A Componential Reduction to the Euler-Lagrange Equation Using Energy Structure Theory

The Euler-Lagrange equation can be used for a variety of the thermal processes from microscopic and macroscopic points of view [1-3]. In this case, the main challenge is calculating the potential energy using the Lagrangian density. Since the energy structure equation has the effects of the second law of thermodynamics as its base, in this paper, this equation is used as potential energy for the Euler-Lagrange equation. Since the energy structure equation has been presented based on the energy components as well as independent and dependent energy components concepts, therefore, a componential reduction to the Euler-Lagrange equation will be extracted. The resultant equation will be satisfied for all independent components activated in the performed process. Also, the resultant equation can be used to investigate different paths whenever the same amount of energy is applied to the system in different conditions. Also, a quasi-static path is used as a reference path.