The Hagedorn Temperature and Partition Thermodynamics

Abstract

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 function of temperature and baryochemical potential.

Dedicated to Rolf Hagedorn, 1919-2003. 11 pages, 3 figures. Final version accepted for publication in the European Physical Journal C

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