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Entropy, Volume 14, Issue 3 (March 2012), Pages 390-598

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Research

Jump to: Review

Open AccessArticle Bumps on the Road to Here (from Eternity)
Entropy 2012, 14(3), 390-406; doi:10.3390/e14030390
Received: 20 December 2011 / Revised: 14 February 2012 / Accepted: 16 February 2012 / Published: 23 February 2012
Cited by 1 | PDF Full-text (448 KB) | HTML Full-text | XML Full-text
Abstract
In his recent book, From Eternity to Here, and in other more technical papers, Sean Carroll (partly in collaboration with Jennifer Chen) has put forward an intriguing new way to think about the origin of the Universe. His approach, in a [...] Read more.
In his recent book, From Eternity to Here, and in other more technical papers, Sean Carroll (partly in collaboration with Jennifer Chen) has put forward an intriguing new way to think about the origin of the Universe. His approach, in a nutshell, is to raise certain worries about a standard Boltzmannian picture of statistical mechanics, and to present certain commitments that he thinks we ought to hold—commitments that the standard picture doesn’t share. He then proposes a cosmological model—one that purports to give us insight into what sort of process brought about the “initial state” of the universe—that can uniquely accommodate those commitments. The conclusion of Carroll’s argument is that statistical mechanical reasoning provides grounds for provisionally accepting that cosmological model. My goal in this paper is to reconstruct and critically assess this proposal. I argue that “statistical cosmology” requires a careful balance of philosophical intuitions and commitments against technical, scientific considerations; how much stock we ought to place in these intuitions and commitments should depend on where they lead us—those that lead us astray scientifically might well be in need of philosophical re‑examination. Full article
(This article belongs to the Special Issue Arrow of Time)
Open AccessArticle Temporal Asymmetry, Entropic Irreversibility, and Finite-Time Thermodynamics: From Parmenides–Einstein Time-Reversal Symmetry to the Heraclitan Entropic Arrow of Time
Entropy 2012, 14(3), 407-455; doi:10.3390/e14030407
Received: 3 February 2012 / Accepted: 17 February 2012 / Published: 28 February 2012
Cited by 6 | PDF Full-text (356 KB) | HTML Full-text | XML Full-text
Abstract
In this paper, we combine the two universalisms of thermodynamics and dynamical systems theory to develop a dynamical system formalism for classical thermodynamics. Specifically, using a compartmental dynamical system energy flow model we develop a state-space dynamical system model that captures the [...] Read more.
In this paper, we combine the two universalisms of thermodynamics and dynamical systems theory to develop a dynamical system formalism for classical thermodynamics. Specifically, using a compartmental dynamical system energy flow model we develop a state-space dynamical system model that captures the key aspects of thermodynamics, including its fundamental laws. In addition, we establish the existence of a unique, continuously differentiable global entropy function for our dynamical system model, and using Lyapunov stability theory we show that the proposed thermodynamic model has finite-time convergent trajectories to Lyapunov stable equilibria determined by the system initial energies. Finally, using the system entropy, we establish the absence of Poincaré recurrence for our thermodynamic model and develop clear and rigorous connections between irreversibility, the second law of thermodynamics, and the entropic arrow of time. Full article
(This article belongs to the Special Issue Arrow of Time)
Open AccessArticle The Mathematical Structure of Information Bottleneck Methods
Entropy 2012, 14(3), 456-479; doi:10.3390/e14030456
Received: 2 December 2011 / Revised: 7 February 2012 / Accepted: 24 February 2012 / Published: 1 March 2012
Cited by 2 | PDF Full-text (221 KB) | HTML Full-text | XML Full-text
Abstract
Information Bottleneck-based methods use mutual information as a distortion function in order to extract relevant details about the structure of a complex system by compression. One of the approaches used to generate optimal compressed representations is by annealing a parameter. In this [...] Read more.
Information Bottleneck-based methods use mutual information as a distortion function in order to extract relevant details about the structure of a complex system by compression. One of the approaches used to generate optimal compressed representations is by annealing a parameter. In this manuscript we present a common framework for the study of annealing in information distortion problems. We identify features that should be common to any annealing optimization problem. The main mathematical tools that we use come from the analysis of dynamical systems in the presence of symmetry (equivariant bifurcation theory). Through the compression problem, we make connections to the world of combinatorial optimization and pattern recognition. The two approaches use very different vocabularies and consider different problems to be “interesting”. We provide an initial link, through the Normalized Cut Problem, where the two disciplines can exchange tools and ideas. Full article
(This article belongs to the Special Issue The Information Bottleneck Method)
Open AccessArticle Interval Entropy and Informative Distance
Entropy 2012, 14(3), 480-490; doi:10.3390/e14030480
Received: 20 December 2011 / Revised: 4 February 2012 / Accepted: 7 February 2012 / Published: 2 March 2012
Cited by 7 | PDF Full-text (119 KB) | HTML Full-text | XML Full-text
Abstract
The Shannon interval entropy function as a useful dynamic measure of uncertainty for two sided truncated random variables has been proposed in the literature of reliability. In this paper, we show that interval entropy can uniquely determine the distribution function. Furthermore, we [...] Read more.
The Shannon interval entropy function as a useful dynamic measure of uncertainty for two sided truncated random variables has been proposed in the literature of reliability. In this paper, we show that interval entropy can uniquely determine the distribution function. Furthermore, we propose a measure of discrepancy between two lifetime distributions at the interval of time in base of Kullback-Leibler discrimination information. We study various properties of this measure, including its connection with residual and past measures of discrepancy and interval entropy, and we obtain its upper and lower bounds. Full article
(This article belongs to the Special Issue Concepts of Entropy and Their Applications)
Open AccessArticle The Optimal Evaporation Temperature of Subcritical ORC Based on Second Law Efficiency for Waste Heat Recovery
Entropy 2012, 14(3), 491-504; doi:10.3390/e14030491
Received: 1 February 2012 / Revised: 23 February 2012 / Accepted: 27 February 2012 / Published: 6 March 2012
Cited by 15 | PDF Full-text (161 KB) | HTML Full-text | XML Full-text
Abstract
The subcritical Organic Rankine Cycle (ORC) with 28 working fluids for waste heat recovery is discussed in this paper. The effects of the temperature of the waste heat, the critical temperature of working fluids and the pinch temperature difference in the evaporator [...] Read more.
The subcritical Organic Rankine Cycle (ORC) with 28 working fluids for waste heat recovery is discussed in this paper. The effects of the temperature of the waste heat, the critical temperature of working fluids and the pinch temperature difference in the evaporator on the optimal evaporation temperature (OET) of the ORC have been investigated. The second law efficiency of the system is regarded as the objective function and the evaporation temperature is optimized by using the quadratic approximations method. The results show that the OET will appear for the temperature ranges investigated when the critical temperatures of working fluids are lower than the waste heat temperatures by 18 ± 5 K under the pinch temperature difference of 5 K in the evaporator. Additionally, the ORC always exhibits the OET when the pinch temperature difference in the evaporator is raised under the fixed waste heat temperature. The maximum second law efficiency will decrease with the increase of pinch temperature difference in the evaporator. Full article
Open AccessArticle Minimum Error Entropy Filter for Fault Detection of Networked Control Systems
Entropy 2012, 14(3), 505-516; doi:10.3390/e14030505
Received: 22 February 2012 / Revised: 27 February 2012 / Accepted: 28 February 2012 / Published: 6 March 2012
Cited by 3 | PDF Full-text (126 KB) | HTML Full-text | XML Full-text
Abstract
In this paper, fault detection of networked control systems with random delays, packet dropout and noises is studied. The filter is designed using a minimum error entropy criterion. The residual generated by the filter is then evaluated to detect faults in networked [...] Read more.
In this paper, fault detection of networked control systems with random delays, packet dropout and noises is studied. The filter is designed using a minimum error entropy criterion. The residual generated by the filter is then evaluated to detect faults in networked control systems. An illustrative networked control system is used to verify the effectiveness of the proposed approach. Full article
(This article belongs to the Special Issue Information Theory Applied to Communications and Networking)
Open AccessArticle Energy and Exergy Analysis for Improving the Energy Performance of Air-Cooled Liquid Chillers by Different Condensing-Coil Configurations
Entropy 2012, 14(3), 517-532; doi:10.3390/e14030517
Received: 13 December 2011 / Revised: 15 February 2012 / Accepted: 2 March 2012 / Published: 8 March 2012
Cited by 1 | PDF Full-text (260 KB) | HTML Full-text | XML Full-text
Abstract
This study constructed a parameter analysis for improving the energy performance of air-cooled water chillers by altering the angle configuration of the condenser coils. The mathematical models for energy and exergy analyses of the individual components and overall system of air-cooled water [...] Read more.
This study constructed a parameter analysis for improving the energy performance of air-cooled water chillers by altering the angle configuration of the condenser coils. The mathematical models for energy and exergy analyses of the individual components and overall system of air-cooled water chillers are presented. This study investigated the potential enhancement of performance efficiency in air-cooled chillers and the energy conversion efficiency of each component, in order to determine how the angle configuration of condenser coils influences chiller performance. This study found that the overall performance of an air-cooled chiller could be improved by approximately 3.4%, and the total irreversibility could be reduced by approximately 2.7%. With each 1% increase in average wind speed over the condenser coils, the overall performance of an air‑cooled chiller was found to be enhanced by approximately 0.43%, and its total irreversibility was reduced by approximately 0.35%. The results of this study can be effectively applied to air-cooled condenser units, and can provide an important basis of reference for developing and enhancing the energy efficiency of air-cooled chillers. Full article
Open AccessArticle Curvature Entropy for Curved Profile Generation
Entropy 2012, 14(3), 533-558; doi:10.3390/e14030533
Received: 20 December 2011 / Revised: 28 February 2012 / Accepted: 6 March 2012 / Published: 9 March 2012
PDF Full-text (323 KB) | HTML Full-text | XML Full-text
Abstract
In a curved surface design, the overall shape features that emerge from combinations of shape elements are important. However, controlling the features of the overall shape in curved profiles is difficult using conventional microscopic shape information such as dimension. Herein two types [...] Read more.
In a curved surface design, the overall shape features that emerge from combinations of shape elements are important. However, controlling the features of the overall shape in curved profiles is difficult using conventional microscopic shape information such as dimension. Herein two types of macroscopic shape information, curvature entropy and quadrature curvature entropy, quantitatively represent the features of the overall shape. The curvature entropy is calculated by the curvature distribution, and represents the complexity of a shape (one of the overall shape features). The quadrature curvature entropy is an improvement of the curvature entropy by introducing a Markov process to evaluate the continuity of a curvature and to approximate human cognition of the shape. Additionally, a shape generation method using a genetic algorithm as a calculator and the entropy as a shape generation index is presented. Finally, the applicability of the proposed method is demonstrated using the side view of an automobile as a design example. Full article
Open AccessArticle Entropy and the Complexity of Graphs Revisited
Entropy 2012, 14(3), 559-570; doi:10.3390/e14030559
Received: 16 January 2012 / Revised: 5 March 2012 / Accepted: 12 March 2012 / Published: 14 March 2012
Cited by 23 | PDF Full-text (133 KB) | HTML Full-text | XML Full-text
Abstract
This paper presents a taxonomy and overview of approaches to the measurement of graph and network complexity. The taxonomy distinguishes between deterministic (e.g., Kolmogorov complexity) and probabilistic approaches with a view to placing entropy-based probabilistic measurement in context. Entropy-based measurement is the [...] Read more.
This paper presents a taxonomy and overview of approaches to the measurement of graph and network complexity. The taxonomy distinguishes between deterministic (e.g., Kolmogorov complexity) and probabilistic approaches with a view to placing entropy-based probabilistic measurement in context. Entropy-based measurement is the main focus of the paper. Relationships between the different entropy functions used to measure complexity are examined; and intrinsic (e.g., classical measures) and extrinsic (e.g., Körner entropy) variants of entropy-based models are discussed in some detail. Full article
Open AccessArticle Benefit-Cost Analysis of Security Systems for Multiple Protected Assets Based on Information Entropy
Entropy 2012, 14(3), 571-580; doi:10.3390/e14030571
Received: 18 January 2012 / Revised: 27 February 2012 / Accepted: 29 February 2012 / Published: 14 March 2012
Cited by 3 | PDF Full-text (174 KB) | HTML Full-text | XML Full-text
Abstract
This article proposes a quantitative risk assessment for security systems which have multiple protected assets and a risk-based benefit-cost analysis for decision makers. The proposed methodology consists of five phases: identification of assets, security unit and intrusion path, security unit effectiveness estimation, [...] Read more.
This article proposes a quantitative risk assessment for security systems which have multiple protected assets and a risk-based benefit-cost analysis for decision makers. The proposed methodology consists of five phases: identification of assets, security unit and intrusion path, security unit effectiveness estimation, intrusion path effectiveness estimation, security system risk assessment and benefit-cost estimation. Key innovations in this methodology include its use of effectiveness entropy to measure the degree of uncertainty of a security system to complete a protection task, and the fact it measures risk like information theory measures the amount of information. A notional example is provided to demonstrate an application of the proposed methodology. Full article

Review

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Open AccessReview Application of Solution NMR Spectroscopy to Study Protein Dynamics
Entropy 2012, 14(3), 581-598; doi:10.3390/e14030581
Received: 30 January 2012 / Revised: 13 March 2012 / Accepted: 16 March 2012 / Published: 22 March 2012
Cited by 8 | PDF Full-text (1541 KB) | HTML Full-text | XML Full-text
Abstract
Recent advances in spectroscopic methods allow the identification of minute fluctuations in a protein structure. These dynamic properties have been identified as keys to some biological processes. The consequences of this structural flexibility can be far‑reaching and they add a new dimension [...] Read more.
Recent advances in spectroscopic methods allow the identification of minute fluctuations in a protein structure. These dynamic properties have been identified as keys to some biological processes. The consequences of this structural flexibility can be far‑reaching and they add a new dimension to the structure-function relationship of biomolecules. Nuclear Magnetic Resonance (NMR) spectroscopy allows the study of structure as well as dynamics of biomolecules in a very broad range of timescales at atomic level. A number of new NMR methods have been developed recently to allow the measurements of time scales and spatial fluctuations, which in turn provide the thermodynamics associated with the biological processes. Since NMR parameters reflect ensemble measurements, structural ensemble approaches in analyzing NMR data have also been developed. These new methods in some instances can even highlight previously hidden conformational features of the biomolecules. In this review we describe several solution NMR methods to study protein dynamics and discuss their impact on important biological processes. Full article
(This article belongs to the Special Issue Loop Entropy)

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