Diffusive hydrodynamics of inhomogenous Hamiltonians

Abstract We derive a large-scale hydrodynamic equation, including diffusive and dissipative effects, for systems with generic static position-dependent driving forces coupling to local conserved quantities. show that this equation predicts entropy increase thermal states as the only stationary states. The applies any system number of local, parity time-symmetric quantities, in arbitrary dimension. It is fully expressed terms elements an extended Onsager matrix. In integrable systems, matrix admits expansion density excitations. evaluate exactly its two-particle–hole contribution, which dominates at low density, scattering phase dispersion quasiparticles, giving lower bound production. conclude molecular dynamics simulation, demonstrating thermalisation over time scales Toda interacting particle model inhomogeneous energy field.