Entropy-cost type Propagation of Chaos for Mean Field Particle System with Bounded Measurable Interaction

In this paper, the quantitative entropy-cost type propagation of chaos for mean field interacting particle system is obtained, where the interaction is only assumed to be bounded measurable and the initial distribution of a single particle converges to that of the corresponding McKean-Vlasov SDEs in $L^1$-transportation cost ${\text{W}}_1^{\mathrm{\Psi }}$ induced by some cost function $\mathrm{\Psi }$. The mean field interacting particle system with common noise is also investigated and the quantitative entropy-cost type conditional propagation of chaos is established. The results weaken the initial assumption of the existing entropy-entropy type propagation of chaos in some sense.