Under Floquet ETH, the trace distance between energy-filtered and thermal states is bounded by O(√δ), where δ is the filter width.
Bravyi, Upper bounds on entangling rates of bipartite Hamiltonians, Physical Review A76, 052319 (2007)
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How thermal is a filtered state?
Under Floquet ETH, the trace distance between energy-filtered and thermal states is bounded by O(√δ), where δ is the filter width.