  In Clearing Up Mysteries -- The Original Goal (Maximum Entropy and Bayesian
Methods: Cambridge, England, 1988 Springer, pp. 1-27) Jaynes derived Fick's Law
for a dilute binary solution from Bayes' Theorem by considering,
probabilistically, the motion of dilute solute molecules. Modifying Jaynes'
prior, changing the frame of reference, and allowing for multicomponent
systems, one can follow Jaynes' logic to arrive at several expressions for the
diffusion coefficient that are widely used in application to solvent-polymer
systems. These results, however, do not generally satisfy required conditions
over the full concentration range. This limitation is resolved by considering
the joint motion of all components in the solution with the inclusion of known
physical constraints. Doing so, one arrives at a new set of constitutive
equations for binary and multicomponent diffusion that include Darken's form as
a limit and provide means to characterize inter-species correlations, removing
the need for the ad hoc modifications of the thermodynamic term or substitution
of bulk compositions with local compositions that have been proposed in the
literature. In binary systems, the Bayesian expression for the mutual diffusion
coefficient provides explicit limits on non-ideal mutual diffusion behavior,
given component self-diffusion coefficients, that can be attributed to
inter-species correlation versus stronger intra- and inter-species clustering.
Applications of the model to published data for a set of binary systems are
presented, along with pointers to further directions for research.
