Random systems described with stochastic velocities

Kinematics of stochastic mechanics is used to study diffusion problems at a more general level, without forcing a link to Newtonian mechanics. Stochastic velocities are taken from Nelsonʹs kinematics to study nonlinear random systems. Random effects are systematically separated from the deterministic motion via a transformation to fluctuation variables. Then, closed expressions for stochastic velocities are written, and as a consequence, analytical applications can be developed. A system is studied to show the difference between detailed and nondetailed balance. Besides, a one-dimensional problem is considered to characterize the relaxation process. The concept of entropy is introduced to find an expression describing stationary processes, so that one has two kind of tools to study this type of problems. The final result is that a few simple techniques are put together to describe a wide amount of phenomena.