  This paper presents a nonequilibrium, first-principles,
thermodynamic-ensemble based model for the relaxation process of interacting
non-equilibrium systems. This model is formulated using steepest-entropy-ascent
quantum thermodynamics (SEAQT) and its equation of motion for a grand canonical
ensemble and is applied to a many particle system of classical or
indistinguishable particles. Two kinds of interactions are discussed, including
pure heat diffusion and heat and mass diffusion together. Since no local
equilibrium assumption is made, the conjugate fluxes and forces are intrinsic
to the subspaces of the state space of one system and/or of the state space of
the two interacting systems. They are derived via the concepts of
hypoequilibrium state and nonequilibrium intensive properties, which describe
the nonmutual equilibrium status between subspaces of the thermodynamic state
space of a single system and/or of the state space of the two interacting
systems. The Onsager relations are shown to be thermodynamic kinematic features
of the system and are found without knowledge of the detailed mechanics of the
dynamic process. A fundamental thermodynamic explanation for the measurement of
each intensive property of a system in a nonequilibrium state is given. The
fundamental thermodynamic definition of reservoir is also discussed. Finally,
the equation of motion for a system undergoing multiple interactions is
provided, which permits the modeling of a network of local systems in
nonequilibrium at any spatial and temporal scale.
