Statistical mechanics of Floquet quantum matter: exact and emergent conservation laws

Equilibrium statistical mechanics rests on the assumption of ergodic dynamics of a system modulo the conservation laws of local observables: extremization of entropy immediately gives Gibbs' ensemble (GE) for energy conserving systems and a generalized version of it (GGE) when the number of local conserved quantities (LCQ) is more than one. Through the last decade, statistical mechanics has been extended to describe the late-time behavior of periodically driven (Floquet) quantum matter starting from a generic state. The structure built on the fundamental assumptions of ergodicity and identification of the relevant ``conservation laws" in this inherently non-equilibrium setting. More recently, it has been shown that the statistical mechanics has a much richer structure due to the existence of {\it emergent} conservation laws: these are approximate but stable conservation laws arising {\it due to the drive}, and are not present in the undriven system. Extensive numerical and analytical results support the perpetual stability of these emergent (though approximate) conservation laws, probably even in the thermodynamic limit. This banks on the recent finding of a sharp ergodicity threshold for Floquet thermalization in clean, interacting non-integrable Floquet systems. This opens up a new possibility of stable Floquet engineering in such systems. This review intends to give a theoretical overview of these developments. We conclude by briefly surveying the experimental scenario.