  We investigate different measures of stability of quantum statistical
ensembles with respect to local measurements. We call a quantum statistical
ensemble "stable" if a small number of local measurements cannot significantly
modify the total-energy distribution representing the ensemble. First, we
numerically calculate the evolution of the stability measure introduced in our
previous work [Phys. Rev. E 94, 062106 (2016)] for an ensemble representing a
mixture of two canonical ensembles with very different temperatures in a
periodic chain of interacting spins-1/2. Second, we propose other possible
stability measures and discuss their advantages and disadvantages. We also show
that, for small system sizes available to numerical simulations of local
measurements, finite-size effects are rather pronounced.
