  We introduce new classes of hydrodynamic theories inspired by the recently
discovered fracton phases of quantum matter. Fracton phases are characterized
by elementary excitations (fractons) with restricted mobility. The hydrodynamic
theories we introduce describe thermalization in systems with fracton-like
mobility constraints, including fluids where charge and dipole moment are both
locally conserved, and fluids where charge is conserved along every line or
plane of a lattice. Each of these fluids is subdiffusive, and constitutes a new
universality class of hydrodynamic behavior. There are infinitely many such
classes, each with distinct subdiffusive exponents, all of which are captured
by our formalism. Our framework naturally explains recent results on dynamics
with constrained quantum circuits, as well as recent experiments with ultracold
atoms in tilted optical lattices. We identify crisp experimental signatures of
these novel hydrodynamics, and explain how they may be realized in near term
ultracold atom experiments.
