  Gas infalling into the gravitational potential wells of massive galaxy
clusters is expected to experience one or more shocks on its journey to
becoming part of the intracluster medium (ICM). These shocks are important for
setting the thermodynamic properties of the ICM and can therefore impact
cluster observables such as X-ray emission and the Sunyaev-Zel'dovich (SZ)
effect. We investigate the possibility of detecting signals from cluster shocks
in the averaged thermal SZ profiles of galaxy clusters. Using zoom-in
hydrodynamic simulations of massive clusters from the Three Hundred Project, we
show that if cluster SZ profiles are stacked as a function of $R/R_{200m}$,
shock-induced features appear in the averaged SZ profile. These features are
not accounted for in standard fitting formulae for the SZ profiles of galaxy
clusters. We show that the shock features should be detectable with samples of
clusters from ongoing and future SZ surveys. We also demonstrate that the
location of these features is correlated with the cluster accretion rate, as
well as the location of the cluster splashback radius. Analyses of ongoing and
future surveys, such as SPT-3G, AdvACT, Simons Observatory and CMB-S4, that
include gas shocks will gain a new handle on the properties and dynamics of the
outskirts of massive halos, both in gas and in mass.
