  Inflation in the early Universe is a grand phase transition which have
produced the seeds of all the structures we now observe. We focus on the
non-equilibrium aspect of this phase transition especially the inevitable
infrared (IR) divergence associated to the the quantum and classical fields
during the inflation. There is a long history of research for removing this IR
divergence for healthy perturbation calculations. On the other hand, the same
IR divergence is quite relevant and have developed the primordial density
fluctuations in the early Universe. We develop a unified formalism in which the
IR divergence is clearly separated from the microscopic quantum field theory
but only appear in the statistical classical structure. We derive the classical
Langevin equation for the order parameter within the quantum field theory
through the instability of the de Sitter vacuum during the inflation. This
separation process is relevant in general to develop macroscopic structures and
to derive the basic properties of statistical mechanics in the quantum field
theory.
