Statistical mechanics of systems subject to constraints

The statistical mechanics of systems subject to constraints is discussed. For integrable constraints Dirac's method to deal with singular lagrangeans is introduced and a hamiltonian is obtained. From this hamiltonian the phase-space Fokker-Planck equation and the diffusion equation are derived. Another derivation for the diffusion equation is proposed which makes no use of Hamilton's formalism and that may, therefore, be applied both to integrable and non-integrable constraints which preserve volume in coordinate-velocity space. The existence of a diffusion equation for non-integrable constraints and possible analogies to quantum mechanics of similar systems is discussed. (Author)