Eigenstate-specific temperatures in two-level paramagnetic spin lattices.

Increasing interest in the thermodynamics of small and/or isolated systems, in combination with recent observations of negative temperatures of atoms in ultracold optical lattices, has stimulated the need for estimating the conventional, canonical temperature T of systems in equilibrium with heat baths using eigenstate-specific temperatures (ESTs). Four distinct ESTs-continuous canonical, discrete canonical, continuous microcanonical, and discrete microcanonical-are accordingly derived for two-level paramagnetic spin lattices (PSLs) in external magnetic fields. At large N, the four ESTs are intensive, equal to T, and obey all four laws of thermodynamics.