96-219 C. Landim and H.-T. Yau

Fluctuation--dissipation equation of asymmetric simple exclusion processes (281K, ps) May 21, 96

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Abstract. We consider asymmetric simple exclusion processes on the lattice $\Bbb Z^d$ in dimension $d\ge 3$. We denote by $L$ the generator of the process, $\nabla$ the lattice gradient, $\eta$ the configuration, and $w$ the current of the dynamics associated to the conserved quantity. We prove that the fluctuation--dissipation equation $w = L u + D \nabla \eta $ has a solution for some function $u$ and some constant $D$ identified to be the diffusion coefficient. Intuitively, $Lu$ represents rapid fluctuation and this equation describes a decomposition of the current into fluctuation and gradient of the density field, representing the dissipation.

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