  We develop holographic prescriptions for obtaining spectral functions in
non-equilibrium states and space-time dependent non-equilibrium shifts in the
energy and spin of quasi-particle like excitations. We reproduce strongly
coupled versions of aspects of non-equilibrium dynamics of Fermi surfaces in
Landau's Fermi-liquid theory. We find that the incoming wave boundary condition
at the horizon does not suffice to obtain a well-defined perturbative expansion
for non-equilibrium observables. Our prescription, based on analysis of
regularity at the horizon, allows such a perturbative expansion to be achieved
nevertheless and can be precisely formulated in a universal manner independent
of the non-equilibrium state, provided the state thermalizes. We also find that
the non-equilibrium spectral function furnishes information about the
relaxation modes of the system. Along the way, we argue that in a typical
non-supersymmetric theory with a gravity dual, there may exist a window of
temperature and chemical potential at large N, in which a generic
non-equilibrium state can be characterized by just a finitely few operators
with low scaling dimensions, even far away from the hydrodynamic limit.
