Next Issue
Previous Issue

E-Mail Alert

Add your e-mail address to receive forthcoming issues of this journal:

Journal Browser

Journal Browser

Table of Contents

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

  • Issues are regarded as officially published after their release is announced to the table of contents alert mailing list.
  • You may sign up for e-mail alerts to receive table of contents of newly released issues.
  • PDF is the official format for papers published in both, html and pdf forms. To view the papers in pdf format, click on the "PDF Full-text" link, and use the free Adobe Readerexternal link to open them.
View options order results:
result details:
Displaying articles 1-6
Export citation of selected articles as:

Research

Open AccessArticle Thermodynamics of Regular Cosmological Black Holes with the de Sitter Interior
Entropy 2011, 13(12), 1967-1991; doi:10.3390/e13121967
Received: 3 August 2011 / Revised: 14 November 2011 / Accepted: 16 November 2011 / Published: 28 November 2011
Cited by 10 | PDF Full-text (311 KB) | HTML Full-text | XML Full-text
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 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)
Open AccessArticle Effects of Radiation Heat Transfer on Entropy Generation at Thermosolutal Convection in a Square Cavity Subjected to a Magnetic Field
Entropy 2011, 13(12), 1992-2012; doi:10.3390/e13121992
Received: 1 June 2011 / Revised: 27 June 2011 / Accepted: 21 July 2011 / Published: 28 November 2011
PDF Full-text (2620 KB) | HTML Full-text | XML Full-text
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 [...] 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)
Open AccessArticle Coincidences and Estimation of Entropies of Random Variables with Large Cardinalities
Entropy 2011, 13(12), 2013-2023; doi:10.3390/e13122013
Received: 1 November 2011 / Revised: 8 December 2011 / Accepted: 15 December 2011 / Published: 19 December 2011
Cited by 10 | PDF Full-text (246 KB) | HTML Full-text | XML Full-text
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 [...] 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
Open AccessArticle Fluctuation, Dissipation and the Arrow of Time
Entropy 2011, 13(12), 2024-2035; doi:10.3390/e13122024
Received: 8 November 2011 / Revised: 6 December 2011 / Accepted: 12 December 2011 / Published: 19 December 2011
Cited by 6 | PDF Full-text (556 KB) | HTML Full-text | XML Full-text
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 [...] 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)
Figures

Open AccessArticle Eigenvalue Estimates Using the Kolmogorov-Sinai Entropy
Entropy 2011, 13(12), 2036-2048; doi:10.3390/e13122036
Received: 31 October 2011 / Revised: 28 November 2011 / Accepted: 12 December 2011 / Published: 20 December 2011
Cited by 1 | PDF Full-text (153 KB) | HTML Full-text | XML Full-text
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 [...] 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)
Open AccessArticle Information Theory Consequences of the Scale-Invariance of Schröedinger’s Equation
Entropy 2011, 13(12), 2049-2058; doi:10.3390/e13122049
Received: 26 September 2011 / Revised: 25 November 2011 / Accepted: 5 December 2011 / Published: 20 December 2011
Cited by 1 | PDF Full-text (240 KB) | HTML Full-text | XML Full-text
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 [...] 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

Journal Contact

MDPI AG
Entropy Editorial Office
St. Alban-Anlage 66, 4052 Basel, Switzerland
entropy@mdpi.com
Tel. +41 61 683 77 34
Fax: +41 61 302 89 18
Editorial Board
Contact Details Submit to Entropy
Back to Top