Nonequilibrium fluctuations and moderate deviations for the occupation time of the SSEP with Glauber dynamics

We study the symmetric simple exclusion process with Glauber dynamics. When the process starts from a nonequilibrium measure, we prove central limit theorems for the occupation time in dimension two, and sample path moderate deviation principles in dimension one. For the fluctuations, we use the martingale method and the sharp relative entropy method from [Jara and Menezes, arXiv:1810.09526]. For the moderate deviations, the main idea is to relate the occupation time to the density fluctuation field by using the logarithmic Sobolev inequality from the Glauber dynamics.