Entropies based on fractional calculus
arXiv:0902.2726 · doi:10.1016/j.physleta.2009.05.026
Abstract
We propose entropy functions based on fractional calculus. We show that this new entropy has the same properties than the Shannon entropy except additivity, therefore making this entropy non-extensive. We show that this entropy function satisfies the Lesche and thermodynamic stability criteria.
9 pages, two figures, references added, proof on Lesche's stability has been corrected
References in corpus (8)
- A Formulation of Noether's Theorem for Fractional Problems of the Calculus of Variations
- Stability of Tsallis antropy and instabilities of Renyi and normalized Tsallis entropies: A basis for q-exponential distributions
- Gauge invariance in fractional field theories
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- Stabilities of generalized entropies
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- Least informative distributions in Maximum q-log-likelihood estimation
- Boltzmann-Gibbs entropy is sufficient but not necessary for the likelihood factorization required by Einstein
- Inter-occurrence times and universal laws in finance, earthquakes and genomes
- Shannon Entropy Reinterpreted
- Extended fractional cumulative past and paired phi-entropy measures
- Extensions of the Shannon Entropy and the Chaos Game Algorithm to Hyperbolic Numbers Plane
- Reconciling fractional entropy and black hole entropy compositions
- Group theory, entropy and the third law of thermodynamics
- Density matrix for a consistent non-extensive thermodynamics
- A note on the connection between non-additive entropy and -derivative