FIZIKA B 16 (2007) 1, 17  38
ENTROPY OF COLORED QUARKS STATES AT FINITE TEMPERATURE
DAVID E. MILLER^{a,b} and ABDELNASSER TAWFIK^{a}
^{a}Fakultät für Physik, Universität Bielefeld, D33501 Bielefeld,
Germany
Email addresses: om0@psu.edu, dmiller@physik.unibielefeld.de
^{b}Department of Physics, Pennsylvania State University, Hazleton, PA
18201, USA
Email address:
tawfik@physik.unibielefeld.de
Received 23 March 2006; Accepted 20 September 2006
Online 22 May 2007
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}.
PACS numbers: 12.39.x, 24.85.+p, 05.50.+q
UDC 539.125, 536.75
Keywords: hadrons, colored quarks, quantum entropy, SU(2)_{c}
and SU(3)_{c}, singlet states, octet states, Ising and quantum XY spin
chains
