Caratheodory’s Theorem on the Second Law of Thermodynamics
E. C. Zachanoglou · SIAM Journal on Applied Mathematics · 1973
It is shown in this paper that if in every sufficiently small neighborhood of a point $x^0 $ there are points which cannot be connected with $x^0 $ by piecewise smooth integral curves of a Pfaffian equation, then in a neighborhood of $x^0 $ there is an integral surface of the equation passing through $x^0 $.This result is a generalization of a theorem proved by Caratheodory in his axiomatic treatment of thermodynamics. The proof is new.