Exact solution of a heterogeneous multilane asymmetric simple exclusion process

We have proved an exact solution of a multilane totally asymmetric simple exclusion process (TASEP) with heterogeneous lane-changing rates on a torus. In the expression, the TASEP in each lane and lane-changing transition can be separable. Moreover, the lane-changing transitions satisfy the detailed balance condition, and this is the key to constructing the solution. Using the saddle-point method, the current of particles has been derived in a simple form in a thermodynamic limit. It is interesting that the dynamics depends only on a set of lane-changing parameters, not on the configuration of lanes.