  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.
