Statistical mechanics is one of the foundational pillars of modern physics. At its core is the idea of thermal equilibrium, which allows for a simple description of a many-particle system in terms of a few macroscopic, equilibrium properties like temperature or pressure. Although many of the fundamentals of quantum statistical mechanics were formulated almost a century ago, recent developments have motivated a rebirth of this subject.
In this talk, I will discuss some recent advances in our understanding of quantum statistical mechanics, focusing in particular on settings in which systems fail to reach thermal equilibrium.  This out-of-equilibrium setting can allow for novel phases of matter which are disallowed by the usual rules of statistical mechanics. This includes the recent discovery of time-crystals as a new out-of-equilibrium phase of matter, and I'll describe our work in predicting and creating these time-crystalline phases.