  Prethermalization refers to the physical phenomenon where a system evolves
toward some long-lived non-equilibrium steady state before eventual
thermalization sets in. One general scenario where this occurs is in driven
systems with dynamics governed by an effective Hamiltonian (in some rotating
frame), such that ergodicity of the latter is responsible for the approach to
the prethermal state. This begs the question whether it is possible to have a
prethermal state not associated to any effective Hamiltonian. Here, we answer
this question in the affirmative. We exhibit a natural class of systems in
which the prethermal state is defined by emergent, global symmetries, but where
the dynamics that takes the system to this state has no additional conservation
laws, in particular energy. We explain how novel prethermal phases of matter
can nevertheless emerge under such settings, distinct from those previously
discussed.
