  We are interested in exploring interacting particle systems that can be seen
as microscopic models for a particular structure of coupled transport flux
arising when different populations are jointly evolving. The scenarios we have
in mind are inspired by the dynamics of pedestrian flows in open spaces and are
intimately connected to cross-diffusion and thermo-diffusion problems holding a
variational structure. The tools we use include a suitable structure of the
relative entropy controlling TV-norms, the construction of Lyapunov functionals
and particular closed-form solutions to nonlinear transport equations, a
hydrodynamics limiting procedure due to Philipowski, as well as the
construction of numerical approximates to both the continuum limit problem in
2D and to the original interacting particle systems.
