2 5 N ov 2 00 6 On the extended Kolmogorov - Nagumo information - entropy theory , the q → 1 q duality and its possible implications for a non - extensive two dimensional

Nongeneralizability of Tsallis Entropy by means of Kolmogorov-Nagumo averages under pseudo-additivity

As additivity is a characteristic property of the classical information measure, Shannon entropy, pseudo-additivity of the form x+qy = x+y+(1−q)xy is a characteristic property of Tsallis entropy. Rényi in [1] generalized Shannon entropy by means of Kolmogorov-Nagumo averages, by imposing additivity as a constraint. In this paper we show that there exists no generalization for Tsallis entropy, b...

ar X iv : q ua nt - p h / 04 11 17 2 v 1 2 3 N ov 2 00 4 Information and Entropy in Quantum Theory

1 N ov 2 00 3 Semistable abelian Varieties over Q

We prove that for N = 6 and N = 10, there do not exist any non-zero semistable abelian varieties over Q with good reduction outside primes dividing N . Our results are contingent on the GRH discriminant bounds of Odlyzko. Combined with recent results of Brumer–Kramer and of Schoof, this result is best possible: if N is squarefree, there exists a non-zero semistable abelian variety over Q with g...

Black Holes: Fermions at the Extremal Limit?

I present exact results matching Kerr-Newman Black Hole thermodynamics in the extremal limit to the two-dimensional Fermi Gas. Two dimensions are consistent with the membrane paradigm of black holes. Key in the analysis is the thermodynamic Riemannian curvature scalar R, negative for most ordinary thermodynamic systems, including those near the critical point, but mostly positive for the Kerr-N...

Generalized thermostatistics and Kolmogorov-Nagumo averages

We introduce a generalized thermostatistics based on Kolmogorov-Nagumo averages and appropriately selected information measures. The formalism includes Tsallis non-extensive thermostatistics, but also extensive thermostatistics based on Rényi entropy. The Curie-Weiss model is discussed as an example.