  We consider the effects of long-range temporal correlations in many-particle
systems, focusing particularly on fluctuations about the typical behaviour. For
a specific class of memory dependence we discuss the modification of the large
deviation principle describing the probability of rare currents and show how
superdiffusive behaviour can emerge. We illustrate the general framework with
detailed calculations for a memory-dependent version of the totally asymmetric
simple exclusion process as well as indicating connections to other recent
work.
