  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
