Recent works on the decoherent histories formalism suggest that slowly evolving macroscopic quantities (extensive sums of local observables) in quantum many-body systems can be consistently monitored: The existence of past measurements does not alter future outcome distribution. Here, for Gaussian weak measurements, we show that fluctuations of macroscopic quantities cannot be consistently monitored in general, in contrast to their intensive mean value. Exceptions include fluctuations at infinite temperature, at critical points, and in semiclassical systems. We analytically quantify nonconsistency in terms of susceptibility and obtain related results on entropy growth under noisy unitary.

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• Quantum coherence & coherence measures
• Quantum measurements
• Quantum-to-classical transition
• Quantum many-body systems
• Exact solutions for many-body systems