Two level system
(Microcanonical ensemble, canonical ensemble and negative temperature)

Each constituent of the system takes either one of two states, independently from the state of other constituents. In the microcanonical ensemble, the enregy is kept constant and thus the system changes the state keeping the number of consituents in upper and lower levels. In the canonical ensemble, the probability that the system takes a atate of energy E is given by the Boltzman factor exp[-E/kT], and thus the number of consituents in upper and lower levels varies as the time passes.

When the energy of upper and lower levels are interchanged suddenly in thermal equilibrium, the population of constituents in upper and lower levels are inverted for a certain time period. This temporal state can be regarded as a state in a negative temperature.