Generalized thermostatistics based on multifractal phase space

We consider the self-similar phase space with reduced fractal dimension d being distributed within domain 0 < d < 1 with spectrum f(d). Related thermostatistics is shown to be governed by the Tsallis’ formalism of the non-extensive statistics, where role of the non-additivity parameter plays inverted value τ̄(q) ≡ 1/τ(q) > 1 of the multifractal function τ(q) = qd(q)− f(d(q)), being the specific heat, q ∈ (1,∞) 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.