Is the Clausius inequality a consequence of the second law?
  We present an analysis of the foundations of the well known Clausius inequality. It is shown that, in general, the inequality is not a logical consequence of the Kelvin-Planck formulation of the second law of thermodynamics. Some thought experiments demonstrating the violation of the Clausius inequality are considered. The possibility of experimental detection of the violation is pointed out. 
Alexey V. Gavrilov
physics.class-ph cond-mat.stat-mech