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In this paper we consider three classes of interacting particle systems on$\mathbb Z$: independent random walks, the exclusion process, and the inclusionprocess. We allow particles to switch their jump rate (the rate identifies thetype of particle) between $1$ (fast particles) and $\epsilon\in[0,1]$ (slowparticles). The switch between the two jump rates happens at rate$\gamma\in(0,\infty)$. In the exclusion process, the interaction is such thateach site can be occupied by at most one particle of each type. In theinclusion process, the interaction takes places between particles of the sametype at different sites and between particles of different type at the samesite. We derive the macroscopic limit equations for the three systems, obtainedafter scaling space by $N^{-1}$, time by $N^2$, the switching rate by $N^{-2}$,and letting $N\to\infty$. The limit equations for the macroscopic densitiesassociated to the fast and slow particles is the well-studied doublediffusivity model. This system of reaction-diffusion equations was introducedto model polycrystal diffusion and dislocation pipe diffusion, with the goal toovercome the limitations imposed by Fick's law. In order to investigate themicroscopic out-of-equilibrium properties, we analyse the system on$[N]=\{1,\ldots,N\}$, adding boundary reservoirs at sites $1$ and $N$ of fastand slow particles, respectively. Inside $[N]$ particles move as before, butnow particles are injected and absorbed at sites $1$ and $N$ with prescribedrates that depend on the particle type. We compute the steady-state densityprofile and the steady-state current. It turns out that uphill diffusion ispossible, i.e., the total flow can be in the direction of increasing totaldensity. This phenomenon, which cannot occur in a single-type particle system,is a violation of Fick's law made possible by the switching between types.

Switching interacting particle systems: scaling limits, uphill diffusion and boundary layer