Systematics of Carnot cycles at positive and negative Kelvin temperatures

Abstract

The set of possible Carnot cycles involving positive and/or negative Kelvin temperatures is analysed in terms of graphs and of transported entropy and entropy production. The formulations of the second law of thermodynamics, allowing for the existence of negative Kelvin temperatures, proposed by Ramsey (1956) and by Landsberg (1977) are shown to be logically equivalent. Some properties of the limiting temperatures T+0, +or- infinity , -0 are also investigated and a generalised third law is formulated.