Abstract
We obtain the large deviation functional of a density profile for the asymmetric exclusion process of L sites with open boundary conditions when the asymmetry scales like 1L . We recover as limiting cases the expressions derived recently for the symmetric (SSEP) and the asymmetric (ASEP) cases. In the ASEP limit, the nonlinear differential equation one needs to solve can be analysed by a method which resembles the WKB method.
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Enaud, C., Derrida, B. Large Deviation Functional of the Weakly Asymmetric Exclusion Process. Journal of Statistical Physics 114, 537–562 (2004). https://doi.org/10.1023/B:JOSS.0000012501.43746.cf
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DOI: https://doi.org/10.1023/B:JOSS.0000012501.43746.cf