Understanding how fluctuations propagate across spatial scales is central to our understanding of inanimate matter from turbulence to critical phenomena. In contrast to these systems, many non-equilibrium systems are organised into a spatial hierarchy of nested processes on different spatial scales, including biological and robotic systems. In this talk, I will discuss physical principles underlying the propagation of fluctuations in these multi-scale systems. I will also show how manipulating probability fluxes across spatial scales is used to perform biological signal processing.