  We investigate the role of higher-form symmetries and two kinds of 't Hooft
anomalies in non-equilibrium systems. To aid our investigation, we extend the
coset construction to account for $p$-form symmetries at zero and finite
temperature. One kind of anomaly arises when a $p$-form symmetry is
spontaneously broken: in a $d+1$-dimensional spacetime there often exists an
emergent $d-p-1$-form symmetry with mixed 't Hooft anomaly. That is, the
$p$-form and $d-p-1$-form symmetries cannot be gauged simultaneously. At the
level of the coset construction, this mixed anomaly prevents the Goldstones for
the $p$- and $d-p-1$-form symmetries from appearing in the same Maurer-Cartan
form. As a result, whenever such a mixed anomaly exists, we find the emergence
of dual theories -- one involving the $p$-form Goldstone and the other
involving the $d-p-1$-form Goldstone -- that are related to each other by a
kind of Legendre transform. Such an anomaly can exist at zero and finite
temperature. The other kind of 't Hooft anomaly can only arise in
non-equilibrium systems; we therefore term it the non-equilibrium 't Hoof
anomaly. In this case, an exact symmetry of the non-equilibrium effective
action fails to have a non-trivial, conserved Noether current. This anomalous
behavior arises when a global symmetry cannot be gauged in the non-equilibrium
effective action and can arise in both open and closed systems. We construct
actions for a number of systems including chemically reacting fluids,
Yang-Mills theory, Chern-Simons theory, magnetohydrodynamic systems, and dual
superfluid and solid theories. Finally, we find that the interplay of these two
kinds of anomalies has a surprising result: in non-equilibrium systems, whether
or not a symmetry appears spontaneously broken can depend on the time-scale
over which the system is observed.
