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Generalized thermostatistics based on multifractal phase space

A. I. Olemskoi
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Abstract

We consider the self-similar phase space with reduced fractal dimension $d$ being distributed within domain $0 1$ of the multifractal function $τ(q)= qd(q)-f(d(q))$, being the specific heat, $q\in(1,\infty)$ is multifractal parameter. In this way, the equipartition law is shown to take place. Optimization of the multifractal spectrum $f(d)$ derives the relation between the statistical weight and the system complexity.

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A. I. Olemskoi. 2006-03-01. Generalized thermostatistics based on multifractal phase space. https://arxiv.org/abs/cond-mat/0601665

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