Nonequilibrium dynamics of nonconservative diffusion processes

Fokker-Planck operators of diffusion processes with nonconservative drift fields, in dimension $N\geq 2$, can be directly related with non-Hermitian electromagnetic-type Hamiltonian generators of motion. The induced nonequilibrium dynamics of probability densities points towards an issue of path integral solutions of the Fokker-Planck equation, and calls for revisiting links between known exact path integral formulas for quantum propagators in real and Euclidean time, with these for Fokker-Planck-induced transition probability density functions. In below we shall follow the $N=3$ "magnetic thread", within which one encounters formally and conceptually distinct implementations of the magneti…