  First, the chiral phase transition at nonzero temperature and baryon chemical
potential is studied at mean field level in the sigma model that includes quark
degrees of freedom explicitly. For small bare quark masses the critical point
separating the first order phase transition line and the smooth crossover
region is determined, and the spinodal lines are drawn. Adiabatic lines are
computed showing that the critical point does not serve as focusing point in
the adiabatic expansion. Second, coarse-grained evolution equations for
inhomogeneous chiral condensate fields coupled to a heat bath are derived in
the linear sigma model. Multiple effects of the thermal background on the
Disoriented Chiral Condensate (DCC) are studied within linear response theory.
In-medium modification of the pion dispersion relation is examined. The
deviation from the speed of light of the velocity of soft Goldstone modes is
calculated. Decay widths of pions and sigma mesons are computed at nonzero
temperature at one- and two-loop order in perturbation theory. We show that
elastic scattering processes are significant for the dissipation of DCCs in the
phase transition region. Throughout this work we made sure that Goldstone's
Theorem is fulfilled when chiral symmetry is spontaneously broken.
