Internal energy transfer theory is motivated from the thermodynamic
point of view in which internal energy transfer depends
on intensive state variables as well as extensive state variables.
Internal energy transfer in a quasi-equilibrium (quasi-static) process
is conventionally described only by extensive state variables,
but internal energy in a non-equilibrium process can be stated
by including intensive state variables. Here, the dependence of
intensive state variables for internal energy transfer is addressed.
Euler’s equation of thermodynamics for the internal energy is 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. (2). 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. (2), we can specifically classify non-equilibrium,
quasi-equilibrium, and equilibrium processes. We utilize the definitions
of the thermodynamic potentials