Emergent symmetries of relativistic fluid dynamics from local ergodicity

We show that volume-preserving diffeomorphisms and the chemical shift symmetry defining relativistic Lagrangian ideal fluid dynamics can be derived as an emerging symmetry when ergodicity is assumed to apply locally in a way that is invariant under smooth spacetime foliations. This can be used as a way to derive the ideal hydrodynamic limit in a strongly coupled but strongly fluctuating medium. We comment on the connection with thermalization in small systems, the eigenstate thermalization hypothesis and deviations from the ideal limit.