An analysis of several many-body models shows that spatially localized conserved quantities uniformly fragment the Hilbert or configuration space, yet leave energy transport properties unchanged. The study covers the quantum Volterra model, its nonintegrable classical limit, and two cellular automata derived from the latter. Although such constraints are often associated with lattice gauge theories, the models considered here admit no such interpretation.

In the quantum Volterra model, the authors derive an exact mapping of the dynamics within each Hilbert-space fragment onto a quantum chiral Potts chain. With this tool in hand, they show that energy transport is ballistic and that the transport coefficients are identical across all fragments: the fragmentation does not create sectors with slower or faster dynamics.

In the nonintegrable classical limit, energy transport becomes diffusive, but the conclusion is analogous: the diffusion constant turns out to be independent of whether the constraints are fixed or resolved. The cellular automata further confirm that, while transport remains intact, localized constraints lead to a strong breakdown of local ergodicity.

The upshot is a picture in which fragmentation and transport decouple: the presence of many local conserved quantities suffices to prevent ergodic exploration of configuration space, but not to modify how energy propagates. Whether this decoupling survives in systems with continuous degrees of freedom or in the presence of long-range interactions, where fragmentation might cease to be uniform, remains an open question.