  We have obtained an exact expression for the phase-space volume corresponding
to a microcanonical ensemble of systems under center of mass, total linear and
angular momenta conservation constraints, and arbitrary constraints on the
coordinates of particles of the system. Methods are suggested to calculate the
phase-space volume and density of states from the mean kinetic energy and mean
inverse kinetic energy. Methods to control equilibrium in simulations are also
presented. We have derived exact formulae for several thermodynamic response
functions. It is shown how to obtain the phase-space volume corresponding to
other ensembles when one or several of the constraints are removed. It is shown
that the phase-space volume of a system at positive values of the energy is a
polynomial function of the energy if the potential energy of interaction
between particles of the system consists of a hard-core potential and an
arbitrary negative potential. We have also shown that the coefficients of the
polynomial function can be determined from simulations.
