Finite size effects in fluctuating hydrodynamics

We analyze the large deviation properties in the simple symmetric exclusion process (SSEP) with periodic boundary conditions. Our interest goes to the total current and to the number of configuration changes the system has undergone over an asymptotically large time window. Exact results are provided for the one-dimensional case. We show how universal features, reaching beyond the particular case of the SSEP, are seen to emerge from the incorporation of finite size effects into the fluctuating hydrodynamics approach.