Extended quasi-additivity of Tsallis entropies

We consider statistically independent non-identical subsystems with different entropic indices q1 and q2. A relation between q1, q2 and q' (for the entire system) extends a power law for entropic index as a function of distance r. A few examples illustrate a role of the proposed constraint q' < min(q1, q2) for the Beck's concept of quasi-additivity.Comment: to appear in Physica

Modelling train delays with q-exponential functions

We demonstrate that the distribution of train delays on the British railway network is accurately described by q-exponential functions. We explain this by constructing an underlying superstatistical model.Comment: 12 pages, 5 figure

Axiomatic approach to the cosmological constant

A theory of the cosmological constant Lambda is currently out of reach. Still, one can start from a set of axioms that describe the most desirable properties a cosmological constant should have. This can be seen in certain analogy to the Khinchin axioms in information theory, which fix the most desirable properties an information measure should have and that ultimately lead to the Shannon entropy as the fundamental information measure on which statistical mechanics is based. Here we formulate a set of axioms for the cosmological constant in close analogy to the Khinchin axioms, formally replacing the dependency of the information measure on probabilities of events by a dependency of the cosmological constant on the fundamental constants of nature. Evaluating this set of axioms one finally arrives at a formula for the cosmological constant that is given by Lambda = (G^2/hbar^4) (m_e/alpha_el)^6, where G is the gravitational constant, m_e is the electron mass, and alpha_el is the low energy limit of the fine structure constant. This formula is in perfect agreement with current WMAP data. Our approach gives physical meaning to the Eddington-Dirac large number hypothesis and suggests that the observed value of the cosmological constant is not at all unnatural.Comment: 7 pages, no figures. Some further references adde

Chaotic quantization and the mass spectrum of fermions

In order to understand the parameters of the standard model of electroweak and strong interactions, one needs to embed the standard model into some larger theory that accounts for the observed values. This means some additional sector is needed that fixes and stabilizes the values of the fundamental constants of nature. We describe how such a sector can be constructed using the so-called chaotic quantization method applied to a system of coupled map lattices. We restrict ourselves in this short note on verifying how our model correctly yields the numerical values of Yukawa and gravitational coupling constants of a collection of heavy and light fermions using a simple principle, the local minimization of vacuum energy.Comment: 8 pages, 6 figures. To appear in Chaos, Solitons and Fractals (2008

The R R --matrix action of untwisted affine quantum groups at roots of 1

Let $\hat{\frak g}$ be an untwisted affine Kac-Moody algebra. The quantum group $U_h(\hat{\frak g})$ (over $\mathbb{C}[[h]]$) is known to be a quasitriangular Hopf algebra: in particular, it has a universal $R$--matrix, which yields an $R$--matrix for each pair of representations of $U_h(\hat{\frak g})$. On the other hand, the quantum group $U_q(\hat{\frak g})$ (over $\mathbb{C}(q)$) also has an $R$--matrix for each pair of representations, but it has not a universal $R$--matrix so that one cannot say that it is quasitriangular. Following Reshetikin, one introduces the (weaker) notion of braided Hopf algebra: then $U_q(\hat{\frak g})$ is a braided Hopf algebra. In this work we prove that also the unrestricted specializations of $U_q(\hat{\frak g})$ at roots of 1 are braided: in particular, specializing $q$ at 1 we have that the function algebra $F \big[ \hat{H} \big]$ of the Poisson proalgebraic group $\hat{H}$ dual of $\hat{G}$ (a Kac-Moody group with Lie algebra $\hat{\frak g} \,$) is braided. This is useful because, despite these specialized quantum groups are not quasitriangular, the braiding is enough for applications, mainly for producing knot invariants. As an example, the action of the $R$--matrix on (tensor products of) Verma modules can be specialized at odd roots of 1.Comment: 12 pages, AMS-TeX C, Version 2.1c - this is the author's file of the final version (after the refereeing process), as sent for publicatio

Stable synchronised states of coupled Tchebyscheff maps

Coupled Tchebyscheff maps have recently been introduced to explain parameters in the standard model of particle physics, using the stochastic quantisation of Parisi and Wu. This paper studies dynamical properties of these maps, finding analytic expressions for a number of periodic states and determining their linear stability. Numerical evidence is given for nonlinear stability of these states, and also the presence of exponentially slow dynamics for some ranges of the parameter. These results indicate that a theory of particle physics based on coupled map lattices must specify strong physical arguments for any choice of initial conditions, and explain how stochastic quantisation is obtained in the many stable parameter regions.Comment: 18 pages, postscript figures incorporated into the text; acknowledgements adde