The Clausius inequality: Implications for non-equilibrium thermodynamic steady states with NEMD corroboration

The Clausius inequality for closed systems was deduced from the Riemann integration of closed Carnot cycle loops for irreversible transitions. The corresponding inequalities for open system Carnot cycles are derived here. Their properties indicate that no new non-equilibrium entropy is evident as has been proposed over the decades. It is proven that a sequence of points along a non-equilibrium state space must have excess variables augmenting those for the equilibrium situation and therefore the principle of local equilibrium (PLE) used extensively to describe non-equilibrium systems is an approximation. To demonstrate the breakdown of the principle, verification of the theorem, and the presence of new phenomena, an ab initio steady-state simulation of a simple dimer reaction 2A↔A2 under non-equilibrium conditions was performed and the results compared to the equilibrium conditions to show the regime of breakdown of the principle. The novel dimer reaction presented has a cyclical pathway found in many natural processes, such as laser photochemistry. It is suggested that such reaction pathways can exist and awaits experimental verification. A new algorithm to conserve momentum and energy at the potential switches of the dimer is applied effectively. New atomic and molecular flux flows not present under equilibrium conditions are shown to exist, where the net rate of reaction along the cell is not zero but small, unlike the zero rate equilibrium requirement, leading to the flux presence. The equilibrium constant is also shifted from the value at thermodynamical equilibrium. Unless reinterpreted differently, it is shown that the so-called Curie symmetry principle, fundamental in deciding on the feasibility of flux-force couplings in both theory and experiment in all physical theories, cannot apply to such experimental results. Hence, a far greater freedom in selecting appropriate force-flux couplings is indicated than would be the case if the Curie principle, as commonly interpreted is adopted.