747 research outputs found

    How multiplicity determines entropy and the derivation of the maximum entropy principle for complex systems

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    The maximum entropy principle (MEP) is a method for obtaining the most likely distribution functions of observables from statistical systems, by maximizing entropy under constraints. The MEP has found hundreds of applications in ergodic and Markovian systems in statistical mechanics, information theory, and statistics. For several decades there exists an ongoing controversy whether the notion of the maximum entropy principle can be extended in a meaningful way to non-extensive, non-ergodic, and complex statistical systems and processes. In this paper we start by reviewing how Boltzmann-Gibbs-Shannon entropy is related to multiplicities of independent random processes. We then show how the relaxation of independence naturally leads to the most general entropies that are compatible with the first three Shannon-Khinchin axioms, the (c,d)-entropies. We demonstrate that the MEP is a perfectly consistent concept for non-ergodic and complex statistical systems if their relative entropy can be factored into a generalized multiplicity and a constraint term. The problem of finding such a factorization reduces to finding an appropriate representation of relative entropy in a linear basis. In a particular example we show that path-dependent random processes with memory naturally require specific generalized entropies. The example is the first exact derivation of a generalized entropy from the microscopic properties of a path-dependent random process.Comment: 6 pages, 1 figure. To appear in PNA

    Generalized entropies and the transformation group of superstatistics

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    Superstatistics describes statistical systems that behave like superpositions of different inverse temperatures β\beta, so that the probability distribution is p(ϵi)0f(β)eβϵidβp(\epsilon_i) \propto \int_{0}^{\infty} f(\beta) e^{-\beta \epsilon_i}d\beta, where the `kernel' f(β)f(\beta) is nonnegative and normalized (f(β)dβ=1\int f(\beta)d \beta =1). We discuss the relation between this distribution and the generalized entropic form S=is(pi)S=\sum_i s(p_i). The first three Shannon-Khinchin axioms are assumed to hold. It then turns out that for a given distribution there are two different ways to construct the entropy. One approach uses escort probabilities and the other does not; the question of which to use must be decided empirically. The two approaches are related by a duality. The thermodynamic properties of the system can be quite different for the two approaches. In that connection we present the transformation laws for the superstatistical distributions under macroscopic state changes. The transformation group is the Euclidean group in one dimension.Comment: 5 pages, no figur

    Parkinson's Law Quantified: Three Investigations on Bureaucratic Inefficiency

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    We formulate three famous, descriptive essays of C.N. Parkinson on bureaucratic inefficiency in a quantifiable and dynamical socio-physical framework. In the first model we show how the use of recent opinion formation models for small groups can be used to understand Parkinson's observation that decision making bodies such as cabinets or boards become highly inefficient once their size exceeds a critical 'Coefficient of Inefficiency', typically around 20. A second observation of Parkinson - which is sometimes referred to as Parkinson's Law - is that the growth of bureaucratic or administrative bodies usually goes hand in hand with a drastic decrease of its overall efficiency. In our second model we view a bureaucratic body as a system of a flow of workers, which enter, become promoted to various internal levels within the system over time, and leave the system after having served for a certain time. Promotion usually is associated with an increase of subordinates. Within the proposed model it becomes possible to work out the phase diagram under which conditions bureaucratic growth can be confined. In our last model we assign individual efficiency curves to workers throughout their life in administration, and compute the optimum time to send them to old age pension, in order to ensure a maximum of efficiency within the body - in Parkinson's words we compute the 'Pension Point'.Comment: 15 pages, 5 figure

    The Effect of Active Video Games on the Heart Rate of Older Adults

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    Background: Heart rate is used as a health biomarker. This aim of this study was to investigate the effects of playing active video games on the heart rate of older adults, in comparison to the heart rate after common table recreational activity. Methods: An experimental study with 40 participants was conducted: a control group (n=20) participated in common Pokeno® card games; an experimental group (n=20) played WiiTM bowling. The participants’ pre- and post-activity heart rates were measured and compared between and within groups using t-tests. Results: The findings signified an 11.9% increase (p Conclusions: The inclusion of active video games in older adults’ recreational activities can increase their daily activity level to bring long-term health benefits

    Is the Tsallis entropy stable?

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    The question of whether the Tsallis entropy is Lesche-stable is revisited. It is argued that when physical averages are computed with the escort probabilities, the correct application of the concept of Lesche-stability requires use of the escort probabilities. As a consequence, as shown here, the Tsallis entropy is unstable but the thermodynamic averages are stable. We further show that Lesche stability as well as thermodynamic stability can be obtained if the homogeneous entropy is used as the basis of the formulation of non-extensive thermodynamics. In this approach, the escort distribution arises naturally as a secondary structure.Comment: 6 page

    The phase transition in random catalytic sets

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    The notion of (auto) catalytic networks has become a cornerstone in understanding the possibility of a sudden dramatic increase of diversity in biological evolution as well as in the evolution of social and economical systems. Here we study catalytic random networks with respect to the final outcome diversity of products. We show that an analytical treatment of this longstanding problem is possible by mapping the problem onto a set of non-linear recurrence equations. The solution of these equations show a crucial dependence of the final number of products on the initial number of products and the density of catalytic production rules. For a fixed density of rules we can demonstrate the existence of a phase transition from a practically unpopulated regime to a fully populated and diverse one. The order parameter is the number of final products. We are able to further understand the origin of this phase transition as a crossover from one set of solutions from a quadratic equation to the other.Comment: 7 pages, ugly eps files due to arxiv restriction

    Generalized information entropies depending only on the probability distribution

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    Systems with a long-term stationary state that possess as a spatio-temporally fluctuation quantity β\beta can be described by a superposition of several statistics, a "super statistics". We consider first, the Gamma, log-normal and FF-distributions of β\beta. It is assumed that they depend only on plp_l, the probability associated with the microscopic configuration of the system. For each of the three β\beta-distributions we calculate the Boltzmann factors and show that they coincide for small variance of the fluctuations. For the Gamma distribution it is possible to calculate the entropy in a closed form, depending on plp_l, and to obtain then an equation relating plp_l with βEl\beta E_l. We also propose, as other examples, new entropies close related with the Kaniadakis and two possible Sharma-Mittal entropies. The entropies presented in this work do not depend on a constant parameter qq but on plp_l. For the plp_l-Gamma distribution and its corresponding Bpl(E)B_{p_l}(E) Boltzmann factor and the associated entropy, we show the validity of the saddle-point approximation. We also briefly discuss the generalization of one of the four Khinchin axioms to get this proposed entropy.Comment: 13 pages, 3 figure

    Spectrometry: Report of panel

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    Spectroscopic measurements are required to define the spectral background and provide the detailed spectral information that is essential for the design of species-specific systems and the analysis of data obtained from them. This function of spectroscopic measurements is expected to be an important part of any tropospheric remote-sensing program, and both emission and absorption spectroscopy are relevant in this context. The data from such observations are of value to tropospheric science in their own right, during the initial phases while species-specific techniques and instruments are under development. In addition, there are a number of unresolved problems in tropospheric radiative transfer and spectroscopy which presently limit the accuracy and reliability of all remote sensing methods. Only through a supporting program of spectroscopic measurements can progress be made in improving the understanding of these aspects of radiative transfer and ultimately reaching the desired confidence in the accuracy to species-specific monitoring techniques
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