Dissipation induced non-Gaussian energy fluctuations

Abstract

The influence of dissipation on the fluctuation statistics of the total energy is investigated through both a phenomenological and a stochastic model for dissipative energy-transfer through a cascade of states. In equilibrium the states obey equipartition and the total energy obeys the central limit theorem, giving Gaussian fluctuations. In the presence of dissipation, the fluctuations can be driven non-Gaussian if there is macroscopic energy transfer from large to small scales. We are thus able to equate the non-Gaussian order parameter fluctuations in model equilibrium systems at criticality with energy fluctuations in these dissipative systems. Energy fluctuations in the phenomenological model map directly onto the 1/f^alpha noise problem and numerical simulations of the stochastic model yield results in qualitative agreement with these predictions.