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.
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