From Boltzmann to black holes - many-particle systems in non-equilibrium

The Boltzmann distribution is the starting point for the description of equilibrium many-particle systems in statistical mechanics textbooks. For isolated many-particle systems the situation is actually both more complicated and more interesting than alluded to by conventional textbook treatments. This colloquium presents a closer look at the foundations of statistical mechanics; a topic that has seen a lot of interest in the past decade triggered by experiments on cold atomic gases. There is a plethora of interesting phenomena associated with this question ranging from the Fermi-Pasta-Ulam-Tsingou problem to spin echo experiments, the Unruh effect and black holes. I will give an overview of some key questions, current answers and future directions of research.