A Quantum-Theoretic Analog for a Pair of Noncommuting Observables of the Semiclassical Brillouin Function

We study, with the use of numerical integration, a noncommutative extension of a quantum-theoretic model (an alternative to the semiclassical Brillouin function), recently presented by Brody and Hughston and, independently, Slater, for the thermodynamic behavior of a spin-1/2 particle. Differences between the (broadly similar) predictions yielded by this extended model and those obtained from its conventional (semiclassical/Jaynesian) entropy-maximization counterpart are examined.