Fluctuations in Finite Critical and Turbulent Systems

We show that hyperscaling and finite-size scaling imply that the probability distribution of the order parameter in finite-size critical systems exhibit data collapse. We consider the examples of equilibrium critical systems, and a statistical model of ecology. We propose an explanation for recent observations that the probability distribution of turbulent power fluctuations in closed flows is the same as that of the harmonic 2DXY model.