For asymmetric partial exclusion processes with product jump rates, the gradient condition is equivalent to product invariant measures, and fluctuations converge to the stationary energy solution of the stochastic Burgers equation.
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Characterization of Gradient Condition for Asymmetric Partial Exclusion Processes and Their Scaling Limits
For asymmetric partial exclusion processes with product jump rates, the gradient condition is equivalent to product invariant measures, and fluctuations converge to the stationary energy solution of the stochastic Burgers equation.