Nonequilibrium phase transitions in a two-channel ASEP with binding energies and analytical evaluations via Kullback–Leibler divergence

In order to reflect new physical insights in understanding nonequilibrium phase transition mechanisms of real mesoscopic transport, a new exclusion process with horizontal and vertical binding energies is constructed. Fruitful developments of mean-field theories including developed simple, 2-lattice cluster, 4-lattice cluster and correlation mean-field theories are given. Typical order parameters are analytically solved and verified by simulation statistics. Evolution laws of phase boundaries with varied lane-changing rates, mobilities and binding energies are found via acquisitions of density profiles and phase diagrams. Fitting effects of developed analytical methods are quantitatively compared via Kullback–Leibler divergence. Findings show that developed simple mean-field theory (SMF) achieves better results in the fitting of each phase, while developed 2-lattice cluster mean-field theory (CMF) has better results in the fitting of low-density and coexistence phases. Developed 4-lattice CMF has better results in fitting low-density phase and high-density part of coexistence one, and developed correlation cluster mean-field theory (CCMF) has better results in the fitting except high-density phase. The minimum correlation element is introduced to explain differences among evaluations of analytical solutions under Kullback–Leibler divergence. The minimum correlation element size of SMF, CCMF, 2-lattice CMF and 4-lattice one is found to be 1, 1.5, 2 and 4, respectively. Intrinsic dynamics are found to have a great impact on analysis solutions, which indicate that analytical results brought by different minimum correlation elements need to be comprehensively considered to determine correlation degree, although evaluation results reveal that deviations between analytical solutions and simulation results increase with the minimum size of the related element. Effectiveness of developed theories is achieved in a more scientifically sound manner, which is helpful for evaluating rationality and effectiveness of analytical methods and critical phenomena of spatial correlations in nonequilibrium multi-body particle interaction systems.