Potentials of continuous Markov processes and random perturbations

Abstract With a scalar potential and bivector potential, the vector field associated with drift of diffusion is decomposed into generalized gradient field, perpendicular to gradient, divergence-free field. We give such decomposition probabilistic interpretation by introducing cycle velocity from bivectorial formalism nonequilibrium thermodynamics. New understandings on mean rates thermodynamic quantities are presented. Deterministic dynamical system further proven admit form emerged as Lyapunov function method random perturbations.