Phase transitions in two-channel TASEPs based on a new method of cluster mean-field analyses

A molecular motor transport model which is much closer to the actual situation is studied in this work. The two-chain totally asymmetric simple exclusion process (TASEP) with transverse and longitudinal binding energy is proposed, where particles transport in parallel. A new analytical method of cluster mean-field (CMF) analysis is proposed, which fully considers the boundary effects. The given new method of CMF is found to greatly improve the analytical accuracy of the traditional CMF and simple mean-field (SMF) analyses. Since the interactions among particles in the two channels are heavily considered, the state of the system is found to be sensitive to the change of external energy. Phase diagram and its evolution and the relationship between average density and total flux in the chain are found to be affected by the participation of energy. At the same time, a platform is found in the relationship curve reflecting total current versus average density. This relationship curve is also found to be symmetry to the average density 0.5. This paper presents a new system based on TASEPs in terms of the chain number and coupling binding energy. It will be conducive for proposing physical systems of real active systems and providing a new way for future research on real transport of molecular motors depicted by TASEPs.