  We propose a systematic coset construction of non-equilibrium effective field
theories (EFTs) governing the long-distance and late-time dynamics of
relativistic, finite-temperature condensed matter systems. Our non-equilibrium
coset construction makes significant advances beyond more standard coset
constructions in that it takes advantage of recently-developed techniques,
which allow the formulation of non-equilibrium effective actions that account
for quantum and thermal fluctuations as well as dissipation. Because these
systems exist at finite temperature, the EFTs live on the closed-time-path of
the Schwinger-Keldysh contour. Since the coset construction and the
non-equilibrium effective actions may be unfamiliar to many readers, we include
brief introductions to these topics in an effort to make this paper
self-contained. To demonstrate the legitimacy of this coset construction, we
successfully reproduce the known EFTs for fluids and superfluids at finite
temperature. Then, to demonstrate its utility, we construct novel EFTs for
solids, supersolids, and four phases of liquid crystals, all at finite
temperature. We thereby combine the non-equilibrium effective action and the
coset construction to create a powerful tool that can be used to study
many-body systems out of thermal equilibrium.
