The exact phase diagram for a class of open multispecies asymmetric exclusion processes

Abstract

The asymmetric exclusion process is an idealised stochastic model of transport, whose exact solution has given important insight into a general theory of nonequilibrium statistical physics. In this work, we consider a totally asymmetric exclusion process with multiple species of particles on a one-dimensional lattice in contact with reservoirs. We derive the exact nonequilibrium phase diagram for the system in the long time limit. We find two new phenomena in certain regions of the phase diagram: dynamical expulsion when the density of a species becomes zero throughout the system, and dynamical localisation when the density of a species is nonzero only within an interval far from the boundaries. We give a complete explanation of the macroscopic features of the phase diagram using what we call nested fat shocks.

The Phase Diagram for a Multispecies Left-Permeable Asymmetric Exclusion Process

“…Therefore, the 0's have zero density in the system leading to a high density of 1's in the system. This phenomenon is known as dynamical expulsion [20], where the boundary parameters cause a species to be absent in the bulk of the system only in certain phases. In phase 0 (the low density or LD phase), the shock has positive drift and gets pinned to the right of the system.…”

“…To derive the phase diagram, we will construct a series of exact projections from the odd mLPASEP to the LPASEP. This strategy was successfully used to derive the exact phase diagram for the mASEP [20]. The projection is called the k-colouring and is explained below.…”

“…It was first considered by Cantini, Garbali, de Gier and Wheeler, who proved a formula for the nonequilibrium partition function in [19]. The phase diagram of the mASEP was understood by the first and the third author in [20] using exact projections by the so-called colouring technique. This idea was earlier used to understand the phase diagram of open two-species ASEPs in [9,10,12].…”

Dependence of the transportation time on the sequence in which particles with different hopping probabilities enter a lattice

“…Studies on multi-species ASEP with open boundaries and random updating were undertaken only recently [37,40,41,44,45,52,55]; for example, Ref. [55] obtained the exact phase diagram for a multi-species (more than two-species) ASEP. The present investigation primarily focuses on the problem of minimizing the transportation time, adopting open-boundary conditions and parallel updating.…”

OpenEPSim: An Open Exclusion Process Simulation Tool

“…Kolomeisky et al 1998), and simulation studies. However, there is ongoing interest in extensions and variations of the model -some examples include (Crampe et al 2016;Ayyer and Roy 2017;Ayyer, Finn, and Roy 2018). The aim of OpenEPSim is to make simulating such variations as simple as defining the model mathematically.…”