2018/09/10 by Davide Botto, D Botto, Alessandro Pelizzola +5
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Asymmetric simple exclusion process #Dynamical systems theory #Nonlinear system #Order (exchange) #Relaxation (psychology) #Simple (philosophy) #Singularity #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Transition rate matrix #cond-mat.stat-mech #math-ph #math.MP #nlin.CG
paper · pdf · doi:10.1088/1751-8121/aaf1f8
published as J. Phys. A: Math. Theor. 52, 045001 (2019) · 37 pages (including 16 appendix pages), 6 figures. Submitted to Journal of Physics A
arxiv created 2018/09/10 · openalex created_date 2018/09/27 · openalex publication_date 2018/11/19 · arxiv updated 2020/08/11 · openalex updated_date 2026/08/06
Abstract We develop a mean-field theory for the totally asymmetric simple exclusion process (TASEP) with open boundaries in order to investigate the so-called dynamical transition . The latter phenomenon appears as a singularity in the relaxation rate of the system toward its non-equilibrium steady state. In the high-density (low-density) phase, the relaxation rate becomes independent of the injection (extraction) rate at a certain critical value of the parameter itself, and this transition is not accompanied by any qualitative change in the steady-state behavior. We characterize the relaxation rate by means of bounds, becoming tight in the thermodynamic limit. These results are generalized to the TASEP with Langmuir kinetics, where particles can also bind to empty sites or unbind from occupied ones in the symmetric case of equal binding/unbinding rates. The theory predicts that a dynamical transition will occur in this case as well.