STEEPEST-ASCENT CONSTRAINED APPROACH TO MAXIMUM ENTROPY

A rate equation for a discrete probability distribution is discussed as a route to describe smooth relaxation towards the maximum entropy distribution compatible at all times with one or more linear constraints. The entropy follows the path of steepest ascent compatible with the constraints. The rate equation is consistent with the Onsager theorem of reciprocity and the fluctuation-dissipation theorem. The mathematical formalism was originally developed to obtain a quantum theoretical unification of mechanics and thermodynamics. It is presented here as part of an effort to develop tools for the treatment of nonequilibrium problems with engineering applications.