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Entropy, Volume 13, Issue 12 (December 2011) – 6 articles , Pages 1967-2058

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240 KiB  
Article
Information Theory Consequences of the Scale-Invariance of Schröedinger’s Equation
by Silvana Flego, Angelo Plastino and Angel Ricardo Plastino
Entropy 2011, 13(12), 2049-2058; https://doi.org/10.3390/e13122049 - 20 Dec 2011
Cited by 2 | Viewed by 6411
Abstract
In this communication we show that Fisher’s information measure emerges as a direct consequence of the scale-invariance of Schröedinger’s equation. Interesting, well-known additional results are re-obtained as well, for whose derivation only (and this is the novelty) the scale invariance property is needed, [...] Read more.
In this communication we show that Fisher’s information measure emerges as a direct consequence of the scale-invariance of Schröedinger’s equation. Interesting, well-known additional results are re-obtained as well, for whose derivation only (and this is the novelty) the scale invariance property is needed, without further ado. Full article
153 KiB  
Article
Eigenvalue Estimates Using the Kolmogorov-Sinai Entropy
by Shih-Feng Shieh
Entropy 2011, 13(12), 2036-2048; https://doi.org/10.3390/e13122036 - 20 Dec 2011
Cited by 2 | Viewed by 5547
Abstract
The scope of this paper is twofold. First, we use the Kolmogorov-Sinai Entropy to estimate lower bounds for dominant eigenvalues of nonnegative matrices. The lower bound is better than the Rayleigh quotient. Second, we use this estimate to give a nontrivial lower bound [...] Read more.
The scope of this paper is twofold. First, we use the Kolmogorov-Sinai Entropy to estimate lower bounds for dominant eigenvalues of nonnegative matrices. The lower bound is better than the Rayleigh quotient. Second, we use this estimate to give a nontrivial lower bound for the gaps of dominant eigenvalues of A and A + V. Full article
(This article belongs to the Special Issue Concepts of Entropy and Their Applications)
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556 KiB  
Article
Fluctuation, Dissipation and the Arrow of Time
by Michele Campisi and Peter Hänggi
Entropy 2011, 13(12), 2024-2035; https://doi.org/10.3390/e13122024 - 19 Dec 2011
Cited by 26 | Viewed by 8065
Abstract
The recent development of the theory of fluctuation relations has led to new insights into the ever-lasting question of how irreversible behavior emerges from time-reversal symmetric microscopic dynamics. We provide an introduction to fluctuation relations, examine their relation to dissipation and discuss their [...] Read more.
The recent development of the theory of fluctuation relations has led to new insights into the ever-lasting question of how irreversible behavior emerges from time-reversal symmetric microscopic dynamics. We provide an introduction to fluctuation relations, examine their relation to dissipation and discuss their impact on the arrow of time question. Full article
(This article belongs to the Special Issue Arrow of Time)
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246 KiB  
Article
Coincidences and Estimation of Entropies of Random Variables with Large Cardinalities
by Ilya Nemenman
Entropy 2011, 13(12), 2013-2023; https://doi.org/10.3390/e13122013 - 19 Dec 2011
Cited by 27 | Viewed by 5841
Abstract
We perform an asymptotic analysis of the NSB estimator of entropy of a discrete random variable. The analysis illuminates the dependence of the estimates on the number of coincidences in the sample and shows that the estimator has a well defined limit for [...] Read more.
We perform an asymptotic analysis of the NSB estimator of entropy of a discrete random variable. The analysis illuminates the dependence of the estimates on the number of coincidences in the sample and shows that the estimator has a well defined limit for a large cardinality of the studied variable. This allows estimation of entropy with no a priori assumptions about the cardinality. Software implementation of the algorithm is available. Full article
2620 KiB  
Article
Effects of Radiation Heat Transfer on Entropy Generation at Thermosolutal Convection in a Square Cavity Subjected to a Magnetic Field
by Nejib Hidouri, Mounir Bouabid, Mourad Magherbi and Ammar Ben Brahim
Entropy 2011, 13(12), 1992-2012; https://doi.org/10.3390/e13121992 - 28 Nov 2011
Cited by 6 | Viewed by 7885
Abstract
Thermosolutal convection in a square cavity filled with a binary perfect gas mixture and submitted to an oriented magnetic field taking into account the effect of radiation heat transfer is numerically investigated. The cavity is heated and cooled along the active walls whereas [...] Read more.
Thermosolutal convection in a square cavity filled with a binary perfect gas mixture and submitted to an oriented magnetic field taking into account the effect of radiation heat transfer is numerically investigated. The cavity is heated and cooled along the active walls whereas the two other walls are adiabatic and insulated. Entropy generation due to heat and mass transfer, fluid friction and magnetic effect has been determined for laminar flow by solving numerically: The continuity, momentum energy and mass balance equations, using a Control Volume Finite-Element Method. The structure of the studied flows depends on five dimensionless parameters which are: The Grashof number, the buoyancy ratio, the Hartman number, the inclination angle of the magnetic field and the radiation parameter. Full article
(This article belongs to the Special Issue Entropy Generation Minimization)
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311 KiB  
Article
Thermodynamics of Regular Cosmological Black Holes with the de Sitter Interior
by Irina Dymnikova and Michał Korpusik
Entropy 2011, 13(12), 1967-1991; https://doi.org/10.3390/e13121967 - 28 Nov 2011
Cited by 47 | Viewed by 6864
Abstract
We address the question of thermodynamics of regular cosmological spherically symmetric black holes with the de Sitter center. Space-time is asymptotically de Sitter as r → 0 and as r → ∞. A source term in the Einstein equations connects smoothly two de [...] Read more.
We address the question of thermodynamics of regular cosmological spherically symmetric black holes with the de Sitter center. Space-time is asymptotically de Sitter as r → 0 and as r → ∞. A source term in the Einstein equations connects smoothly two de Sitter vacua with different values of cosmological constant: 8πGTμν = Λδμν as r → 0, 8πGTμν = λδμν as r → ∞ with λ < Λ. It represents an anisotropic vacuum dark fluid defined by symmetry of its stress-energy tensor which is invariant under the radial boosts. In the range of the mass parameter Mcr1 ≤ M ≤ Mcr2 it describes a regular cosmological black hole. Space-time in this case has three horizons: a cosmological horizon rc, a black hole horizon rb < rc, and an internal horizon ra < rb, which is the cosmological horizon for an observer in the internal R-region asymptotically de Sitter as r → 0. We present the basicfeatures of space-time geometry and the detailed analysis of thermodynamics of horizons using the Padmanabhan approach relevant for a multi-horizon space-time with a non-zero pressure. We find that in a certain range of parameters M and q =√Λ/λ there exist a global temperature for an observer in the R-region between the black hole horizon rb and cosmological horizon rc. We show that a second-order phase transition occurs in the course of evaporation, where a specific heat is broken and a temperature achieves its maximal value. Thermodynamical preference for a final point of evaporation is thermodynamically stable double-horizon (ra = rb) remnant with the positive specific heat and zero temperature. Full article
(This article belongs to the Special Issue Black Hole Thermodynamics)
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