Statistical mechanics of confined systems with rotational excitations

New experimental and numerical investigations of confined systems of particles demonstrate the existence of rotational excitations. We develop here a statistical theory of finite systems, including rotational modes, by introducing the angular momentum into the formalism and constructing the relevant distributions. As special applications we study systems driven to a prescribed kinetic energy by negative friction or special isokinetic thermostats. Several distribution functions which are solutions of the Liouville or Fokker–Planck equations are given. The theory is applied to Coulomb clusters confined by parabolic forces.