by a second order derivative in time. The canonical Langevin equations however are usually formulated in terms of a first derivative evolution in time. This difference is unimportant in equilibrium, but modifies real-time properties. In certain circumstances, which I discuss in detail below, the second order evolution effectively leads to a first order (or overdamped) description of certain parts of the system.

The general properties of Langevin field evolutions are that, under very minimal conditions, the fields equilibrate for long times to the canonical (classical) Boltzmann distribution. The dynamics are very rich, realizing and generalizing all the near canonical equilibrium properties of the classical field evolution, including in particular the features captured by the perhaps more familiar time-dependent Ginzburg Landau formulation (TDGL).

In this paper I present a didactic introduction to the underlying formulation of a second time derivative Langevin system and its associated Fokker-Planck equation. Its general dynamical properties are compared to those of other important classes of dynamics such as TDGL and the stochastic non-linear Schrödinger equation (sNLS). This is done mostly in section \[FP\]. (The treatment of the sNLS system is given in Appendix A.) In section \[Sol\] I derive analytic solutions of the Fokker-Planck equation in 