Exergy dynamics of systems in thermal or concentration non-equilibrium

The paper addresses the problem of the existence and quantification of the exergy of non-equilibrium systems. Assuming that both energy and exergy are a priori concepts, the Gibbs "available energy" A is calculated for arbitrary temperature or concentration distributions across the body, with an accuracy that depends only on the information one has of the initial distribution. It is shown that A exponentially relaxes to its equilibrium value, and it is then demonstrated that its value is different from that of the non-equilibrium exergy, the difference depending on the imposed boundary conditions on the system and thus the two quantities are shown to be incommensurable. It is finally argued that all iso-energetic non-equilibrium states can be ranked in terms of their non-equilibrium exergy content, and that each point of the Gibbs plane corresponds therefore to a set of possible initial distributions, each one with its own exergy-decay history. The non-equilibrium exergy is always larger than its equilibrium counterpart and constitutes the "real" total exergy content of the system, i.e., the real maximum work extractable from the initial system. A systematic application of this paradigm may be beneficial for meaningful future applications in the fields of engineering and natural science.