Driven diffusive systems are generically out of equilibrium. Iwill consider two paradigmatic examples, the asymmetric simple exclusionprocess and the zero-range process. I will discuss size effects on thebehavior of fluctuations in the nonequilibrium stationary state of these twoprocesses on a one-dimensional periodic lattice of finite size. Theexclusion process involves hard core particles executing biased diffusionwith a constant rate. In the zero-range process, particles perform biasedhopping between sites with a rate which depends on the occupancy at thedeparture site. In the stationary state, this process shows a phasetransition as a function of the particle density, from a low-densitydisordered phase to a high-density condensed phase. In both these processes,size effects interplay with the nonequilibrium dynamics to bring in richdynamical phenomena otherwise absent in equilibrium.
