  The late-time equilibrium behavior of generic interacting models is
determined by the coupled hydrodynamic equations associated with the globally
conserved quantities. In the presence of an external time-dependent drive,
non-integrable systems typically thermalize to an effectively
infinite-temperature state, losing all memory of their initial states. However,
in the presence of a large time-periodic Floquet drive, there exist special
points in phase-space where the strongly interacting system develops
approximate {\it emergent} conservation laws. Here we present results for an
exactly solvable model of two coupled chaotic quantum dots with multiple
orbitals interacting via random two and four-fermion interactions in the
presence of a Floquet drive. We analyze the phenomenology of dynamically
generated freezing using a combination of exact diagonalization, and
field-theoretic analysis in the limit of a large number of electronic orbitals.
The model displays universal freezing behavior irrespective of whether the
theory is averaged over the disorder configurations or not. We present explicit
computations for the growth of many-body chaos and entanglement entropy, which
demonstrates the long-lived coherence associated with the interacting degrees
of freedom even at late-times at the dynamically frozen points. We also compute
the slow timescale that controls relaxation away from exact freezing in a
high-frequency expansion.
