Are the second law principles of Caratheodory and Kelvin equivalent?

TL;DR

This paper critically examines the claimed equivalence between Caratheodory's and Kelvin's formulations of the second law of thermodynamics, identifying flaws in previous proofs and arguing that their equivalence remains unproven.

Contribution

The paper reveals errors in earlier deductions claiming the equivalence of the two principles and clarifies that their relationship is still unestablished.

Findings

Previous proofs of equivalence are flawed due to inadmissible assumptions.

The equivalence between Caratheodory's and Kelvin's principles remains unproven.

Identifies specific logical fallacies in earlier works.

Abstract

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.