Unbiased Modeling of Stochastic Processes: How to Guess Path Integrals, Fokker-Planck Equations and Langevin-Îto Equations

Abstract

In the previous chapters we have shown how the maximum information entropy principle allows us to derive the distribution functions of nonequilibrium systems by a suitable choice of constraints. While in these chapters we focussed our attention on the steady state distribution function, in the present chapter we wish to study time-dependent distribution functions. A suitable starting point is provided by the maximum calibre principle due to Jaynes, who extended his maximum entropy principle by maximizing an entropy-like functional over a space-time domain. Jaynes himself applied his principle to derive important formulas applicable to irreversible thermodynamics in order to study relaxation processes.