Bivectorial Mesoscopic Nonequilibrium Thermodynamics: Potentials of Continuous Markov Process and Random Perturbations

Ying-Jen Yang, Yu-Chen Cheng

Published 2020-07-17Version 1

With a scalar potential and a bivector potential, the drift of a diffusion is decomposed into the sum of a generalized gradient field, a field perpendicular to the gradient, and a divergence-free field. We give such decomposition a probabilistic interpretation by introducing cycle velocity from a bivectorial formalism of nonequilibrium thermodynamics. New understandings on the mean rates of thermodynamic quantities are presented. Scalar potentials of deterministic dynamics, obtained from three different random perturbations, are compared in terms of their Lyapunov and geometric properties.