Consistent thermostatistics forbids negative absolute temperatures
By Jörn Dunkel, Stefan Hilbert. Nature Physics, 2013
161 citations recorded by the source corpus.
Over the past 60 years, a considerable number of theories and experiments have claimed the existence of negative absolute temperature in spin systems and ultracold quantum gases. This has led to speculation that ultracold gases may be dark-energy analogues and also suggests the feasibility of heat engines with efficiencies larger than one. Here, we prove that all previous negative temperature claims and their implications are invalid as they arise from the use of an entropy definition that is inconsistent both mathematically and thermodynamically. We show that the underlying conceptual deficiencies can be overcome if one adopts a microcanonical entropy functional originally derived by Gibbs. The resulting thermodynamic framework is self-consistent and implies that absolute temperature remains positive even for systems with a bounded spectrum. In addition, we propose a minimal quantum thermometer that can be implemented with available experimental techniques. It is shown that for thermodynamics and statistical physics to be internally consistent, Gibbs’ original—rather than Boltzmann’s widely used—definition of entropy needs to be adopted. Consequently, negative absolute temperatures are strictly forbidden, and cold-atom gases are unlikely to be laboratory analogues to dark energy.
Subfields: Biomedical Engineering, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/8e41f92abe7087f98daf07a483bf09afd03e5ee1
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Citations in the corpus
- Temperature in and out of equilibrium: A review of concepts, tools and attempts (2017, background): “Numerical results show that even such a coarse-grained Gibbs entropy remains constant up to a crossover time t∗( ) ∼ ln(1/ ).”
- Colloquium : Statistical mechanics and thermodynamics at strong coupling: Quantum and classical (2019, background): “Most notably, the thermodynamic expression for ai coincides with its statistical mechanical definition given by the microcanonical average ai 1⁄4 h∂HðλÞ=∂λii (Dunkel and Hilbert, 2014; Hilbert, Hänggi, and Dunkel, 2014).”