On the extended Kolmogorov-Nagumo information-entropy theory, the q -> 1/q duality and its possible implications for a non-extensive two dimensional Ising model
arXiv:cond-mat/0611646 · doi:10.1016/j.physa.2006.11.019
Abstract
The aim of this paper is to investigate the q -> 1/q duality in an information-entropy theory of all q-generalized entropy functionals (Tsallis, Renyi and Sharma-Mittal measures) in the light of a representation based on generalized exponential and logarithm functions subjected to Kolmogorov's and Nagumo's averaging. We show that it is precisely in this representation that the form invariance of all entropy functionals is maintained under the action of this duality. The generalized partition function also results to be a scalar invariant under the q -> 1/q transformation which can be interpreted as a non-extensive two dimensional Ising model duality between systems governed by two different power law long-range interactions and temperatures. This does not hold only for Tsallis statistics, but is a characteristic feature of all stationary distributions described by q-exponential Boltzmann factors.
arXiv comment13 pages, accepted for publication in Physica A
References in corpus (14)
- Superstatistics
- A step beyond Tsallis and Renyi entropies
- Asymptotically scale-invariant occupancy of phase space makes the entropy Sq extensive
- Axioms and uniqueness theorem for Tsallis entropy
- Stability of Tsallis antropy and instabilities of Renyi and normalized Tsallis entropies: A basis for q-exponential distributions
- Long-range interactions and non-extensivity in ferromagnetic spin models
- Generalized entropies from first principles
- When is a quantity additive, and when is it extensive?
- On the meaning of Tsallis functional in astrophysics
- Thermostatistics based on Kolmogorov-Nagumo averages: Unifying framework for extensive and nonextensive generalizations
- Phase Transitions in Non-extensive Spin Systems
- Generalized information-entropy measures and Fisher information
- Thermostatistics of extensive and non-extensive systems using generalized entropies
- On the parameter spectrum of generalized information-entropy measures with no cut-off prescriptions