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This paper links at the formal level the entropy structure of a multi-speciescross-diffusion system of Shigesada-Kawasaki-Teramoto (SKT) type satisfying thedetailed balance condition with the entropy structure of a reversiblemicroscopic many-particle Markov process on a discretised space. The link isestablished by first performing a mean-field limit to a master equation overdiscretised space. Then the spatial discretisation limit is performed in acompletely rigorous way. This by itself provides a novel strategy for provingglobal existence of weak solutions to a class of cross-diffusion systems.

About the entropic structure of detailed balanced multi-species cross-diffusion equations