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In this paper, we propose a general way of computing expectation values inthe zero-range process, using an exact form of the partition function. As anexample, we provide the fundamental diagram (the flux-density plot) of theasymmetric exclusion process corresponding to the zero-range process.We expressthe partition function for the steady state by the Lauricella hypergeometricfunction, and thereby have two exact fundamental diagrams each for the paralleland random sequential update rules. Meanwhile, from the viewpoint ofequilibrium statistical mechanics, we work within the canonical ensemble butthe result obtained is certainly in agreement with previous works done in thegrand canonical ensemble.Comment: 12 pages, 2 figure

Exact solution of the zero-range process: fundamental diagram of the corresponding exclusion process