Generalized symmetries generate exponentially many Krylov sectors in quantum many-body systems, showing that Hilbert space fragmentation does not by itself imply ergodicity breaking.
Entropic order
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New analytic constructions yield quantum lattice models with continuous symmetry breaking and chiral topological order at arbitrarily high temperatures via entropic stabilization.
Coupling to mesoscopic reservoirs generates temperature-increasing entropic barriers that suppress topological defect creation and transport, yielding three-regime correlation lengths in 1D Ising chains and double error reduction in finite-size 2D toric codes.