Entropy

220 KiB

Open AccessArticle

Black Hole Horizons and Thermodynamics: A Quantum Approach

by Valter Moretti and Nicola Pinamonti

Entropy 2010, 12(7), 1833-1854; https://doi.org/10.3390/e12071833 - 23 Jul 2010

Cited by 1 | Viewed by 8372

We focus on quantization of the metric of a black hole restricted to the Killing horizon with universal radius r₀. After imposing spherical symmetry and after restriction to the Killing horizon, the metric is quantized employing the chiral currents formalism. Two [...] Read more.

We focus on quantization of the metric of a black hole restricted to the Killing horizon with universal radius r₀. After imposing spherical symmetry and after restriction to the Killing horizon, the metric is quantized employing the chiral currents formalism. Two "components of the metric" are indeed quantized: The former behaves as an affine scalar field under changes of coordinates, the latter is instead a proper scalar field. The action of the symplectic group on both fields is realized in terms of certain horizon diffeomorphisms. Depending on the choice of the vacuum state, such a representation is unitary. If the reference state of the scalar field is a coherent state rather than a vacuum, spontaneous breaking of conformal symmetry arises and the state contains a Bose-Einstein condensate. In this case the order parameter fixes the actual size of the black hole with respect to r₀. Both the constructed state together with the one associated with the affine scalar are thermal states (KMS) with respect to Schwarzschild Killing time when restricted to half horizon. The value of the order parameter fixes the temperature at the Hawking value as well. As a result, it is found that the quantum energy and entropy densities coincide with the black hole mass and entropy, provided the universal parameter r₀ is suitably chosen, not depending on the size of the actual black hole in particular. Full article

(This article belongs to the Special Issue Entropy in Quantum Gravity)

394 KiB

Open AccessArticle

Roofs and Convexity

by Armin Uhlmann

Entropy 2010, 12(7), 1799-1832; https://doi.org/10.3390/e12071799 - 20 Jul 2010

Cited by 58 | Viewed by 8261

Abstract

Convex roof extensions are widely used to create entanglement measures in quantum information theory. The aim of the article is to present some tools which could be helpful for their treatment. Sections 2 and 3 introduce into the subject. It follows descriptions of [...] Read more.

Convex roof extensions are widely used to create entanglement measures in quantum information theory. The aim of the article is to present some tools which could be helpful for their treatment. Sections 2 and 3 introduce into the subject. It follows descriptions of the Wootters' method, of the "subtraction procedure", and examples on how to use symmetries. Full article

(This article belongs to the Collection Quantum Information)

294 KiB

Open AccessReview

Entropy and Information Approaches to Genetic Diversity and its Expression: Genomic Geography

by William B. Sherwin

Entropy 2010, 12(7), 1765-1798; https://doi.org/10.3390/e12071765 - 15 Jul 2010

Cited by 74 | Viewed by 15242

Abstract

This article highlights advantages of entropy-based genetic diversity measures, at levels from gene expression to landscapes. Shannon’s entropy-based diversity is the standard for ecological communities. The exponentials of Shannon’s and the related “mutual information” excel in their ability to express diversity intuitively, and [...] Read more.

This article highlights advantages of entropy-based genetic diversity measures, at levels from gene expression to landscapes. Shannon’s entropy-based diversity is the standard for ecological communities. The exponentials of Shannon’s and the related “mutual information” excel in their ability to express diversity intuitively, and provide a generalised method of considering microscopic behaviour to make macroscopic predictions, under given conditions. The hierarchical nature of entropy and information allows integrated modeling of diversity along one DNA sequence, and between different sequences within and among populations, species, etc. The aim is to identify the formal connections between genetic diversity and the flow of information to and from the environment. Full article

(This article belongs to the Special Issue Entropy in Genetics and Computational Biology)

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964 KiB

Open AccessArticle

Fitting Ranked Linguistic Data with Two-Parameter Functions

by Wentian Li, Pedro Miramontes and Germinal Cocho

Entropy 2010, 12(7), 1743-1764; https://doi.org/10.3390/e12071743 - 7 Jul 2010

Cited by 48 | Viewed by 11044

Abstract

It is well known that many ranked linguistic data can fit well with one-parameter models such as Zipf’s law for ranked word frequencies. However, in cases where discrepancies from the one-parameter model occur (these will come at the two extremes of the rank), [...] Read more.

It is well known that many ranked linguistic data can fit well with one-parameter models such as Zipf’s law for ranked word frequencies. However, in cases where discrepancies from the one-parameter model occur (these will come at the two extremes of the rank), it is natural to use one more parameter in the fitting model. In this paper, we compare several two-parameter models, including Beta function, Yule function, Weibull function—all can be framed as a multiple regression in the logarithmic scale—in their fitting performance of several ranked linguistic data, such as letter frequencies, word-spacings, and word frequencies. We observed that Beta function fits the ranked letter frequency the best, Yule function fits the ranked word-spacing distribution the best, and Altmann, Beta, Yule functions all slightly outperform the Zipf’s power-law function in word ranked- frequency distribution. Full article

(This article belongs to the Special Issue Complexity of Human Language and Cognition)

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177 KiB

Open AccessReview

Autocatalytic Sets and the Origin of Life

by Wim Hordijk, Jotun Hein and Mike Steel

Entropy 2010, 12(7), 1733-1742; https://doi.org/10.3390/e12071733 - 30 Jun 2010

Cited by 123 | Viewed by 15348

Abstract

The origin of life is one of the most fundamental, but also one of the most difficult problems in science. Despite differences between various proposed scenarios, one common element seems to be the emergence of an autocatalytic set or cycle at some stage. [...] Read more.

The origin of life is one of the most fundamental, but also one of the most difficult problems in science. Despite differences between various proposed scenarios, one common element seems to be the emergence of an autocatalytic set or cycle at some stage. However, there is still disagreement as to how likely it is that such self-sustaining sets could arise “spontaneously”. This disagreement is largely caused by the lack of formal models. Here, we briefly review some of the criticism against and evidence in favor of autocatalytic sets, and then make a case for their plausibility based on a formal framework that was introduced and studied in our previous work. Full article

(This article belongs to the Special Issue Emergence in Chemical Systems)

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1597 KiB

Open AccessArticle

Measurement Back-Action in Quantum Point-Contact Charge Sensing

by Bruno Küng, Simon Gustavsson, Theodore Choi, Ivan Shorubalko, Oliver Pfäffli, Fabian Hassler, Gianni Blatter, Matthias Reinwald, Werner Wegscheider, Silke Schön, Thomas Ihn and Klaus Ensslin

Entropy 2010, 12(7), 1721-1732; https://doi.org/10.3390/e12071721 - 29 Jun 2010

Cited by 6 | Viewed by 12622

Abstract

Charge sensing with quantum point-contacts (QPCs) is a technique widely used in semiconductor quantum-dot research. Understanding the physics of this measurement process, as well as finding ways of suppressing unwanted measurement back-action, are therefore both desirable. In this article, we present experimental studies [...] Read more.

Charge sensing with quantum point-contacts (QPCs) is a technique widely used in semiconductor quantum-dot research. Understanding the physics of this measurement process, as well as finding ways of suppressing unwanted measurement back-action, are therefore both desirable. In this article, we present experimental studies targeting these two goals. Firstly, we measure the effect of a QPC on electron tunneling between two InAs quantum dots, and show that a model based on the QPC’s shot-noise can account for it. Secondly, we discuss the possibility of lowering the measurement current (and thus the back-action) used for charge sensing by correlating the signals of two independent measurement channels. The performance of this method is tested in a typical experimental setup. Full article

(This article belongs to the Collection Quantum Information)

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738 KiB

Open AccessArticle

Ecological Economic Evaluation Based on Emergy as Embodied Cosmic Exergy: A Historical Study for the Beijing Urban Ecosystem 1978–2004

by Jiang Mei Ming, Chen Zhan-Ming, Zhang Bo, Li Shuang Cheng, Xia Xiao Hua, Zhou Shi Yi and Zhou Jiang Bo

Entropy 2010, 12(7), 1696-1720; https://doi.org/10.3390/e12071696 - 29 Jun 2010

Cited by 12 | Viewed by 10864

Abstract

For ecological economic evaluation based on the unified biophysical matrix this research illustrates an updated emergy synthesis in terms of embodied cosmic exergy instead of embodied solar energy, which successes the foundation of systems ecological theory but changes the starting point for the [...] Read more.

For ecological economic evaluation based on the unified biophysical matrix this research illustrates an updated emergy synthesis in terms of embodied cosmic exergy instead of embodied solar energy, which successes the foundation of systems ecological theory but changes the starting point for the estimation from simply the sun to the cosmos. According to the modified definition implicating explicit scarcity and strict additivity based on the fundamental thermodynamics laws, the updated emergy approach overcomes the confusable and intractable deficiencies of traditional one and shows firmer theoretical basis as well as better applicability. As a case study for the regional socio-economic ecosystem, a cosmic emergy based ecological economic evaluation of the Beijing urban ecosystem during the period 1978-2004 is presented. The local and external resources supporting the concerned ecosystem are accounted and analyzed in a common unit, i.e., cosmic Joule, according to which a series of indicators are applied to reveal its evolutional characteristics through five aspects as emergy structure, emergy intensity, emergy welfare, environmental impacts, and degree of exploitation and economic efficiency. During the analyzed period, the major emergy source sustaining the operation of the ecosystem had changed from the renewable resources exploited locally to the nonrenewable resources purchased from outside. Emergy intensity for the Beijing urban ecosystem kept rising owing to the continuous investment of resources, which not only improved the living standard but also intensified the environmental pressure. Moreover, the increase of exploitation degree was accompanied with the decline of economic efficiency, while the rising emergy investment ratio implicates that Beijing was at the risks of resources shortage and high dependence on external resources Full article

(This article belongs to the Special Issue Exergy: Analysis and Applications)

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224 KiB

Open AccessArticle

Principle of Minimum Discrimination Information and Replica Dynamics

by Georgiy P. Karev

Entropy 2010, 12(7), 1673-1695; https://doi.org/10.3390/e12071673 - 28 Jun 2010

Cited by 12 | Viewed by 8330

Abstract

Dynamics of many complex systems can be described by replicator equations (RE). Here we present an effective method for solving a wide class of RE based on reduction theorems for models of inhomogeneous communities. The solutions of the RE minimize the discrimination information [...] Read more.

Dynamics of many complex systems can be described by replicator equations (RE). Here we present an effective method for solving a wide class of RE based on reduction theorems for models of inhomogeneous communities. The solutions of the RE minimize the discrimination information of the initial and current distributions at each point of the system trajectory, not only at the equilibrium, under time-dependent constraints. Applications to inhomogeneous versions of some conceptual models of mathematical biology (logistic and Ricker models of populations and Volterra’ models of communities) are given. Full article

(This article belongs to the Special Issue Entropy in Model Reduction)

410 KiB

Open AccessArticle

Entropy and Energy in Characterizing the Organization of Concept Maps in Learning Science

by Ismo T. Koponen and Maija Pehkonen

Entropy 2010, 12(7), 1653-1672; https://doi.org/10.3390/e12071653 - 24 Jun 2010

Cited by 7 | Viewed by 10882

Abstract

Knowledge structures are often represented in the form of networks or maps of concepts. The coherence and connectivity of such knowledge representations is known to be closely related to knowledge production, acquisition and processing. In this study we use network theory in making [...] Read more.

Knowledge structures are often represented in the form of networks or maps of concepts. The coherence and connectivity of such knowledge representations is known to be closely related to knowledge production, acquisition and processing. In this study we use network theory in making the clustering and cohesion of concept maps measurable, and show how the distribution of these properties can be interpreted through the Maximum Entropy (MaxEnt) method. This approach allows to introduce new concepts of the “energy of cognitive load” and the “entropy of knowledge organization” to describe the organization of knowledge in the concept maps. Full article

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Entropy, Volume 12, Issue 7 (July 2010) – 9 articles , Pages 1653-1854

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