Week 28.10.2024 – 03.11.2024

A closed quantum system thermalizes in the sense of typicality, if any initial state will reach a suitable equilibrium subspace and stay there most of the time. For non-degenerate Hamiltonians, a sufficient condition for thermalization is the eigenstate thermalization hypothesis (ETH). Shiraishi and Tasaki recently proved the ETH for a perturbation of the Hamiltonian of free fermions on a one-dimensional lattice. The perturbation is needed to remove the high degeneracies of the Hamiltonian. We point out that also for degenerate Hamiltonians ETH implies thermalization. Additionally, we develop another strategy for proving thermalization by adding small generic perturbations. This is joint work with Stefan Teufel, Roderich Tumulka, and Cornelia Vogel.

Classical statistical mechanics describes the macroscopic properties of large numbers of particles. It has a hidden weakness: it assumes that the microscopic forces derive from a Hamiltonian. The same mathematical object then controls both the equations of motion, and the Boltzmann distribution. This is why quantities like pressure are not only time averages of forces (on a wall), but also thermodynamic state functions (which exist independently of any wall). Active matter systems are different. Their particles take energy out of the environment, and use it for dissipative self-propulsion, violating Hamiltonian dynamics. Examples include swimming micro-organisms, and synthetic colloids propelled by optical or chemical energy. The absence of a Hamiltonian-derived detailed balance principle requires a rebuild of statistical mechanics, with some surprising outcomes. For example: (i) the pressure of an active fluid on a wall is not a state function -- it depends on the type of wall\DSEMIC (ii) various interfacial phenomena, governed in equilibrium by a single surface tension, now involve different tensions, some of which can be negative. I will survey these among other surprises and, if time allows, say how they affect kinetic questions such as nucleation rates.