Entropy of Colored Quarks States at Finite Temperature

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)c and SU(3)c related to the effects of temperature on the quantum entropy. We show that the entropy of the singlet states monotonically changes with the temperature. However, the structure of the octet states has a greater complexity which can be best characterized by two types, one of which is similar to that of the singlet states, while the other one reflects the existence of strong correlations between only two of the color states. For the sake of comparison, we work out the entropy for the classical Ising and the quantum XY spin chains. In the Ising model, the quantum entropy in the ground state does not directly enter into the 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. But the XY spin chain has a finite entropy at vanishing temperature. With the inclusion of the ground state, the results from the spin models are qualitatively similar to our models for the states of SU(2)c and SU(3)c.