A balance network for the asymmetric simple exclusion process

We investigate a balance network for the totally asymmetric simple exclusion process (TASEP). Subsystems consisting of TASEPs are connected by bidirectional links with each other, which results in balance between every pair of subsystems. The network includes some specific important cases discussed in earlier works such as the TASEP with the Langmuir kinetics, multiple lanes and finite reservoirs. Probability distributions of particles in the steady state are exactly given in factorized forms according to their balance properties. Although the system has nonequilibrium parts, it is well described using expressions in a framework of statistical mechanics based on equilibrium states. Moreover, the overall argument does not depend on the network structures, and the knowledge obtained in this work is applicable to a broad range of problems.

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