  We argue that, because of the quantum-entanglement, the local physics of the
strongly-correlated materials at zero temperature is described in very good
approximation by a simple generalized Gibbs distribution, which depends on a
relatively small number local quantum thermodynamical potentials. We
demonstrate that our statement is exact in certain limits, and we perform
numerical calculations of the iron compounds FeSe and FeTe and of the elemental
cerium by employing the Gutzwiller Approximation (GA) that strongly support our
theory in general.
