Negative temperatures and negative dissipation

Abstract

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.

Statistical Mechanics of Systems with Negative Temperature

“…Population inversions play a fundamental role in the physics of laser systems [31]. The simplest example of a two-level laser discussed by Machlup [32] clarifies that this condition, applied to open systems, implies negative power absorption, i.e. power emission.…”

“…The concept of negative absorption is central in the history of the development of laser systems and dates back to the results by Kramers [34] and the early experiments by Ladenburg and coworkers on an electrically excited Neon gas [35]. It is important to note that the occurrence of population inversions in steady nonequilibrium regimes can not be related to a global negative temperature in the sense of equilibrium thermodynamics (see first point of Ramsey's requirements in Section II B) [32]. If a local equilibrium hypothesis is verified, a negative temperature can be defined to characterize population inversions in a small but still macroscopic portion of the system [36] (see also Section VII).…”

“…In Ref.s [28,119,125] the scalings of S G and T G in the thermodynamic limit are analysed, and it is shown that they provide no useful information about the high-energy regime of models living in bounded phase-space. To clarify this point, let us consider again the simple spin model (32) introduced in Section II B. For this system it is possible to compute explicit values for S B and S G for any fixed number of particles N , and the approach to the thermodynamic limit can be studied.…”

Energy and entropy: Path from game theory to statistical mechanics

“…For a negative-temperature state all pairs (i, j) hold (13). Negative temperatures are known for various systems whose energies are bounded from above (e.g., spin systems) [31][32][33][34][35].…”

Nonexistence of equilibrium states at absolute negative temperatures

“…And second, he never specified a "universal" thermometer that would permit an unambiguous measurement of negative temperatures. Since Ramsey publication [2] there have been many articles [8][9][10][11][12][13][14][15][16][17][18][19][20], as well as brief sections in well known textbooks [5,[21][22][23], addressing the subject. However, the stability or mere existence of those states has not been discussed and that is the purpose and motivation of this article.…”