Emergent entropy production and hydrodynamics in quantum many-body systems

Understand

We study dynamics of a locally conserved energy in ergodic, local many-body quantum systems on a lattice with no additional symmetry.

• The resulting dynamics is well approximated by a coarse grained, classical linear functional diffusion equation for the probability of all spatial configurations of energy.
• This is equivalent to nonlinear stochastic hydrodynamics, describing the diffusion of energy in physical spacetime.
• We find the absence of non-hydrodynamic slow degrees of freedom, a nonlinear fluctuation-dissipation theorem, and the emergence of a (weakly interacting) kinetic theory for hydrodynamic modes near thermal equilibrium.