Approximate time dependent solutions of partial differential equations: the MaxEnt-Minimum Norm approach

A new approach to inverse problems with incomplete data, the MaxEnt-Minimum Norm scheme, was recently introduced by Baker–Jarvis (BJ). This method is based on the application of Jaynesʹs MaxEnt principle to a probability distribution defined on the functional space of all the possible solutions of the problem. In the present work we consider the application of these ideas to non-equilibrium time dependent systems. In the spirit of Jaynesʹs Information Theory approach to Statistical Mechanics, we focus on the behaviour of a small number of physically relevant mean values. By recourse to the BJ procedure, the equations of motion of those mean values are closed and an approximate description of the systemʹs evolution is obtained. It is also shown that the BJ method is closely related to Curadoʹs case (i.e., q=2 and standard mean values) of Tsallis nonextensive thermostatistics.