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Exact relations for thermodynamics of heavy quarks

Abstract

We derive finite-temperature sum rules for excesses in internal energy and in (volume-integrated) pressure arising due to presence of heavy quarks in SU(N) gluon plasma. In the limit of zero temperature our formulae reduce to the Michael-Rothe sum rules. The excesses in energy and pressure of the gluon plasma are related to expectation values of certain gluon condensates, and, simultaneously, to the heavy quark potential. The sum rules lead to a known relation between the internal energy and the potential, and to a new expression for the excess in the pressure. The pressure appears in the free energy as a generalized force associated with variations of the spatial size of the heavy-quark system. We find that the excess in gluonic pressure around a heavy quarkonium is always negative. Finally, we derive an exact equation of state that provides a relationship between the gluonic energy and pressure of heavy quarks.Comment: 7 page

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