Thermodynamics of the Hagedorn mass spectrum

No bootstrap assumption is needed to derive the exponential growth of the Hagedorn hadron mass spectrum: it is a consequence of the second law applied to a relativistic gas, and the assumption that as energy and number of particles of an ideal gas increase without limit their ratio tends to a constant, finite, limiting temperature. A non-interacting mixture of two ideal gases is involved in which there is an analogy between a droplet and surrounding vapor. As the limiting temperature is approached the droplet pressure becomes infinite causing the droplet to burst. There is no second-order phase transition from hadronic to a quark-gluon plasma, at least for the Hagedorn mass distribution where all prefactors must admit a Laplace transform