Are the second law principles of Caratheodory and Kelvin equivalent?
  Lord Kelvin's postulate is a standard form of statement of the second law of thermodynamics. Caratheodory's principle is also considered as a different form of this law. Landsberg deduced Caratheodory's principle from Kelvin's postulate and Dunning-Davies deduced its converse to show the equivalence of the two principles, and these deductions remained forerunners for later works. Here we show that these deductions are flawed and therefore, invalid. The fallacies in these works arose due to the fact that these authors had taken an inadmissible form of statement of Kevin's postulate and had considered an inappropriate cyclic process, for their deductions. The equivalence between Caratheodory's principle and Kelvin's principle of the second law, therefore, remains unproved. 
Radhakrishnamurty Padyala
physics.gen-ph