Temperature is conventionally defined as the average kinetic energy of a collection of particles. More precisely, temperature is related to average energy per

Temperature is conventionally defined as the average kinetic energy of a collection of particles. More precisely, temperature is related to average energy per degree of freedom via the equipartition theorem. This doesn't only break down in case of negative temperatures, but also if continuity is no longer a good approximation for quantized energy levels. See http://physics.stackexchange.com/questions/33750/is-temperature-an-extensive-property-like-density/33752#33752 http://physics.stackexchange.com/questions/33750/is-temperat...