Search results for "Entropy"
showing 10 items of 496 documents
Local Entropy Characterization of Correlated Random Microstructures
1996
A rigorous connection is established between the local porosity entropy introduced by Boger et al. (Physica A 187, 55 (1992)) and the configurational entropy of Andraud et al. (Physica A 207, 208 (1994)). These entropies were introduced as morphological descriptors derived from local volume fluctuations in arbitrary correlated microstructures occuring in porous media, composites or other heterogeneous systems. It is found that the entropy lengths at which the entropies assume an extremum become identical for high enough resolution of the underlying configurations. Several examples of porous and heterogeneous media are given which demonstrate the usefulness and importance of this morphologic…
Extended quasi-additivity of Tsallis entropies
2006
We consider statistically independent non-identical subsystems with different entropic indices q1 and q2. A relation between q1, q2 and q' (for the entire system) extends a power law for entropic index as a function of distance r. A few examples illustrate a role of the proposed constraint q' < min(q1, q2) for the Beck's concept of quasi-additivity.
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…
Phase separation in multi-component mixtures: the four-component case
2002
Abstract Calculation of ternary phase diagrams for several mixtures formed by two salts and a neutral component is presented here. The phase diagrams are obtained by inspection of the shape of the Gibbs free energy of mixing surface (Gmix) as a function of the composition at constant temperature and pressure. The Gmix surface is calculated by the mean spherical approximation (MSA). The model for the mixtures is represented by hard spheres, with the charged components interacting via a Coulomb potential. The results are interpreted in terms of a thermodynamic analysis of the contributions to the Gibbs free energy of mixing, i.e., the configurational energy, the volume and the entropy of mixi…
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…
Statistical mechanics characterization of spatio-compositional inhomogeneity
2009
On the basis of a model system of pillars built of unit cubes, a two-component entropic measure for the multiscale analysis of spatio-compositional inhomogeneity is proposed. It quantifies the statistical dissimilarity per cell of the actual configurational macrostate and the theoretical reference one that maximizes entropy. Two kinds of disorder compete: i) the spatial one connected with possible positions of pillars inside a cell (the first component of the measure), ii) the compositional one linked to compositions of each local sum of their integer heights into a number of pillars occupying the cell (the second component). As both the number of pillars and sum of their heights are conser…
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 …