  Understanding transport processes in complex nanoscale systems, like ionic
conductivities in nanofluidic devices or heat conduction in low dimensional
solids, poses the problem of examining fluctuations of currents within
nonequilibrium steady states and relating those fluctuations to nonlinear or
anomalous responses. We have developed a systematic framework for computing
distributions of time integrated currents in molecular models and relating
cumulants of those distributions to nonlinear transport coefficients. The
approach elaborated upon in this perspective follows from the theory of
dynamical large deviations, benefits from substantial previous formal
development, and has been illustrated in several applications. The framework
provides a microscopic basis for going beyond traditional hydrodynamics in
instances where local equilibrium assumptions break down, which are ubiquitous
at the nanoscale.
