The distribution function for a subsystem experiencing temperature fluctuations

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Abstract
A nonlinear generalization of the Landau-Lifshitz theory of hydrodynamic fluctuations for the simplest case in which only energy flux and temperature fluctuations are observed is used to derive the distribution function for a subsystem with a fluctuating temperature, which coincides with the Levy distribution taken to be one of the main results of the so-called Tsallis’s nonextensive statistics. It is demonstrated that the same distribution function is obtained from the principle of maximum of information entropy if the latter is provided by Renyi’s entropy, which is an extensive quantity. The obtained distribution function is to be used instead of the Gibbs distribution in constructing the thermodynamics of systems with significant temperature fluctuations.

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