  We introduce a spatially extended transport kinetic FitzHugh-Nagumo model
with forced local interactions and prove that its hydrodynamic limit converges
towards the classical nonlocal reaction-diffusion FitzHugh-Nagumo system. Our
approach is based on a relative entropy method, where the macroscopic
quantities of the kinetic model are compared with the solution to the nonlocal
reaction-diffusion system. This approach allows to make the rigorous link
between kinetic and reaction-diffusion models.
