  This thesis considers out-of-equilibrium dynamics of strongly interacting
non-relativistic Fermi gases in several two and three dimensional geometries.
The tools of second-order hydrodynamics and gauge-gravity duality will be
utilized to address this system. Many of the themes of this work are motivated
by the observed similarities in transport properties between strongly
interacting Fermi gases and other very different strongly interacting quantum
fluids such as the quark-gluon plasma, high temperature superconductors, and
quantum field theories described by gauge-gravity duality. In particular, these
systems all nearly saturate the conjectured lower bound on the ratio of shear
viscosity to entropy density $\eta/s \geq \hbar/(4 \pi k_B)$ coming from the
AdS/CFT correspondence. Among other things, this observation, in conjunction
with current experiment and data analysis in atomic, condensed matter, and
nuclear physics lends itself to the following questions: How perfect of a fluid
is the strongly interacting Fermi gas, and can one find a more stringent
constraint on $\eta/s$ in Fermi gases? Do the similarities in transport
properties among strongly interacting quantum systems extend beyond dynamics
controlled by the hydrodynamical shear viscosity? In regards to the first
question, by utilizing second-order hydrodynamics, it will be demonstrated that
higher-order collective modes of a harmonically trapped Fermi gas may serve as
a more sensitive probe of the shear viscosity. For the second question, both
second-order hydrodynamics and a gravity dual theory are used to make
predictions about dynamics occurring on short timescales where hydrodynamics is
expected to break down. In particular the appearance of a class of
"non-hydrodynamic" collective modes not contained within a Navier-Stokes
description of the strongly interacting Fermi gas will be discussed.
