Stimulated by the eect of the nearest neighbor interactions in vehicular trac and motor proteins, we study a 1D driven lattice gas model, in which the nearest neighbor particle interactions are taken in accordance with the thermodynamic concepts. The non-equilibrium steady-state properties of the system are analyzed under both open and periodic boundary conditions using a combination of cluster mean-field analysis and Monte Carlo simulations. Interestingly, the fundamental diagram of current versus density shows a complex behavior with a unimodal dependence for attractions and weak repulsions that turns into the bimodal behavior for stronger repulsive interactions. Specific details of system-reservoir coupling for the open system have a strong eect on the stationary phases. We produce the steady-state phase diagrams for the bulk-adapted coupling to the reservoir using the minimum and maximum current principles. The strength and nature of interaction energy has a striking influence on the number of stationary phases. We observe that interactions lead to correlations having a strong impact on the system dynamical properties. The correlation between any two sites decays exponentially as the distance between the sites increases. Moreover, they are found to be short-range for repulsions and long-range for attractions. Our results also suggest that repulsions and PAPER: Classical statistical mechanics, equilibrium and non-equilibrium

Motivated by biological transport phenomena that involve the motion of interacting molecular motors along linear filaments, we developed a theoretical framework to analyze the dynamics of interacting oligomers (extended size particles) on one-dimensional lattices. Our method extends the asymmetric simple exclusion processes for interacting monomers to particles of arbitrary size, and it utilizes cluster mean-field calculations supplemented by extensive Monte Carlo computer simulations. Interactions between particles are accounted for by a thermodynamically consistent method that views the formation and breaking bonds between particles as a chemical process. The dynamics of the system are analyzed for both periodic and open boundary conditions. It is found that the nature of the current-density relation depends on the strength of interactions, on the size of oligomers and on the way interactions influence particles transition rates. Stationary phase diagram is also fully evaluated, and it is shown how the dynamic properties depend on the interactions and on the sizes of the particles. To explain the dynamic behavior of the system particles density correlations are explicitly analyzed for dierent ranges of parameters. Theoretical calculations generally agree well with the results from the computer PAPER: Classical statistical mechanics, equilibrium and non-equilibrium

Motivated by biological transport phenomena and vehicular traffic flow we investigate the dynamics of interacting molecular motors or interacting vehicles that move along linear filaments (tracks) and can reversibly associate or dissociate from them. To analyze these processes, we introduced a model assimilating the interactions in a totally asymmetric simple exclusion process coupled with nonconserving Langmuir kinetics. The model is analyzed first using the continuum version of the simple mean-field approach that neglects the correlations between the particles. It is shown that even for weak interactions theoretical predictions deviate significantly from computer simulation results. To alleviate the problems, we developed a theoretical method that takes into account some correlations in the system. The effect of interactions on stationary phase diagrams, particle currents, and densities are explicitly evaluated. The analysis of two-point correlation function on the lattice indicates that the correlations are stronger at the locations of localized shocks. Our theoretical calculations are in excellent agreement with Monte Carlo computer simulations.

To mimic the collective motion of interacting molecular motors, we propose and discuss an open two-lane symmetrically coupled interactive TASEP model that incorporates interaction in the thermodynamically consistent fashion. We study the effect of both repulsive and attractive interaction on the system’s dynamical properties using various cluster mean field analysis and extensive Monte Carlo simulations. The interactions bring correlations into the system, which were found to be reduced due to the side motion of particles. We produce the steady-state phase diagrams for symmetrically split interaction strength. The behavior of the maximal particle current with respect to the interaction energy E is analyzed for different coupling rates and interaction splittings. The results suggest that for strong coupling and large splittings, the maximal flow of the motors occurs at a weak attractive interaction strength which matches with the known experimental results on kinesin motor protein.

Biological molecular motors are special enzymes that support biological processes such as intracellular transport, vesicle locomotion, RNA translation and many more. Experimental works suggest that the motor proteins interact among each other and moreover they experience a push by other motors during the intracellular transport. To incorporate these dynamics, we consider a variant of open one-dimensional totally asymmetric simple exclusion process with sitedependent hopping rates and interactions. The qualitative properties of our system do not depend on the hopping rate function. We utilize the simple meaneld, the cluster mean-eld, the correlated cluster mean-eld to theoretically calculate the stationary phase diagrams, density and the maximal particle current. The limitations of all the three theories are extensively discussed. It has been found that although the interactions do not change the number of phases in a phase diagram, it signi cantly changes the density pro les, the phase transition lines and the maximal particle current. The theoretical results obtained are supported by Monte Carlo simulations.