Statistical Power-Law Spectra due to Reservoir Fluctuations

distributions also can be viewed as an approximation for arbitrary particle number distributions in the reservoir up to s ubleading (second) order in the canonical expansion ! ≪ E. For non-ideal systems the general expansion up to second order delivers q = 1−1/C +�T 2 /T 2 , a combined result with the heat capacity and the variance of the temperature of finit e heat bath. These quantities seem to act against each other. Here the variance of the temperature is meant for the estimator 1/S ′ (E) of the thermodynamical temperature, the latter defined by 1/T = hS ′ (E)i. This way in the Gaussian ap