  We use an analytic model to investigate the theoretical uncertainty on the
thermal Sunyaev-Zel'dovich (SZ) power spectrum due to astrophysical
uncertainties in the thermal structure of the intracluster medium. Our model
accounts for star formation and energy feedback (from supernovae and active
galactic nuclei) as well as radially dependent non-thermal pressure support due
to random gas motions, the latter calibrated by recent hydrodynamical
simulations. We compare the model against X-ray observations of low redshift
clusters, finding excellent agreement with observed pressure profiles. Varying
the levels of feedback and non-thermal pressure support can significantly
change both the amplitude and shape of the thermal SZ power spectrum.
Increasing the feedback suppresses power at small angular scales, shifting the
peak of the power spectrum to lower ell. On the other hand, increasing the
non-thermal pressure support has the opposite effect, significantly reducing
power at large angular scales. In general, including non-thermal pressure at
the level measured in simulations has a large effect on the power spectrum,
reducing the amplitude by 50% at angular scales of a few arcminutes compared to
a model without a non-thermal component. Our results demonstrate that
measurements of the shape of the power spectrum can reveal useful information
on important physical processes in groups and clusters, especially at
high-redshift where there exists little observational data. Comparing with the
recent South Pole Telescope measurements of the small-scale cosmic microwave
background power spectrum, we find our model reduces the tension between the
values of sigma_8 measured from the SZ power spectrum and from cluster
abundances.
