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.
Highlights
The one-dimensional asymmetric simple exclusion process (ASEP) with open boundaries has been of great importance as a model system towards understanding nonequilibrium phenomena
The mASEP is defined on a one-dimensional lattice of size n, where each site is occupied by exactly one particle of type {r, ..., 1, 0, 1, ..., r}
In all phases except, the system shows phase coexistence with a sharp interface separating intervals of different density for some particle type, as we show by the illustrative density profiles in Fig. 1 for the mTASEP with r = 2 and Supplementary Fig. S2 for the mASEP with r = 1
Summary
The one-dimensional asymmetric simple exclusion process (ASEP) with open boundaries has been of great importance as a model system towards understanding nonequilibrium phenomena. The matrix ansatz, which has since become an important tool[1], was developed to compute the nonequilibrium steady state (NESS) of the totally asymmetric version of the single-species ASEP2 (TASEP). Using this ansatz, various measurable quantities such as the density and current were calculated in the NESS, from which the exact nonequilibrium phase diagram was derived. The large deviation functional for the density profiles[5] and the large deviation function for the current[6,7] was derived using the matrix ansatz These calculations helped in the formulation of two general principles for driven diffusive systems; the additivity principle[8] and the macroscopic fluctuation theory[9].
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