As an open system interacts with a thermal environment, fluctuations inevitably emerge in measurable quantities such as nonequilibrium particle and energy currents, or wait times between detectable events. These fluctuations can be significant in magnitude at the nanoscale, and are typically taken to be a hindrance: noise standing in the way of measuring a signal. However, as this talk will cover, the properties of probability distributions for fluctuating quantities, beyond their mean values, give rise to a rich framework for exploring hidden details of open systems and evaluating the methods used to study them.

I will introduce master equation methods and full counting statistics--techniques by which fluctuating quantities in open systems, both classical and quantum, are described and modelled. On this classical side, I will discuss how fluctuations, characterized using full counting statistics, can reveal hidden information about the nontrivial underlying network structure of continuous-time random walks. I will also address questions concerning open quantum systems, namely, in assessing the thermodynamic consistency (via fluctuation symmetry) of a quantum master equation that takes into account the effects of coherences, focusing on the case of heat transport between thermal baths at differing temperatures.