一般非线性Fokker-Planck方程规范场的涨落与Fisher信息矩阵的协变形式
Fluctuation of gauge field for general nonlinear Fokker-Planck equation and covariant version of Fisher information matrix
摘要：
我们澄清了一般非线性Fokker-Planck方程与规范场与非平衡动力学和系统的Fisher信息之间的强联系。文献中提出了非平衡Fokker-Planck方程的阿贝尔规范理论的概念，其中相关曲率代表内部几何。我们提出规范场的涨落可以分解为三个部分。我们进一步表明，如果我们通过使用协变导数来定义Fisher信息矩阵，那么它会给出通量分量的相关性，但它不是规范不变的。
英文摘要：
We clarify a strong link between general nonlinear Fokker-Planck equations with gauge fields associated with nonequilibrium dynamics and the Fisher information of the system. The notion of Abelian gauge theory for the non-equilibrium Fokker-Planck equation has proposed in the literature, in which the associated curvature represents internal geometry. We present the fluctuation of the gauge field can be decomposed into three parts. We further show that if we define the Fisher information matrix by using a covariant derivative then it gives correlation of the flux components but it is not gauge invariant.
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