连续马氏过程的位势与随机扰动
Potentials of Continuous Markov Process and Random Perturbations
摘要：
利用标量势和双矢量势，将扩散漂移的矢量场分解为广义梯度场、垂直于梯度的场和无发散场。我们给这样的分解概率解释引入循环速度从一个双矢量形式主义的非平衡态热力学。对热力学量的平均速率提出了新的认识。利用随机扰动的方法，进一步证明了确定性动力系统的李雅普诺夫函数为广义梯度形式。
英文摘要：
With a scalar potential and a bivector potential, the vector field associated with the drift of a diffusion is decomposed into 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. Deterministic dynamical system is further proven to admit a generalized gradient form with the emerged potential as the Lyapunov function by the method of random perturbations.
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