Stability of quantum statistical ensembles with respect to random local measurements

We define a quantum statistical ensemble as 'stable', if a small number of local measurements cannot significantly modify the total-energy distribution representing the ensemble. This stability criterion is applied to lattices of spins-1/2, for which different measures of the quantum ensemble stability are investigated. In the context of the foundations of quantum statistical physics, our results justify the use of statistical ensembles with narrow energy distributions such as canonical or microcanonical ensembles.
References:
[1] W. Hahn and B. V. Fine, Phys. Rev. E 94, 062106 (2016)
[2] W. Hahn and B. V. Fine, J. Stat. Mech: Theory and Experiment 2018, 023107 (2018).