Hydrodynamic phonon transport phenomena, like second sound, have been
observed in liquid Helium temperatures more than 50 years ago. More recently
second sound has been observed in graphite at over 200\,K using transient
thermal grating techniques. In this work we explore the signatures of second
sound in ultrafast electron diffuse scattering (UEDS) patterns. We use density
functional theory and solve the Boltzmann transport equation to determine
time-resolved non-equilibrium phonon populations and subsequently calculate
one-phonon structure factors and diffuse scattering patterns to simulate
experimental data covering the regimes of ballistic, diffusive, and
hydrodynamic phonon transport. For systems like graphite, UEDS is capable of
extracting time-dependent phonon occupancies across the entire Brillouin zone
and ultimately lead to a more fundamental understanding of the hydrodynamic
phonon transport regime.Comment: 7 pages, 4 figure