We first introduce a class of 1D translationally invariant and local classical and quantum dynamics that have an unusual approach to equilibrium. In one of our examples, expectation values of local operators relax in a time which is exponentially large in system size, implying an unusual kind of hydrodynamics. In another example, a system can only relax when coupled to a bath which is at least exponentially large in the system's size, a phenomenon that we call fragile fragmentation. A field of mathematics called geometric group theory plays an important role in constructing these examples. We then consider ground states of a two-dimensional generalizations of these models and find a plethora of unusual entanglement properties such as (1) area laws emerging entirely from long range correlations and (2) power law violations of area law scaling.
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