On the deduction of Carathéodory's axiom from Kelvin's principle

Abstract

Landsberg recently proved that Carathéodory's axiom is a logical consequence of Kelvin's principle. His proof is here modified, so that the consequences of an implicit assumption become apparent. The result may be summarised as follows: Purely mechanical systems are the only systems that obey Kelvin's principle but not Carathéodory's axiom.