  We define an entropy for a quantum field theory by combining quantum
fluctuations, scaling and the maximum entropy concept. This entropy has
different behavior in asymptotically free and non--asymptotically free
theories. We find that the transition between the two regimes (from the
asymptotically free to the non--asymptotically free) takes place via a
continuous phase transition. For asymptotically free theories there exist
regimes where the ``temperatures" are negative. In asymptotically free theories
there exist maser--like states mostly in the infrared; furthermore, as one goes
into the ultraviolet and more matter states contribute to quantum processes,
the quantum field system can shed entropy and cause the formation of
thermodynamically stable {\it entropy--ordered} states. It is shown how the
known heavier quarks can be thus described.
