Itineration of the Internet over nonequilibrium stationary states in Tsallis statistics

Entropy defect in thermodynamics

This paper describes the physical foundations of the newly discovered "entropy defect" as a basic concept of thermodynamics. The entropy defect quantifies the change in entropy caused by the order induced in a system through the additional correlations among its constituents when two or more subsystems are assembled. This defect is closely analogous to the mass defect that arises when nuclear particle systems are assembled. The entropy defect determines how the entropy of the system compares to its constituent's entropies and stands on three fundamental properties: each constituent's entropy must be (i) separable, (ii) symmetric, and (iii) bounded. We show that these properties provide a solid foundation for the entropy defect and for generalizing thermodynamics to describe systems residing out of the classical thermal equilibrium, both in stationary and nonstationary states. In stationary states, the consequent thermodynamics generalizes the classical framework, which was based on the Boltzmann-Gibbs entropy and Maxwell-Boltzmann canonical distribution of particle velocities, into the respective entropy and canonical distribution associated with kappa distributions. In nonstationary states, the entropy defect similarly acts as a negative feedback, or reduction of the increase of entropy, preventing its unbounded growth toward infinity.

Some Properties of Weighted Tsallis and Kaniadakis Divergences

We are concerned with the weighted Tsallis and Kaniadakis divergences between two measures. More precisely, we find inequalities between these divergences and Tsallis and Kaniadakis logarithms, prove that they are limited by similar bounds with those that limit Kullback-Leibler divergence and show that are pseudo-additive.

Nonextensive Statistical Mechanics: Equivalence Between Dual Entropy and Dual Probabilities

The concept of duality of probability distributions constitutes a fundamental “brick” in the solid framework of nonextensive statistical mechanics—the generalization of Boltzmann–Gibbs statistical mechanics under the consideration of the q-entropy. The probability duality is solving old-standing issues of the theory, e.g., it ascertains the additivity for the internal energy given the additivity in the energy of microstates. However, it is a rather complex part of the theory, and certainly, it cannot be trivially explained along the Gibb’s path of entropy maximization. Recently, it was shown that an alternative picture exists, considering a dual entropy, instead of a dual probability. In particular, the framework of nonextensive statistical mechanics can be equivalently developed using q- and 1/q- entropies. The canonical probability distribution coincides again with the known q-exponential distribution, but without the necessity of the duality of ordinary-escort probabilities. Furthermore, it is shown that the dual entropies, q-entropy and 1/q-entropy, as well as, the 1-entropy, are involved in an identity, useful in theoretical development and applications.

Keyword extraction by nonextensivity measure

The presence of a long-range correlation in the spatial distribution of a relevant word type, in spite of random occurrences of an irrelevant word type, is an important feature of human-written texts. We classify the correlation between the occurrences of words by nonextensive statistical mechanics for the word-ranking process. In particular, we look at the nonextensivity parameter as an alternative metric to measure the spatial correlation in the text, from which the words may be ranked in terms of this measure. Finally, we compare different methods for keyword extraction.

Occupancy of rotational population in molecular spectra based on nonextensive statistics

The procedure to obtain gas temperature in plasmas is to fit the experimental rotational spectrum to a theoretical one based on the Boltzmann distribution. For many systems a single distribution fails to account for the occupation of the levels. Researchers have improved the fitting by coupling two distributions and obtaining two distinct temperatures. They assigned the lowest temperature to the gas. Here, we show that these systems should be described by Tsallis nonextensive statistics and its unique associated temperature. Experimental and simulated spectra are tested and excellent agreement is obtained.

Nonextensivity and natural time: The case of seismicity

Nonextensive statistical mechanics, pioneered by Tsallis, has recently achieved a generalization of the Gutenberg-Richter law for earthquakes. This remarkable generalization is combined here with natural time analysis, which enables the distinction of two origins of self-similarity, i.e., the process' memory and the process' increments infinite variance. By using also detrended fluctuation analysis for the detection of long-range temporal correlations, we demonstrate the existence of both temporal and magnitude correlations in real seismic data of California and Japan. Natural time analysis reveals that the nonextensivity parameter q , in contrast to some published claims, cannot be considered as a measure of temporal organization, but the Tsallis formulation does achieve a satisfactory description of real seismic data for Japan for q=1.66 when supplemented by long-range temporal correlations.

Gradient mechanism in a communication network

We study the efficiency of the gradient mechanism of message transfer in a two-dimensional communication network of regular nodes and randomly distributed hubs. Each hub on the network is assigned some randomly chosen capacity and hubs with lower capacities are connected to the hubs with maximum capacity. The average travel times of single messages traveling on the lattice decrease rapidly as the number of hubs increase. The functional dependence of the average travel times on the hub density shows q-exponential behavior with a power-law tail. We also study the relaxation behavior of the network when a large number of messages are created simultaneously at random locations and travel on the network toward their designated destinations. For this situation, in the absence of the gradient mechanism, the network can show congestion effects due to the formation of transport traps. We show that if hubs of high betweenness centrality are connected by the gradient mechanism, efficient decongestion can be achieved. The gradient mechanism is less prone to the formation of traps than other decongestion schemes. We also study the spatial configurations of transport traps and propose minimal strategies for their elimination.

Human pol II promoter prediction: time series descriptors and machine learning

Although several in silico promoter prediction methods have been developed to date, they are still limited in predictive performance. The limitations are due to the challenge of selecting appropriate features of promoters that distinguish them from non-promoters and the generalization or predictive ability of the machine-learning algorithms. In this paper we attempt to define a novel approach by using unique descriptors and machine-learning methods for the recognition of eukaryotic polymerase II promoters. In this study, non-linear time series descriptors along with non-linear machine-learning algorithms, such as support vector machine (SVM), are used to discriminate between promoter and non-promoter regions. The basic idea here is to use descriptors that do not depend on the primary DNA sequence and provide a clear distinction between promoter and non-promoter regions. The classification model built on a set of 1000 promoter and 1500 non-promoter sequences, showed a 10-fold cross-validation accuracy of 87% and an independent test set had an accuracy >85% in both promoter and non-promoter identification. This approach correctly identified all 20 experimentally verified promoters of human chromosome 22. The high sensitivity and selectivity indicates that n-mer frequencies along with non-linear time series descriptors, such as Lyapunov component stability and Tsallis entropy, and supervised machine-learning methods, such as SVMs, can be useful in the identification of pol II promoters.

Necessity of q-expectation value in nonextensive statistical mechanics

In nonextensive statistical mechanics, two kinds of definitions have been considered for expectation value of a physical quantity: one is the ordinary definition and the other is the normalized q-expectation value employing the escort distribution. Since both of them lead to the maximum-Tsallis-entropy distributions of a similar type, it is of crucial importance to determine which the correct physical one is. A point is that the definition of expectation value is indivisibly connected to the form of generalized relative entropy. Studying the properties of the relative entropies associated with these two definitions, it is shown how the use of the escort distribution is essential. In particular, the Shore-Johnson theorem for consistent minimum cross-entropy (i.e., relative-entropy) principle is found to select the formalism with the normalized q-expectation value and to exclude the possibility of using the ordinary expectation value from nonextensive statistical mechanics.