  We investigate aspects of non-equilibrium dynamics of strongly coupled field
theories within holography. We establish a hydrodynamic description for
anomalous quantum field theories subject to a strong external field for the
first time in the literature. Within holography, we explicitly demonstrate
which transport coefficients are non-zero due to the chiral anomaly and thus
important for the transport. We show that the standard treatment of the
hydrodynamics for spontaneously broken translational invariance is more subtle
and has to be revised since the description is missing a novel thermodynamic
coefficient. Within holographic massive gravity, we lay out a road map for
extensions of hydrodynamics to momentum dissipation. Furthermore, we study the
imprint of spontaneously broken translations beyond linear response theory in
terms of periodically driven strongly coupled quantum field theories. Another
important non-equilibrium scenario specially important for the understanding of
our universe is quantum gravity in de-Sitter. Recently, the bold claim of the
so-called swampland conjectures has attracted great interest since it banishes
all stable theories of quantum gravity on de-Sitter with matter into swampland.
Within the well-defined framework of the DS/dS correspondence, we set out to
derive consistency conditions on the matter content in de-Sitter. Surprisingly,
our proposed bound is violated by any reasonable form of matter. In our
discussion, we find a novel one-parameter family of entangling surfaces. The
last chapter is dedicated to solvable irrelevant deformations in quantum field
theory -- the $T\bar T$ deformation. Within holography, we derive the
entanglement entropies for generic subintervals on a sphere. We also resolve
the confusion in the literature about a seeming mismatch between the
holographic field theory results for the entanglement entropy in general
dimensions.
