PhD-Seminar: How to impose holonomic constraints of densities?

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A holonomic constraint between components of a classical mechanical system leads to a well-studied problem.

However, if a kinetic description for the system is used. It is not that clear how the holonomic constraint generalizes to this case. In my talk, I presented an approach to apply the ideas of kinetic theory to these systems.

In fact, I was quite happy that I found a nice formulation using push-forwards. However, a few days later I figured out that it was quite standart in kinetic theory, so the cool trick I discovered was not new at all and I had most likely seen it earlier somewhere.