论文标题
连续马尔可夫过程和随机扰动的潜力
Potentials of Continuous Markov Process and Random Perturbations
论文作者
论文摘要
具有标量电势和双向运动电位，与扩散漂移相关的矢量场被分解为广义梯度场，垂直于梯度的场和无差异场。我们通过从非平衡热力学的双向形式主义引入循环速度来给出这种分解的概率解释。对热力学量的平均速率进行了新的理解。确定性的动力系统进一步证明可以通过随机扰动的方法作为Lyapunov函数允许作为Lyapunov函数出现的广义梯度形式。
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.
