derived and examined thoroughly before[@dickinson_brownian_1985; @wolynes_dynamical_1977; @hernandez-contreras_brownian_1996], but for the sake of clarity and completeness they are reviewed in Appendices \[app:projection-operator-tech\] and \[app:neglecting-bath-inertia\], in particular highlighting their range of applicability. The derived LEs naturally contain the full rotational-translational coupling which is crucial in the DDFT derivation that follows. In Section \[sec:continuity-current-equation\], we follow[@goddard_general_2012; @goddard_unification_2013] and integrate the Kramer’s equation over all but one particle, yielding a continuity equation for the density distribution and a time-evolution equation for the current. At this point we require closure approximations to obtain a final equation dependent on the density distribution only. These approximations, discussed in detail in Section \[sec:extended-unified-DDFT\], are: (i) the local-equilibrium approximation for the one-body distribution function; (ii) the adiabatic approximation involving the equilibrium free-energy functional; (iii) separation of the $N$-body distribution into local equilibrium and non-equilibrium contributions; and (iv) an approximation for the two-body interactions. We then arrive at the central result of this work, i.e. a generalised DDFT equation to describe systems of orientable particles taking account of both inertia and HIs. Finally, we compare our derived DDFT with previous DDFTs. As expected, if the rotational degrees of freedom are ignored, our DDFT reduces to the one obtained for point-like 