  By suitable reformulations, we cast the mathematical frameworks of several
well-known different approaches to the description of non-equilibrium dynamics
into a unified formulation, which extends to such frameworks the concept of
Steepest Entropy Ascent (SEA) dynamics introduced by the present author in
previous works on quantum thermodynamics. The present formulation constitutes a
generalization also for the quantum thermodynamics framework. In the SEA
modeling principle a key role is played by the geometrical metric with respect
to which to measure the length of a trajectory in state space. In the near
equilibrium limit, the metric tensor is related to the Onsager's generalized
resistivity tensor. Therefore, through the identification of a suitable metric
field which generalizes the Onsager generalized resistance to the arbitrarily
far non-equilibrium domain, most of the existing theories of non-equilibrium
thermodynamics can be cast in such a way that the state exhibits a spontaneous
tendency to evolve in state space along the path of SEA compatible with the
conservation constraints and the boundary conditions. The resulting unified
family of SEA dynamical models is intrinsically and strongly consistent with
the second law of thermodynamics. Non-negativity of the entropy production is a
readily proved general feature of SEA dynamics. In several of the different
approaches to non-equilibrium description we consider here, the SEA concept has
not been investigated before. We believe it defines the precise meaning and the
domain of general validity of the so-called Maximum Entropy Production
Principle. It is hoped that the present unifying approach may prove useful in
providing a fresh basis for effective, thermodynamically consistent, numerical
models and theoretical treatments of irreversible conservative relaxation
towards equilibrium from far non-equilibrium states.
