Current reversal and exclusion processes with history-dependent random walks

A class of exclusion processes in which particles perform
history-dependent random walks is introduced, stimulated by dynamic
phenomena in some biological and artificial systems. The particles
locally interact with the underlying substrate by breaking and
reforming lattice bonds. We determine the steady-state current on a
ring, and find current-reversal as a function of particle density.
This phenomenon is attributed to the non-local interaction between
the walkers through their trails, which originates from strong
correlations between the dynamics of the particles and the lattice.
We rationalize our findings within an effective description in
terms of quasi-particles which we call front barriers. Our
analytical results are complemented by stochastic simulations.