  A non-linear backward equation with diffusive terms is postulated for the
probability density that depends on the Bohmian quantum potential. An
associated nonlinear Schr\"{o}dinger equation is also introduced and extension
of the analysis to several particle compounds is sketched along with the
implications following from this formalism regarding the non-conservation of
probability in the non-equilibrium regime. Some further conclusions are educed
with respect to the Onsager's relations and the generalized optical theorem.
