  A stochastic dynamics has a natural decomposition into a drift capturing mean
rate of change and a martingale increment capturing randomness. They are two
statistically uncorrelated, but not necessarily independent mechanisms
contributing to the overall fluctuations of the dynamics, representing the
uncertainties in the past and in the future. A generalized Einstein relation is
a consequence solely because the dynamics being stationary; and the Green-Kubo
formula reflects a balance between the two mechanisms. Equilibrium with
reversibility is characterized by a novel covariance symmetry.
