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The Statistical Bootstrap Model and the related concept of the limiting temperature began the discussion about phase transitions in the hadronic matter. This was also the origin of the quark-gluon plasma concept. We discuss here to which extent lattice studies of QCD critical behavior at non-zero chemical potential are compatible with the statistical bootstrap model calculations.

A brief history of the observation of the onset of deconfinement—the beginning of the creation of quark-gluon plasma in nucleus–nucleus collisions with increasing collision energy—is presented. It starts with the measurement of the hadron mass spectrum and Hagedorn’s hypothesis of the limiting temperature of hadronic matter (the Hagedorn temperature). Then the conjecture that the Hagedorn temperature is the phase transition temperature was formulated with the crucial Hagedorn participation. It was confirmed by the observation of the onset of deconfinement in lead–lead collisions at the CERN SPS energies.

LBL has been the cradle where relativistic heavy ion physics began, and where the Hagedorn Statistical Model was first connected to relativistic heavy ion physics. The early program of research at the Bevalac and its development into an international program at CERN, paying tribute to the seminal effort by Howel Pugh, is described.

My appreciation of Rolf Hagedorn motivates me to look back at my more than 40 years of trial and error in relativistic heavy ion physics. More than once, wise colleagues helped me move forward to new and better understandings. Rolf Hagedorn was one of these important people. At first, I met him anonymously in the mid 1970s when reading his 1971 Cargèse Lectures in Physics, and later in person for many years in and around CERN. I wonder what this modest person would say about his impact on physics in this millennium. As he is not here to answer, I and others give our answers in this book. I focus my report on the beginning of the research program with relativistic heavy ions, the move to CERN-SPS and the development of the heavy ion collaboration at the CERN-LHC.

I retrace the developments from Hagedorn’s concept of a limiting temperature for hadronic matter to the discovery and characterization of the quark-gluon plasma as a new state of matter. My recollections begin with the transformation more than 30 years ago of Hagedorn’s original concept into its modern interpretation as the “critical” temperature separating the hadron gas and quark-gluon plasma phases of strongly interacting matter. This was followed by the realization that the QCD phase transformation could be studied experimentally in high-energy nuclear collisions. I describe here my personal effort to help develop the strangeness experimental signatures of quark and gluon deconfinement and recall how the experimental program proceeded soon to investigate this idea, at first at the SPS, then at RHIC, and finally at LHC. As is often the case, the experiment finds more than theory predicts, and I highlight the discovery of the “perfectly” liquid quark-gluon plasma at RHIC. I conclude with an outline of future opportunities, especially the search for a critical point in the QCD phase diagram.

This is a personal recollection of the influence that Rolf Hagedorn had on the launch of the CERN heavy-ion program and on the physics choices made by my colleagues and myself in that context.

This introductory article presents in popular language how the view of the early Universe was evolving through 1968 under the influence of than new and recent insights about the thermodynamic properties of strongly interacting matter (by JR, editor).

I describe the long way from the first theoretical ideas about multiple particle production up to the situation in which constructing of a statistical model of strong interactions seemed natural. I begin in 1936, and argue that the statistical method came to be from a large network of observations and theoretical ideas. I shall pick up only a few primary lines, chosen for their common end point: the statistical bootstrap model of 1964/65.

I present the context in which Hagedorn withdrew his first work on limiting temperature, show his withdrawal note, and discuss what was lost from view for 50 years while the manuscript shown in Chap.  lingered in the archives. I close describing the contemporary meaning of Hagedorn temperature.

A new kind of thermodynamical model for strong interactions at high energies is proposed. We start from the fact that strong interactions produce so many possible particle states (from over its resonances to nucleons, strange particles and their resonances, up to highly excited ‘fireballs’) that in an actual process each of these states practically never occurs more than once. We use this in order to treat the very first instant of a high-energy collision by statistical thermodynamics of a system of an illimited number of distinguishable particles. The model shows surprising properties: there exists a universal highest possible temperature of the order of 150–200 MeV (corresponding to ≈ 10 K) which governs all high-energy processes of strongly interacting particles, independently of the actual energy and independently of the particle number, from cosmic ray jets down to elastic scattering. If a Lorentz contracted volume is introduced, the transverse momentum distribution in jets as well as in elastic scattering is described in agreement with experimental results. Paradoxically, this distribution is independent of whether or not ‘thermal equilibrium’ is reached. If it is not reached—in the majority of cases it is not reached—then the jet structure for production processes is the consequence. If the model turns out to be as good as present experiments indicated, then the existence of a highest temperature is very likely; it implies that, from higher and higher energy experiments, not much new can be learnt about the structure of strong interactions, since the mode of excitation (which depends on the dynamical details we would like to know) has no influence on what is finally observed. The situation would then be similar to that in ordinary thermodynamics, where no experiment could possibly reveal how a certain system was brought into its thermodynamical state. In astrophysics, the method of thermodynamics of distinguishable particles may have important consequences for the treatment of the highly compressed interior of heavy stars (‘neutron stars’) where Fermi statistics would have to be replaced by the one used here.