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

TL;DR

This paper introduces a new entropy concept for quantum field theories, revealing phase transitions and entropy behavior differences between asymptotically free and non-free regimes, and explaining the formation of stable entropy-ordered states.

Contribution

It defines a novel entropy for quantum field theories and analyzes its behavior across different regimes, uncovering phase transitions and stable entropy-ordered states.

Findings

Transition between regimes is a continuous phase transition.

Existence of negative temperature regimes in asymptotically free theories.

Formation of stable entropy-ordered states in quantum fields.

Abstract

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.