  We consider the fundamental problem of high temperature phase transitions in
the system of high density two-level atoms off-resonantly interacting with a
pump field in the presence of optical collisions (OCs) and placed in the
cavity. OCs are considered in the framework of thermalization of atomic dressed
state (DS) population. For the case of a strong atom-field coupling condition
we analyze the problem of thermodynamically equilibrium superradiant phase
transition for the order parameter representing a real amplitude of cavity mode
and taking place as a result of atomic DSs thermalization process. Such
transition is also connected with condensed (coherent) properties of low branch
(LB) DS-polaritons occurring in the cavity. For describing non-equilibrium
phase transitions we derive Maxwell-Bloch like equations which account for
cavity decay rate, collisional decay rate and spontaneous emission. Various
aspects of transitions to laser field formation by using atomic DS levels for
both positive and negative detuning of a pump field from atomic transition
frequency are studied in detail. It is revealed, that for positive atom-light
detuning DS lasing can be obtained in the presence of quasi-equilibrium DS
population that corresponds to a true two-level atomic system with the
inversion in nonresonant limit.
