  It is shown how Adler's trace dynamics can be applied to stochastic mechanics
and other complex classical dynamical systems. Emergent non-commutivity due to
the fractal nature of sample trajectories is closely related to the fact that
the forward and backward time derivatives are different for these diffusions. A
new variational approach to stochastic mechanics based on trace dynamics is
introduced. It is shown that Yasue's method and Guerra and Morato's method can
both be generalized to allow for any diffusion constant in a stochastic model
of Schrodinger's equation, and that they can all also describe dissipative
diffusion. Then it is shown that the trace dynamical theory seems to only
describe dissipative diffusion unless an extra quantum mechanical potential
term is added to the Hamiltonian.
  The differential space theory of Wiener and Siegel is reconsidered as a
useful tool in this framework, and is generalized to stochastic processes
instead of deterministic ones for the hidden trajectories of observables. It is
proposed that the natural measure space for Wiener-Siegel theory is Haar
measure for random unitary matrices. A new interpretation of the polychotomic
algorithm is given.
