Large deviations for out of equilibrium correlations in the symmetric simple exclusion process

Abstract

For finite size Markov chains, the Donsker-Varadhan theory fully describes the large deviations of the time averaged empirical measure. We are interested in the extension of the Donsker-Varadhan theory for a large size non-equilibrium system: the one-dimensional symmetric simple exclusion process connected with reservoirs at different densities. The Donsker-Varadhan functional encodes a variety of scales depending on the observable of interest. In this paper, we focus on the time-averaged two point correlations and investigate the large deviations from the steady state behaviour. To control two point correlations out of equilibrium, the key input is the construction of a simple approximation to the invariant measure. This approximation is quantitative in time and space as estimated through relative entropy bounds building on the work of Jara and Menezes arXiv:1810.09526.

arXiv commentAccepted version, added discussion of steady state entropy in the open symmetric simple exclusion process

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Cited by in corpus (1)

• Full $\Gamma$-expansion of reversible Markov chains level two large deviations rate functionals