Influence of inhomogeneous stochasticity on the falsifiability of mean-field theories and examples from accretion disc modelling

Despite spatial and temporal fluctuations in turbulent astrophysical systems, mean-field theories can be used to describe their secular evolution. However, observations taken over time scales much shorter than dynamical capture a system single state of its turbulence ensemble. Comparing with theory falsify the latter only if is additionally supplied quantified precision. The central limit theorem provides appropriate estimates precision when contribute linearly an observable constant coherent scales. Here we introduce error propagation formula that relaxes both limitations, allowing for nonlinear functional forms observables inhomogeneous amplitudes fluctuations. method exemplified context accretion disc theories, where surface temperature are propagated emission spectrum--the being non-local function former. derived depends non-monotonically on frequency. Using same method, investigate how binned spectral telescope data change resolving power. We discuss broader implications falsifiability theory.