Non-equilibrium phase transition in the heterogenous TASEPs with binding and unbinding processes among the adjacent subsystems

Non-equilibrium phase transition is always one of the most important issue for complexity science, since it can reveal physical mechanisms of abundant physical phenomena. Exploring applications of non-equilibrium phase transitions in basic paradigm models of complexity science is vital for better comprehending essences of real physical processes. Among these processes, totally asymmetric simple exclusion process (TASEP) stands out owing to important theoretical significances and practical value, whose importance is regarded as being equivalent to Ising model. In this paper, a heterogeneous interacting particle system constituted by three-lane TASEPs with binding and unbinding processes affected by interacting energies among adjacent subsystems is proposed. Nonlinear equations about all particle configuration states of boundaries and bulk are established. We find and analyze numerical local densities and currents by performing simple and cluster mean-field analyses. Nine species of phases including homogeneous phases and mixed ones are discovered. Specifically, as for mixed phases, densities of middle channel are much larger and smaller than those of neighboring ones when specific interacting energy is positive and negative, respectively. All triple points are found to move to upper left corner of phase space with increasing interacting energy. Current phase diagrams mapped into density phase ones are explored, which reveal currents in homogenous phases rely on just one critical governing parameter (namely, injecting rate or escaping one) while those in mixed phases are controlled by the coupling effects of these two critical governing rates. Theoretical results from mean-field analyses are confirmed by simulations, which yield to fine coincidences. This work will improve understanding of non-equilibrium phase transition mechanisms in such basic paradigm models and stochastic dynamics in corresponding critical phenomena to a certain extent, especially cluster effects and related dynamic processes of self-driven particles in such systems in the area of complex system science and statistical physics at mesoscopic scale.