Anomalous scaling of dynamical large deviations

The typical values and fluctuations of time-integrated observables of nonequilibrium processes driven in steady states are known to be characterized by large deviation functions, generalizing the entropy and free energy to nonequilibrium systems. The definition of these functions involves a scaling limit, similar to the thermodynamic limit, in which the integration time $\tau$ appears linearly, unless the process considered has long-range correlations, in which case $\tau$ is generally replaced by $\tau^\xi$ with $\xi\neq 1$. Here we show that such an anomalous power-law scaling in time of large deviations can also arise without long-range correlations in Markovian processes as simple as the Langevin equation. We describe the mechanism underlying this scaling using path integrals and discuss its physical consequences for more general processes.