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CRC Press eBooks

Negative temperature

James H. Luscombe

Published Jul 15, 2026• 0 citations
Publisher

Abstract

Can absolute temperature be negative ? Several considerations would indicate not. Yet, starting with the Purcell-Pound experiment in the 1950s [ 74 ] and continuing to the present, [ 75 ] experiments have been reported that are consistent with negative temperature. 1
DOI
10.1201/9781003729532-11

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Negative absolute temperature, defined in terms of the Boltzmann factor, corresponds to an upside-down energy pyramid. The example of the laser shows population inversion to be accompanied by the switch from absorption to emission, that is, from positive to negative dissipation, from increasing disorder throughout a system to increasing order in a subsystem. Early treatments of the negative-temperature concept are by Onsager and by Ramsey. Ramsey’s ’’essential requirements’’ are shown to be too strong. A TS diagram for a Carnot cycle operating between two negative temperatures clarifies the origin of amplification. Some biological negative-resistance amplifiers (nerve, muscle), in particular those involving ordered arrays of water molecules, are conjectured to have negative-temperature subsystems.
An isolated spin system that is in internal thermodynamic equilibrium and that has an upper limit to its allowed energy states can possess a negative temperature. We calculate the thermodynamic characteristics and the concurrence in this system over the entire range of positive and negative temperatures. Our calculation was performed for different real structures, which can be used in experiments. It is found that the temperature dependence of the concurrence is substantially asymmetrical similarly to other thermodynamic characteristics. At a negative temperature the maximum concurrence and the absolute temperature of the entanglement appearance are significantly larger than those at a positive temperature. The concurrence can be characterized by two dimensionless parameters: the ratio between the Zeeman and dipolar energies and the ratio of the thermal and dipolar energies. It was shown that for all considered structures the dimensionless temperatures of the transition between entanglement and separability of the first and second spins are independent of spin structure and the number of spins.
Absolute temperature is usually bound to be positive. Under special conditions, however, negative temperatures-in which high-energy states are more occupied than low-energy states-are also possible. Such states have been demonstrated in localized systems with finite, discrete spectra. Here, we prepared a negative temperature state for motional degrees of freedom. By tailoring the Bose-Hubbard Hamiltonian, we created an attractively interacting ensemble of ultracold bosons at negative temperature that is stable against collapse for arbitrary atom numbers. The quasimomentum distribution develops sharp peaks at the upper band edge, revealing thermal equilibrium and bosonic coherence over several lattice sites. Negative temperatures imply negative pressures and open up new parameter regimes for cold atoms, enabling fundamentally new many-body states.