  Post-starburst galaxies are typically considered to be a transition
population, en route to the red sequence after a recent quenching event.
Despite this, recent observations have shown that these objects typically have
large reservoirs of cold molecular gas. In this paper we study the star-forming
gas properties of a large sample of post-starburst galaxies selected from the
cosmological, hydrodynamical EAGLE simulations. These objects resemble observed
high-mass post-starburst galaxies both spectroscopically and in terms of their
space density, stellar mass distribution and sizes. We find that the vast
majority of simulated post-starburst galaxies have significant gas reservoirs,
with star-forming gas masses of ~10$^9$ M$_{\odot}$, in good agreement with
those seen in observational samples. The simulation reproduces the observed
time evolution of the gas fraction of the post-starburst galaxy population,
with the average galaxy losing ~90 per cent of its star-forming interstellar
medium in only ~600 Myr. A variety of gas consumption/loss processes are
responsible for this rapid evolution, including mergers and environmental
effects, while active galactic nuclei play only a secondary role. The fast
evolution in the gas fraction of post-starburst galaxies is accompanied by a
clear decrease in the efficiency of star formation, due to a decrease in the
dense gas fraction. We predict that forthcoming ALMA observations of the gas
reservoirs of low-redshift post-starburst galaxies will show that the molecular
gas is typically compact and has disturbed kinematics, reflecting the
disruptive nature of many of the evolutionary pathways that build up the
post-starburst galaxy population.
