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By suitable reformulations, we cast the mathematical frameworks of severalwell-known different approaches to the description of non-equilibrium dynamicsinto a unified formulation, which extends to such frameworks the concept ofSteepest Entropy Ascent (SEA) dynamics introduced by the present author inprevious works on quantum thermodynamics. The present formulation constitutes ageneralization also for the quantum thermodynamics framework. In the SEAmodeling principle a key role is played by the geometrical metric with respectto which to measure the length of a trajectory in state space. In the nearequilibrium limit, the metric tensor is related to the Onsager's generalizedresistivity tensor. Therefore, through the identification of a suitable metricfield which generalizes the Onsager generalized resistance to the arbitrarilyfar non-equilibrium domain, most of the existing theories of non-equilibriumthermodynamics can be cast in such a way that the state exhibits a spontaneoustendency to evolve in state space along the path of SEA compatible with theconservation constraints and the boundary conditions. The resulting unifiedfamily of SEA dynamical models is intrinsically and strongly consistent withthe second law of thermodynamics. Non-negativity of the entropy production is areadily proved general feature of SEA dynamics. In several of the differentapproaches to non-equilibrium description we consider here, the SEA concept hasnot been investigated before. We believe it defines the precise meaning and thedomain of general validity of the so-called Maximum Entropy ProductionPrinciple. It is hoped that the present unifying approach may prove useful inproviding a fresh basis for effective, thermodynamically consistent, numericalmodels and theoretical treatments of irreversible conservative relaxationtowards equilibrium from far non-equilibrium states.

Steepest Entropy Ascent Model for Far-Non-Equilibrium Thermodynamics. Unified Implementation of the Maximum Entropy Production Principle