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We use kinetic Monte Carlo simulations to investigate current fluctuations in boundary driven generalized exclusion processes, in different dimensions. Simulation results are in full agreement with predictions based on the additivity principle and the macroscopic fluctuation theory. The current statistics are independent of the shape of the contacts with the reservoirs, provided they are macroscopic in size. In general, the current distribution depends on the spatial dimension. For the special cases of the symmetric simple exclusion process and the zero-range process, the current statistics are the same for all spatial dimensions. ; We thank Christian Van den Broeck for bringing this problem to our attention. We are grateful to Bart Partoens and Carlo Vanderzande for a careful reading of the manuscript. This work was supported by the Flemish Science Foundation (Fonds Wetenschappelijk Onderzoek), Project No. G038811N. The computational resources and services used in this work were provided by the VSC (Flemish Supercomputer Center), funded by the Hercules Foundation and the Flemish Government-department EWI.

We study the adsorption and desorption kinetics of interacting particles moving on a one-dimensional lattice. Confinement is introduced by limiting the number of particles on a lattice site. Adsorption and desorption are found to proceed at different rates, and are strongly influenced by the concentration-dependent transport diffusion. Analytical solutions for the transport and self-diffusion are given for systems of length 1 and 2 and for a zero-range process. In the last situation the self- and transport diffusion can be calculated analytically for any length. ; This work was supported by the Flemish Science Foundation (FWO-Vlaanderen). The computational resources and services used in this work were provided by the VSC (Flemish Supercomputer Center), funded by the Hercules Foundation and the Flemish Government – department EWI.