Entropy concept and ordering of states. II

Abstract

In this paper, the second of two, the Second Law of Thermodynamics is again regarded primarily as an essential link in an argument leading directly to the existence of a certain order amongst the states of an adiabatically enclosed system, and to the consequent definition of a continuous empirical entropy function. The mode of reasoning is now topological in character. To achieve the desired result the following physically acceptable statement is assumed to be true: “If a state$\mathfrak{S}$ of an adiabatically enclosed system is inaccessible from a state$\mathfrak{S}'$ then every state in a certain neighbourhood of$\mathfrak{S}'$ is inaccessible from every state in a certain neighbourhood of$\mathfrak{S}$.” A clear-cut separation is thus effected between the contents of the Second Law on the one hand and that of the other principal Laws of Thermodynamics on the other, the First Law in particular no longer being invoked at all.