Asymmetrically coupled two lane totally asymmetric simple exclusion process with extended Langmuir kinetics

The proposed study is motivated by the transport phenomena where the particle hopping, attachment, and detachment dynamics rely on the occupancy state of the corresponding site on another lane. To depict this kind of scenario, we consider an open two-lane Totally Asymmetric Simple Exclusion Process with the presence of asymmetrically coupled and extended Langmuir kinetics regulations. We have analyzed the steady-state properties of the system by calculating characteristics including phase diagrams, density profiles, phase transitions, and finite size effect. The theoretical results are captured by utilizing the framework of a mean-field theory, and it is recognized that numerical findings match closely with the Monte Carlo simulation outcomes.