Distinction between non-equilibrium and equilibrium depends on
whether temperature, pressure, and chemical potential are larger
than their corresponding activation temperature, activation pressure,
and activation chemical potential.
In summary, we analyze that there are two contributions in
internal energy transfer in Eq. (3). The first contribution originates
from external variable changes, and the second contribution comes
from the internal variable changes. The Gibbs–Duhem relation
holds only for the quasi-equilibrium process.
Based on Eq. (3), we can specifically classify non-equilibrium,
quasi-equilibrium, and equilibrium processes. We utilize the definitions
of the thermodynamic potentials