  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.
