  The nonequilibrium Fokker-Planck dynamics with a non-conservative drift
field, in dimension $N\geq 2$, can be related with the non-Hermitian quantum
mechanics in a real scalar potential $V$ and in a purely imaginary vector
potential -$iA$ of real amplitude $A$. Since Fokker-Planck probability density
functions may be obtained by means of Feynman's path integrals, the previous
observation points towards a general issue of "magnetically affine"
propagators, possibly of quantum origin, in real and Euclidean time. In below
we shall follow the $N=3$ "magnetic thread", within which one may keep under a
computational control formally and conceptually different implementations of
magnetism (or surrogate magnetism) in the dynamics of diffusion processes. We
shall focus on interrelations (with due precaution to varied, not evidently
compatible, notational conventions) of: (i) the pertinent non-conservatively
drifted diffusions, (ii) the classic Brownian motion of charged particles in
the (electro)magnetic field, (iii) diffusion processes arising within so-called
Euclidean quantum mechanics (which from the outset employs non-Hermitian
"magnetic" Hamiltonians), (iv) limitations of the usefulness of the Euclidean
map $\exp(-itH_{quant}) \rightarrow \exp(-tH_{Eucl})$, regarding the
probabilistic significance of inferred (path) integral kernels in the
description of diffusion processes.
