  We study various dynamical aspects of systems possessing a first order phase
transition in their phase diagram. We isolate three qualitatively distinct
types of theories depending on the structure of instabilities and the nature of
the low temperature phase. The non-equilibrium dynamics is modeled by a dual
gravitational theory in 3+1 dimension which is coupled to massive scalar field
with self interacting potential. By numerically solving the Einstein-matter
equations of motion with various initial configurations, we investigate the
structure of the final state arising through coalescence of phase domains. We
find that static phase domains, even quite narrow are very long lived and we
find a phenomenological equation for their lifetime. Within our framework we
also analyze moving phase domains and their collision as well as the effects of
spinodal instability and dynamical instability on an expanding boost invariant
plasma.
