Basic Equation for the Different Coupled Equations between the First and Second Laws of Thermodynamics at Strong Coupling

For some physical processes, the first and second laws of thermodynamics can be at strong coupling. Also, it is possible that the familiar inequalities of macroscopic thermodynamics cannot be used in the analysis of the system, and it is needed that the inequalities rewrote as equalities. In these cases, the work, internal energy, dissipated energy, and entropy production must be considered and identified together. In this paper, the basic equation for the different coupled equations between the first and second laws of thermodynamics at strong coupling is extracted. Also, inspired by the first and second laws of thermodynamics and different approaches to the second law, a thermophysical equation for thermodynamics is extracted. This equation can be used instead of the first and second laws of thermodynamics as to the analysis of the performed process these laws must be established together. It is tried that effective internal energy, directly to be related to the entropy or vice versa, in one general equation. Also, the presented equation is in the same line with the different approaches to the second law and energy structure theory.