In this talk, I will present the recent work on Kinetic Optimal Transport, due to Jan Maas, Filippo Quattrocchi, and myself.
I introduce our construction, with the definition of a second-order kinetic discrepancy between probability measures on the phase space, based on Newton's equations.
Then, I focus on the proof of our main result: absolutely continuous curves of measures in the kinetic setting are in a one-to-one correspondence with solutions to Vlasov's equations.