Equation of State and Phase Transitions in the Nuclear and Hadronic Systems

TL;DR

This paper reviews and extends models describing the equation of state and phase transitions in nuclear and hadronic matter, emphasizing finite volume effects, surface entropy, and signals of deconfinement in high energy nuclear physics.

Contribution

It provides rigorous solutions for statistical models of phase transitions, extends these to finite volumes, and offers practical methods for analyzing freeze-out and deconfinement signals.

Findings

Finite volume effects influence phase transition properties.

Bounds for surface entropy of physical clusters were calculated.

Inclusion of heavy quark-gluon bag widths improves statistical descriptions.

Abstract

An investigation of strongly interacting matter equation of state remains one of the major tasks of modern high energy nuclear physics for almost a quarter of century. The present work is my doctor of science thesis which contains my contribution (42 works) to this field made between 1993 and 2008. Inhere I mainly discuss the common physical and mathematical features of several exactly solvable statistical models which describe the nuclear liquid-gas phase transition and the deconfinement phase transition. Luckily, in some cases it was possible to rigorously extend the solutions found in thermodynamic limit to finite volumes and to formulate the finite volume analogs of phases directly from the grand canonical partition. It turns out that finite volume (surface) of a system generates also the temporal constraints, i.e. the finite formation/decay time of possible states in this finite system. Among other results I would like to mention the calculation of upper and lower bounds for the surface entropy of physical clusters within the Hills and Dales model; evaluation of the second virial coefficient which accounts for the Lorentz contraction of the hard core repulsing potential between hadrons; inclusion of large width of heavy quark-gluon bags into statistical description. I believe that the suggested mathematical solution of the freeze-out problem in relativistic hydrodynamic model and in hydro-cascade model has not only an academic interest, but also has some practical value. In addition I hope that the experience gained in working out some partly successful signals of deconfinement transition can be useful for other researchers to go further in this direction.