen : a finite plasma with a Debye length comparable or larger than its size ; a self confined gravitational system (i.e. a globular cluster) which is always a dilute system with a finite number of stars ; we discuss the validity of a statistical description of such a physical system. J. Physique 48 (1987) 591-599 AVRIL 1987, Classification Physics Abstracts 51.10 98.20