Title:
On the Derivation of Power-Law Distributions in the Canonical Ensemble
Author(s):
Rudolf Hanel, Stefan Thurner
Paper #:
04-06-013
Date:
June 1, 2004
Abstract:
We note the possibility within classical thermodynamics to derive power-law distributions in the canonical ensemble. We do so by systematically finding a class of microcanonical distributions that allow for a separation of the total system energy from the reservoir. We demonstrate that all separable distributions are parametrized by a separation constant Q which is one to one related to the q parameter in Tsallis distributions. The power-laws obtained are formally(!) equivalent to those obtained by maximizing Tsallis entropy under q constraints. We comment on the possibility in finite systems that the equilibrium point and the expectation value do not coincide, and show that also for that case the variational principle holds after a transformation of variables. These results might help to explain the ubiquity of Tsallis distributions in nature.
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