Surprisal analysis of diffusion processes

We report a preliminary step in the application of information theory motivated surprisal analysis to irreversible processes but having linear equations of motion. Here we aim to describe the dynamics of varied Smoluchowski diffusion processes. In surprisal analysis, the probability density over the sample space is written as an exponential function of linear combination of observables that pose as constraints to the density evolution. The coefficients of this expansion can be interpreted as Lagrange multipliers that arise in the maximum entropy formalism. Known solutions of diffusion processes can be reproduced exactly using such a description. An exponent that is a linear combination of observables can also provide a close approximation for the dominant behavior of the solution of some other interesting examples for which there are no known exact results.