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Simon Braun and collaborators prepared a state with negative temperature for motional degrees of freedom in an ultracold atomic system. They tailored a lattice model so the occupied high-energy states were compatible with the relevant upper-energy bound.^[ref]

In this regime $\beta =\partial (S/k_B)/\partial E<0$: increasing energy reduces the entropy of the constrained system. The state is not colder than absolute zero. Its population favours high-energy states, and its thermodynamic ordering differs from the positive-temperature branch. The experimental energy bounds and stability conditions are essential.