The Clausius inequality: implications for nonequilibrium 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 the recently developed open system Carnot cycles are derived here and their properties indicate that no new nonequilibrium entropy results from them as has been proposed over the decades. A simulation using a unique dimer molecule with a hysteresis potential - which fulfills all the dynamical laws - is used to show breakdown of the local equilibrium hypothesis. The cardinal Curie principle is shown inadequate as a paradigm to select force-flux relationships 
Christopher Gunaseelan Jesudason