General, combinatorial formula for the density of states: insights into the energy equipartition principle and the theory of phase transitions

A completely new approach to the problem of energy distribution in statistical mechanics is developed that results in a general, combinatorial formula for the density of states. Relying on the approach the energy equipartition principle is reexamined and a new perspective on the theory of phase transitions (as resulting from nontrivial patterns of energy distribution characterized by the well-defined classes of forbidden microstates) is given.