Analysis of Open System Carnot Cycle and State Functions

A basic analysis of the fundamental aspects of entropy in thermodynamics is given, and the results obtained are compared to the standard formulations founded on the Gibbsian open system state functions. The variance of the two approaches are discussed. Some rigorous theorems are deduced which proves the inadequacy of the standard local equilibrium hypothesis, which is a fundamental assumption when modeling nonequilibrium systems in chemical engineering and other applications. It is deduced that another theory is required for nonequilibirum processes, which reduces to the equilibrium results where vanishing field gradients in temperature and possibly other variables apply