The Hagedorn temperature and partition thermodynamics
Fakultät für Physik, Universität Bielefeld, Postfach 100 131, 33501, Bielefeld, Germany
2 Centro de Física das Interacções Fundamentais (CFIF) Instituto Superior Técnico, Av. Rovisco Pais, 1049-001, Lisbon, Portugal
We review the resonance gas formalism of hadron thermodynamics and recall that an exponential increase of the resonance spectrum leads to a limiting temperature of hadronic matter. We then show that the number p(n) of ordered partitions of an integer n grows exponentially with n and satisfies the integer counterpart of the statistical bootstrap equation. Considering the set of all partitions as a Gibbs ensemble provides a partition thermodynamics which is also governed by a limiting temperature, determined by the combinatorial structure of the problem. Further associating intrinsic quantum numbers to integers results in a phase diagram equivalent to that found in QCD for hadronic matter as a function of temperature and baryochemical potential.
© Springer-Verlag, 2004