Greifswald Physics Colloquium: Horst-Holger Boltz (Greifswald): Kinetic theory beyond mean-field for generalized dynamics in active matter

This talk addresses the fundamental challenges in classical statistical physics that arise when bridging agent-level dynamics to collective behavior in complex systems. Flocking of birds, motility induced phase separation, large assemblies of bacteria, driven granular particles are of interest to statistical physicists as collective phenomenona, but many of the standard tools such as ensemble theory or thermodynamic ensembles are conceptually unsuited for this type of questions.

Many complex systems feature a specific scale separation, wherein larger groups of interacting agents or units of interest are considered with emerging meso- or macroscalic behavior being of interest whereas the internal machinations on smaller scales are likely inaccessible, but definitely intractable. The generalized dynamics on the new smallest scales are often found phenomenologically and not subject to the same constraints as microscopic equations of motion. In particular, the Newtonian axioms and conservation laws of standard mechanics are no longer valid: stored energy can be used to drive the system out-of-equilibrium, interactions can be based on perception and therefore non-reciprocal.

I will introduce active matter as a concept and experimental reality and highlight some of the key findings that constitute "new physics" in these systems. We will see that an effective equilibrium treatment is only possible, if the equations of motion of a very specific, non-generic structure and I will then explain how to extend kinetic theory, an approach to statistical physics that is rooted in systematically starting from equations of motion, to such generalized, potentially stochastic dynamics. Adapting ideas originating in plasma physics, we will derive the Boltzmann- and Landau-equations the essential mesoscalic dynamic equations beyond the pervasive mean-field approximation. The technical basis of this is using the assumption of one-sided molecular chaos to close the BBGKY hierarchy, a rephrasing of the Fokker-Planck equation, equations and track correlations during interactions.