  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.
