  Post-starburst galaxies (PSBs) belong to a short-lived transition population
between star-forming (SF) and quiescent galaxies. Deciphering their heavily
discussed evolutionary pathways is paramount to understanding galaxy evolution.
We aim to determine the dominant mechanisms governing PSB evolution in both the
field and in galaxy clusters. Using the cosmological hydrodynamical simulation
suite Magneticum Pathfinder, we identify 647 PSBs with $z \sim 0$ stellar mass
$M_* \geq 5 \cdot 10^{10} \, \mathrm{M_{\odot}}$. We track their galactic
evolution, merger history, and black hole activity over a time-span of 3.6Gyr.
Additionally, we study cluster PSBs identified at different redshifts and
cluster masses. Independent of environment and redshift, we find that PSBs,
like SF galaxies, have frequent mergers. At z=0, 89% of PSBs have experienced
mergers and 65% had at least one major merger within the last 2.5Gyr, leading
to strong star formation episodes. In fact, 23% of z=0 PSBs were rejuvenated
during their starburst. Following the mergers, field PSBs are generally
shutdown via a strong increase in AGN feedback (power output $P_{AGN,PSB} \geq
10^{56}\,$erg/Myr). We find agreement with observations for both stellar mass
functions and z = 0.9 line-of-sight phase space distributions of PSBs in galaxy
clusters. Finally, we find that $z \lesssim 0.5$ cluster PSBs are predominantly
infalling, especially in high mass clusters and show no signs of enhanced AGN
activity. Thus, we conclude that the majority of cluster PSBs are shutdown via
an environmental quenching mechanism such as ram-pressure stripping, while
field PSBs are mainly quenched by AGN feedback.
