Describing states and dynamics in far from equilibrium systems. Needed a metric within a system state space

The realms of classical and non-equilibrium thermodynamics are characterized by very different behaviors and laws: also different definitions for equilibrium states apply. Very often laws, state variables and state functions defined in the classical realm are used in the other, which doesnʹt help to manage with systems behavior in a correct way. Far from equilibrium states are poorly defined nor adequate criteria offered to assess the distance among them as well as the complexity of the system under investigation (distance from thermodynamic equilibrium). These criteria are stressed in the paper, together with a critical survey of the most relevant approaches developed to study self-organizing, far from equilibrium systems. Finally, a general criterion is proposed to check the suitability of these and other approaches in providing a global measure of systems complexity.