Expansion Potentials for Exact Far-from-Equilibrium Spreading of Particles and Energy

The rates at which energy and particle densities move to equalize arbitrarily large temperature and chemical potential differences in an isolated quantum system have an emergent thermodynamical description whenever the energy or particle current commutes with the Hamiltonian. Concrete examples include the energy current in the 1D spinless fermion model with nearest-neighbor interactions (XXZ spin chain), the energy current in Lorentz-invariant theories or the particle current in interacting Bose gases in arbitrary dimension. Even far from equilibrium, these rates are controlled by state functions, which we call "expansion potentials," expressed as integrals of equilibrium Drude weights. This relation between nonequilibrium quantities and linear response implies nonequilibrium Maxwell relations for the Drude weights. We verify our results via density-matrix renormalization group calculations for the XXZ chain.