Algebraic topological entropy. This 'algebraic variational principle' should not only nicely illustrate the 'feed-back' of methods developed for quantum dynamical systems to the classical theory, but it could also be proved directly by 'algebraic' methods and could thus further simplify the original proof of the variational principle at least 'in principle'. Combinatorial Image Entropy. The concept of entropy for an image on a discrete two dimensional grid is introduced.

## Book Cultural Residues Chile In Transition Mcsa Cultural Studies Of The Americas

This concept is used as an information theoretic bound on the coding rate for the image. It is proved that this quantity exists as a limit for arbitrary sets satisfying certain conditions Maximum Entropy Fundamentals. Jaynes, starting in the mid-fifties. The principle dictates that one should look for a distribution, consistent with available information, which maximizes the entropy. However, this principle focuses only on distributions and it appears advantageous to bring information theoretical thinking more prominently into play by also focusing on the "observer" and on coding.

This view was brought forward by the second named author in the late seventies and is the view we will follow-up on here. It leads to the consideration of a certain game, the Code Length Game and, via standard game theoretical thinking, to a principle of Game Theoretical Equilibrium. This principle is more basic than the Maximum Entropy Principle in the sense that the search for one type of optimal strategies in the Code Length Game translates directly into the search for distributions with maximum entropy.

In the present paper we offer a self-contained and comprehensive treatment of fundamentals of both principles mentioned, based on a study of the Code Length Game. Though new concepts and results are presented, the reading should be instructional and accessible to a rather wide audience, at least if certain mathematical details are left aside at a rst reading. The most frequently studied instance of entropy maximization pertains to the Mean Energy Model which involves a moment constraint related to a given function, here taken to represent "energy".

This type of application is very well known from the literature with hundreds of applications pertaining to several different elds and will also here serve as important illustration of the theory.

## Stolen Child

But our approach reaches further, especially regarding the study of continuity properties of the entropy function, and this leads to new results which allow a discussion of models with so-called entropy loss. These results have tempted us to speculate over. Maximum entropy methods. For some years now two different expressions have been in use for maximum entropy image restoration and there has been some controversy over which one is appropriate for a given problem.

Here two further entropies are presented and it is argued that there is no single correct algorithm. The properties of the four different methods are compared using simple 1D simulations with a view to showing how they can be used together to gain as much information as possible about the original object.

Entanglement entropy and duality. Using the algebraic approach to entanglement entropy , we study several dual pairs of lattice theories and show how the entropy is completely preserved across each duality. Our main result is that a maximal algebra of observables in a region typically dualizes to a non-maximal algebra in a dual region. In particular, we show how the usual notion of tracing out external degrees of freedom dualizes to a tracing out coupled to an additional summation over superselection sectors.

We briefly comment on possible extensions of our results to more intricate dualities, including holographic ones. Maximum entropy tokamak configurations.

The new entropy concept for the collective magnetic equilibria is applied to the description of the states of a tokamak subject to ohmic and auxiliary heating. The condition for the existence of steady state plasma states with vanishing entropy production implies, on one hand, the resilience of specific current density profiles and, on the other, severe restrictions on the scaling of the confinement time with power and current. These restrictions are consistent with Goldston scaling and with the existence of a heat pinch. Information entropy for static spherically symmetric black holes.

By using the new equation of state density derived from the generalized uncertainty relation, the number of the quantum states near event horizon is obtained, with which then the information entropy of static spherically symmetric black holes has been discussed.

It is found that the divergent integral of quantum states near the event horizon can be naturally avoided if using the new equation of state density without introducing the ultraviolet cut-off. The information entropy of black holes can be obtained precisely by the residue theorem, which is shown to be proportional to the horizon area. The information entropy of black holes obtained agrees with the Bechenstein-Hawking entropy when the suitable cutoff factor is adopted. The information entropy of black holes obtained agrees with the Bechensteinâ€”Hawking entropy when the suitable cutoff factor is adopted.

Stationary neutrino radiation transport by maximum entropy closure. The authors obtain the angular distributions that maximize the entropy functional for Maxwell-Boltzmann classical , Bose-Einstein, and Fermi-Dirac radiation. In the low and high occupancy limits, the maximum entropy closure is bounded by previously known variable Eddington factors that depend only on the flux. For intermediate occupancy, the maximum entropy closure depends on both the occupation density and the flux.

The Fermi-Dirac maximum entropy variable Eddington factor shows a scale invariance, which leads to a simple, exact analytic closure for fermions. This two-dimensional variable Eddington factor gives results that agree well with exact Monte Carlo neutrino transport calculations out of a collapse residue during early phases of hydrostatic neutron star formation.

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Algebraic entropy for algebraic maps. We propose an extension of the concept of algebraic entropy , as introduced by Bellon and Viallet for rational maps, to algebraic maps or correspondences of a certain kind. The corresponding entropy is an index of the complexity of the map. The definition inherits the basic properties from the definition of entropy for rational maps. A Note on Quantum Entropy. Incremental information, as measured by the quantum entropy , is increasing when two ensembles are united.

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This result was proved by Lieb and Ruskai, and it is the foundation for the proof of strong subadditivity of quantum entropy. We present a truly elementary proof of this fact in the context of the broader family of matrix entropies introduced by Chen and Tropp.

## Federal Register Vol. 81, No.208,

Hansen, Frank, E-mail: frank. Fuzzy entropy has been widely used to analyze and design fuzzy systems, and many fuzzy entropy formulae have been proposed. For further in-deepth analysis of fuzzy entropy , the axioms and some important formulae of fuzzy entropy are introduced. Some equivalence results among these fuzzy entropy formulae are proved, and it is shown that fuzzy entropy is a special distance measurement. Jayanta K Bhattacharjee. General Article Volume 6 Issue 9 September pp Click here to view fulltext PDF. Entropy in Physics. Consider the integral. We shall call this function the entropy of state A.

This is the basic assumption of Dynamic Cross- Entropy. Complexity measures for time series have been used in many applications to quantify the regularity of one dimensional time series, however many dynamical systems are spatially distributed multidimensional systems. We introduced Dynamic Cross- Entropy DCE a novel multidimensional complexity measure that quantifies the degree of regularity of EEG signals in selected frequency bands. Time series generated by discrete logistic equations with varying control parameter r are used to test DCE measures. Sliding window DCE analyses are able to reveal specific period doubling bifurcations that lead to chaos.

A similar behavior can be observed in seizures triggered by electroconvulsive therapy ECT. Sample entropy data show the level of signal complexity in different phases of the ictal ECT. The transition to irregular activity is preceded by the occurrence of cyclic regular behavior.

A significant increase of DCE values in successive order from high frequencies in gamma to low frequencies in delta band reveals several phase transitions into less ordered states, possible chaos in the human brain. To our knowledge there are no reliable techniques able to reveal the transition to chaos in case of multidimensional times series. The applied technique may offer new approaches to better understand nonlinear brain activity. All rights reserved. Rescaling Temperature and Entropy.

These units obscure some important aspects of the natures of these thermodynamic quantities.