Stochastic Motion and Diffusion

Abstract

In the globally stochastic region of the phase space for a system with two degrees of freedom, in which KAM curves spanning the phase coordinate do not exist, a complete description of the motion is generally impractical. We can then seek to treat the motion in a statistical sense. That is, the evolution of certain average quantities can be determined, rather than the trajectory corresponding to a given set of initial conditions (e.g., Chandrasekhar, 1943; Wang and Uhlenbeck, 1945). Such a formulation in terms of average quantities is also the basis for statistical mechanics (see, for example, Penrose, 1970).