Universality of Jaynes’ approach to the evolution of time-dependent probability distributions

In order to ascertain which are the essential requirements that allow for the application of MaxEnt techniques in connection with evolution problems, we study time-dependent probability distributions governed by a general, linear evolution equation that admits, as particular instances, the Lioville, diffusion and Fokker–Planck ones. A general variational principle is introduced and the properties of an appropriately devised MaxEnt ansatz are investigated. The functional relation that gives the time derivative of the entropy in terms of the time-dependent MaxEnt distribution function is seen to be always of the same form as the one that holds in the case of exact solutions.