  In quantum systems of a macroscopic size V, such as interacting many
particles and quantum computers with many qubits, there exist pure states such
that fluctuations of some intensive operator A is anomalously large, <\delta
A^2> = O(V^0), which is much larger than that assumed in thermodynamics,
<\delta A^2> = O(1/V). By making full use of the locality, we show, starting
from Hamiltonians of macroscopic degrees of freedom, that such states decohere
at anomalously fast rates when they are weakly perturbed from environments.
