Nonlinear Vlasov-Fokker-Planck dynamics admit a GENERIC structure that reduces to a generalized Wasserstein gradient flow whose trajectorial dissipation captures the nonlinear interaction and whose partial degeneracy produces a metric decomposition supporting a partial HWI inequality.
Kac, Foundations of kinetic theory.Proceedings of the Third Berkeley Symposium on Mathematical Sta- tistics and Probability, 1954–1955, vol
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Nonlinear Vlasov-Fokker-Planck equations: From generalized Wasserstein gradient flow to GENERIC structure
Nonlinear Vlasov-Fokker-Planck dynamics admit a GENERIC structure that reduces to a generalized Wasserstein gradient flow whose trajectorial dissipation captures the nonlinear interaction and whose partial degeneracy produces a metric decomposition supporting a partial HWI inequality.