Narrow Results

Here we reanalyze various quasiparticle models of quark gluon plasma from the statistical mechanics and thermodynamics point of view. We investigate the statistical mechanics and thermodynamics inconsistencies involved in these models and their consequences in the observables. Quasiparticle models are phenomenological models with few parameters and by adjusting them all models fit the results of lattice gauge simulation of gluon plasma [G. Boyd et al., Phys. Rev. Lett.75, 4169 (1995); G. Boyd et al., Nucl. Phys. B469, 419 (1996)]. However, after fixing two of the three parameters of the model by physical arguments, only one quasiparticle model, which is consistent with both statistical mechanics and thermodynamics, fits the Bielefeld lattice data [G. Boyd et al., Phys. Rev. Lett.75, 4169 (1995); G. Boyd et al., Nucl. Phys. B469, 419 (1996)]. The same model also fits the recent lattice results of Wuppertal–Budapest group [S. Borsanyi et al., arXiv:1204.6184v1 [hep-lat]], which deals with precision SU(3) thermodynamics for a large temperature range, reasonably well.

Landau's formalism of statistical mechanics [following L. D. Landau and E. M. Lifshitz, Statistical Physics (Pergamon Press, Oxford, 1980)] is applied to the quasi-particle model of quark–gluon plasma. Here, one starts from the expression for pressure and develop all thermodynamics. It is a general formalism and consistent with our earlier studies [V. M. Bannur, Phys. Lett. B647, 271 (2007)] based on Pathria's formalism [following R. K. Pathria, Statistical Mechanics (Butterworth-Heinemann, Oxford, 1977)]. In Pathria's formalism, one starts from the expression for energy density and develop thermodynamics. Both the formalisms are consistent with thermodynamics and statistical mechanics. Under certain conditions, which are wrongly called thermodynamic consistent relation, we recover other formalism of quasi-particle system, like in M. I. Gorenstein and S. N. Yang, Phys. Rev. D52, 5206 (1995), widely studied in quark–gluon plasma.