相关论文: Information theory and generalized statistics
Gauss' law of error is generalized in Tsallis statistics such as multifractal systems, in which Tsallis entropy plays an essential role instead of Shannon entropy. For the generalization, we apply the new multiplication operation determined…
By using the Zubarev nonequilibrium statistical operator method, and the Liouville equation with fractional derivatives, a generalized diffusion equation with fractional derivatives is obtained within the Renyi statistics. Averaging in…
We carry out a systematic study of uncertainty measures that are generic to dynamical processes of varied origins, provided they induce suitable continuous probability distributions. The major technical tool are the information theory…
In the 21st century, many of the crucial scientific and technical issues facing humanity can be understood as problems associated with understanding, modelling, and ultimately controlling complex systems: systems comprised of a large number…
Alternative definitions are given of basic concepts of generalized thermostatistics. In particular, generalizations of Shannon's entropy, of the Boltzmann-Gibbs distribution, and of relative entropy are considered. Particular choices made…
Entropic uncertainty relations are interesting in their own rights as well as for a lot of applications. Keeping this in mind, we try to make the corresponding inequalities as tight as possible. The use of parametrized entropies also allows…
We link, by means of a semiclassical approach, the fractional statistics of particles obeying the Haldane exclusion principle to the Tsallis statistics and derive a generalized quantum entropy and its associated statistics.
We discuss here the use of generalized forms of entropy, taken as information measures, to characterize phase transitions and critical behavior in thermodynamic systems. Our study is based on geometric considerations pertaining to the space…
The equipartition theorem states that inverse temperature equals the log-derivative of the density of states. This relation can be generalized by introducing a proportionality factor involving an increasing positive function phi(x). It is…
The conventional approach to data-driven inversion framework is based on Gaussian statistics that presents serious difficulties, especially in the presence of outliers in the measurements. In this work, we present maximum likelihood…
If the generalized statistics suggested by Tsallis are used in statistical mechanics, the fluctuation-dissipation theorem no longer holds. Only in the limiting case where Boltzmann statistics are recovered is the theorem applicable. In…
We show how Fisher's information already known particular character as the fundamental information geometric object which plays the role of a metric tensor for a statistical differential manifold, can be derived in a relatively easy manner…
This text presents an unified approach of probability and statistics in the pursuit of understanding and computation of randomness in engineering or physical or social system with prediction with generalizability. Starting from elementary…
We introduce a hierarchical classification of theories that describe systems with fundamentally limited information content. This property is introduced in an operational way and gives rise to the existence of mutually complementary…
This article proposes a new two-parameter generalized entropy, which can be reduced to the Tsallis and the Shannon entropy for specific values of its parameters. We develop a number of information-theoretic properties of this generalized…
Integrated Information Theory is one of the leading models of consciousness. It aims to describe both the quality and quantity of the conscious experience of a physical system, such as the brain, in a particular state. In this contribution,…
In this study, our effort is to introduce Tsallis thermostatistics in some details and to give a brief review of the magnetic systems which have been studied in the frame of this formalism.
In this article we discuss the formal structure of a generalized information theory based on the extension of the probability calculus of Kolmogorov to a (possibly) non-commutative setting. By studying this framework, we argue that quantum…
We describe in detail two numerical simulation methods valid to study systems whose thermostatistics is described by generalized entropies, such as Tsallis. The methods are useful for applications to non-trivial interacting systems with a…
The recent discoveries of new forms of quantum statistics require a close look at the under-lying Fock space structure. This exercise becomes all the more important in order to provide a general classification scheme for various forms of…