Search results for " Entropy"
showing 10 items of 236 documents
Substitution systems and nonextensive statistics
2015
Abstract Substitution systems evolve in time by generating sequences of symbols from a finite alphabet: At a certain iteration step, the existing symbols are systematically replaced by blocks of N k symbols also within the alphabet (with N k , a natural number, being the length of the k th block of the substitution). The dynamics of these systems leads naturally to fractals and self-similarity. By using B -calculus (Garcia-Morales, 2012) universal maps for deterministic substitution systems both of constant and non-constant length, are formulated in 1D. It is then shown how these systems can be put in direct correspondence with Tsallis entropy. A ‘Second Law of Thermodynamics’ is also prove…
Lyapunov exponent and topological entropy plateaus in piecewise linear maps
2013
We consider a two-parameter family of piecewise linear maps in which the moduli of the two slopes take different values. We provide numerical evidence of the existence of some parameter regions in which the Lyapunov exponent and the topological entropy remain constant. Analytical proof of this phenomenon is also given for certain cases. Surprisingly however, the systems with that property are not conjugate as we prove by using kneading theory.
SPECTRAL ANALYSIS WITH TAPERED DATA
1983
. A new method based on an upper bound for spectral windows is presented for investigating the cumulants of time series statistics. Using this method two classical results are proved for tapered data. In particular, the asymptotic normality for a class of spectral estimates including estimates for the spectral function and the covariance function is proved under integrability conditions on the spectra using the method of cumulants.
Analysis of resources distribution in economics based on entropy
2002
We propose a new approach to the problem of e0cient resources distribution in di1erent types of economic systems. We also propose to use entropy as an indicator of the e0ciency of resources distribution. Our approach is based on methods of statistical physics in which the states of economic systems are described in terms of the density functions � (g; � ) of the variable — — — — � �
Entropy flux in non-equilibrium thermodynamics
2004
Abstract An important problem in thermodynamics is the link between the entropy flux and the heat flux, for phenomena far from equilibrium. As an illustration we consider here the case of a rigid heat conductor subject to heating. The expression of the entropy flux is determined by the expressions of the evolution equations of the basic variables. It is shown that the coefficient relating entropy and heat fluxes differs far from equilibrium from the inverse of the non-equilibrium temperature θ . The particular case in which these two quantities are identical is examined in detail. A simple but intuitive physical illustration of the results is proposed. A comparison with information theory i…
Thermodynamic approach to vortex production and diffusion in inhomogeneous superfluid turbulence
2014
In this paper, we use a non-equilibrium thermodynamic framework to generalize a previous nonlocal model of counterflow superfluid turbulence to incorporate some new coupled terms which may be relevant in the evolution of inhomogeneous vortex tangles. The theory chooses as fundamental fields the energy density, the heat flux, and the averaged vortex line length per unit volume. The constitutive quantities are assumed to depend on the fundamental fields and on their first spatial derivatives, allowing us to describe thermal dissipation, vortex diffusion and a new contribution to vortex formation. The restrictions on the constitutive relations are deduced from the entropy principle, using the …
Entropic measure of spatial disorder for systems of finite-sized objects
2000
We consider the relative configurational entropy per cell S_Delta as a measure of the degree of spatial disorder for systems of finite-sized objects. It is highly sensitive to deviations from the most spatially ordered reference configuration of the objects. When applied to a given binary image it provides the quantitatively correct results in comparison to its point object version. On examples of simple cluster configurations, two-dimensional Sierpinski carpets and population of interacting particles, the behaviour of S_Delta is compared with the normalized information entropy H' introduced by Van Siclen [Phys. Rev. E 56, (1997) 5211]. For the latter example, the additional middle-scale fe…
Global stability of protein folding from an empirical free energy function
2013
The principles governing protein folding stand as one of the biggest challenges of Biophysics. Modeling the global stability of proteins and predicting their tertiary structure are hard tasks, due in part to the variety and large number of forces involved and the difficulties to describe them with sufficient accuracy. We have developed a fast, physics-based empirical potential, intended to be used in global structure prediction methods. This model considers four main contributions: Two entropic factors, the hydrophobic effect and configurational entropy, and two terms resulting from a decomposition of close-packing interactions, namely the balance of the dispersive interactions of folded an…
An entropic analysis of approximate quantum error correction
2013
The concept of entropy and the correct application of the Second Law of thermodynamics are essential in order to understand the reason why quantum error correction is thermodynamically possible and no violation of the Second Law occurs during its execution. We report in this work our first steps towards an entropic analysis extended to approximate quantum error correction (QEC). Special emphasis is devoted to the link among quantum state discrimination (QSD), quantum information gain, and quantum error correction in both the exact and approximate QEC scenarios.
Geometric Entropies of Mixing (EOM)
2005
Trigonometric and trigonometric-algebraic entropies are introduced. Regularity increases the entropy and the maximal entropy is shown to result when a regular $n$-gon is inscribed in a circle. A regular $n$-gon circumscribing a circle gives the largest entropy reduction, or the smallest change in entropy from the state of maximum entropy which occurs in the asymptotic infinite $n$ limit. EOM are shown to correspond to minimum perimeter and maximum area in the theory of convex bodies, and can be used in the prediction of new inequalities for convex sets. These expressions are shown to be related to the phase functions obtained from the WKB approximation for Bessel and Hermite functions.