David Lavis (KCL): “Suppose Temperature is Negative. What Then?”

Abstract: We show that it is quite easy to construct simple model systems exhibiting negative temperatures and we explore the thermodynamic consequences of this possibility particularly in relation to the second law. Approaching thermodynamics from the perspective of the Lieb–Yngvason formulation we demonstrate that both negative temperatures and heat capacities are compatible with the Carathéodory version of the second law. Then by examining all cases of heat engines and pumps working cyclically between isothermal reservoirs we show that the Kelvin–Planck version of the second law needs to be modified if the temperature can be negative and that both the Kelvin–Planck and Clausius versions need to be modified if both the temperature and heat capacity can be negative. We discuss the relevance of these conclusions for the ongoing dispute about the correct entropy for the microcanonical distribution in statistical mechanics.