  Time-dependent orbital-free DFT is an efficient method for calculating the
dynamic properties of large scale quantum systems due to the low computational
cost compared to standard time-dependent DFT. We formalize this method by
mapping the real system of interacting fermions onto a fictitious system of
non-interacting bosons. The dynamic Pauli potential and associated kernel
emerge as key ingredients of time-tependent orbital-free DFT. Using the uniform
electron gas as a model system, we derive an approximate frequency-dependent
Pauli kernel. Pilot calculations suggest that space nonlocality is a key
feature for this kernel. Nonlocal terms arise already in the second order
expansion with respect to unitless frequency and reciprocal space variable
($\frac{\omega}{q\, k_F}$ and $\frac{q}{2\, k_F}$, respectively). Given the
encouraging performance of the proposed kernel, we expect it will lead to more
accurate orbital-free DFT simulations of nanoscale systems out of equilibrium.
Additionally, the proposed path to formulate nonadiabatic Pauli kernels
presents several avenues for further improvements which can be exploited in
future works to improve the results.
