Inertia and hydrodynamic interactions in dynamical density functional theory

We study the dynamics of a colloidal fluid in the full position-momentum phase space, including hydrodynamic interactions, which strongly influence the non-equilibrium properties of the system. For large systems, the number of degrees of freedom prohibits direct simulation and a reduced model is necessary. Under standard assumptions, we derive a dynamical density functional theory (DDFT), which is a generalisation of many existing DDFTs, and shows good agreement with stochastic simulations.