Negative absolute temperature
This chapter discusses the conditions under which absolute temperature can be a negative quantity. It considers exceptional systems that can temporarily exist in states of negative absolute temperature. The universality of Carnot's theorem implies that absolute temperature can be formulated independently of the thermometric properties of materials. Intensive thermodynamic quantities have the same value at all spatial locations of the system, and for a system truly in equilibrium people can speak of the temperature. A nominal "refrigerator" operating between reservoirs at negative temperature would require that work be done on the environment. Systems with negative temperature are characterized by a population inversion: Higher-lying energy states are more populated than lower-energy states. Conversely, a beam of electromagnetic energy passed though a system in which higher-energy states are more populated than lower-energy states, will increase the intensity of the beam through stimulated emission, the process that underlies the operation of lasers.