Entropy for Colored Quark States at Finite Temperature

Abstract

The quantum entropy at finite temperatures is analyzed by using models for colored quarks making up the physical states of the hadrons. We explicitly work out some special models for the structure of the states of SU(2) and SU(3) relating to the effects of the temperature on the quantum entropy. We show that the entropy of the singlet states monotonically decreases meaning that the mixing of these states continually diminishes with the temperature. It has been found that the structure of the octet states is more complex so that it can be best characterized by two parts. One part is very similar to that of the singlet states. The other one reflects the existence of strong correlations between two of the three color states. Furthermore, we work out the entropy for the {\it classical} Ising and the {\it quantum} XY spin chains. In Ising model the quantum (ground state) entropy does not directly enter into the canonical partition function. It also does not depend on the number of spatial dimensions, but only on the number of quantum states making up the ground state. Whereas, the XY spin chain has a finite entropy at vanishing temperature. The results from the spin models qualitatively analogous to our models for the states of SU(2) and SU(3).