The Renormalization Group , Entropy , Thermodynamic Phase Transitions and Order in Quantum Field Theory

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 entropy–ordered states. It is shown how the known heavier quarks can be thus described.