  Filtering theory gives an explicit models for the flow of information and
thereby quantifies the rates of change of information supplied to and
dissipated from the filter's memory. Here we extend the analysis of Mitter and
Newton from linear Gaussian models to general nonlinear filters involving
Markov diffusions.The rates of entropy production are now generally the average
squared-field (co-metric) of various logarithmic probability densities, which
may be interpreted as Fisher information associate with Gaussian perturbations
(via de Bruijn's identity). We show that the central connection is made through
the Mayer-Wolf and Zakai Theorem for the rate of change of the mutual
information between the filtered state and the observation history. In
particular, we extend this Theorem to cover a Markov diffusion controlled by
observations process, which may be interpreted as the filter acting as a
Maxwell's Daemon applying feedback to the system.
