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Journal articles on the topic 'Entropy'

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Published: 4 June 2021

Last updated: 29 July 2024

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1

Siagian, Ruben Cornelius, Lulut Alfaris, Arip Nurahman, and Eko Pramesti Sumarto. "TERMODINAMIKA LUBANG HITAM: HUKUM PERTAMA DAN KEDUA SERTA PERSAMAAN ENTROPI." Jurnal Kumparan Fisika 6, no. 1 (May 11, 2023): 1–10. http://dx.doi.org/10.33369/jkf.6.1.1-10.

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ABSTRAK Artikel ini membahas konsep termodinamika yang berlaku pada Lubang Hitam, yaitu hukum termodinamika pertama dan kedua. Hukum pertama termodinamika menghubungkan perubahan massa dengan perubahan entropi dan kerja, memungkinkan Lubang Hitam diperlakukan sebagai sistem termodinamika dengan suhu dan entropi. Hukum kedua termodinamika menyatakan bahwa entropi suatu sistem terisolasi dalam kesetimbangan termodinamika selalu meningkat atau tetap konstan, termasuk untuk Lubang Hitam. Metode penulisan yang digunakan dalam artikel ini melibatkan derivasi matematis untuk entropi Lubang Hitam, dengan menggabungkan hukum kedua termodinamika dan konsep termodinamika Lubang Hitam, di mana entropi dapat dinyatakan sebagai fungsi luas cakrawala peristiwa. Artikel ini menyoroti pentingnya konsep entropi dan termodinamika Lubang Hitam dalam memahami alam semesta, serta penerapannya di berbagai bidang sains. Kata kunci—Lubang Hitam, Termodinamika, Entropi, Hukum pertama termodinamika, Hukum kedua termodinamika ABSTRACT This article delves into the concepts of thermodynamics that apply to Lubang Hitams, namely the first and second laws of thermodynamics. The first law of thermodynamics connects changes in mass with changes in entropy and work, allowing Lubang Hitams to be treated as thermodynamic systems with temperature and entropy. The second law of thermodynamics states that the entropy of an isolated system in thermodynamic equilibrium always increases or remains constant, including for Lubang Hitams. The writing approach employed in this article involves mathematical derivations for Lubang Hitam entropy, combining the second law of thermodynamics with the concept of Lubang Hitam thermodynamics, where entropy can be expressed as a function of the event horizon's surface area. This article highlights the significance of entropy and Lubang Hitam thermodynamics in understanding the universe, as well as their applications in various scientific fields. Keywords—Lubang Hitam, Thermodynamics, Entropy, First law of thermodynamics, Second law of thermodynamics

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2

Kang, Jin-Wen, Ke-Ming Shen, and Ben-Wei Zhang. "A Note on the Connection between Non-Additive Entropy and h-Derivative." Entropy 25, no. 6 (June 9, 2023): 918. http://dx.doi.org/10.3390/e25060918.

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In order to study as a whole a wide part of entropy measures, we introduce a two-parameter non-extensive entropic form with respect to the h-derivative, which generalizes the conventional Newton–Leibniz calculus. This new entropy, Sh,h′, is proved to describe the non-extensive systems and recover several types of well-known non-extensive entropic expressions, such as the Tsallis entropy, the Abe entropy, the Shafee entropy, the Kaniadakis entropy and even the classical Boltzmann–Gibbs one. As a generalized entropy, its corresponding properties are also analyzed.

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Li, Shu-Nan, and Bing-Yang Cao. "On Entropic Framework Based on Standard and Fractional Phonon Boltzmann Transport Equations." Entropy 21, no. 2 (February 21, 2019): 204. http://dx.doi.org/10.3390/e21020204.

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Generalized expressions of the entropy and related concepts in non-Fourier heat conduction have attracted increasing attention in recent years. Based on standard and fractional phonon Boltzmann transport equations (BTEs), we study entropic functionals including entropy density, entropy flux and entropy production rate. Using the relaxation time approximation and power series expansion, macroscopic approximations are derived for these entropic concepts. For the standard BTE, our results can recover the entropic frameworks of classical irreversible thermodynamics (CIT) and extended irreversible thermodynamics (EIT) as if there exists a well-defined effective thermal conductivity. For the fractional BTEs corresponding to the generalized Cattaneo equation (GCE) class, the entropy flux and entropy production rate will deviate from the forms in CIT and EIT. In these cases, the entropy flux and entropy production rate will contain fractional-order operators, which reflect memory effects.

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4

KOSSAKOWSKI, A., M. OHYA, and N. WATANABE. "QUANTUM DYNAMICAL ENTROPY FOR COMPLETELY POSITIVE MAP." Infinite Dimensional Analysis, Quantum Probability and Related Topics 02, no. 02 (June 1999): 267–82. http://dx.doi.org/10.1142/s021902579900014x.

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A dynamical entropy for not only shift but also completely positive (CP) map is defined by generalizing the AOW entropy1 defined through quantum Markov chain and AF entropy defined by a finite operational partition. Our dynamical entropy is numerically computed for several models.

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5

Jawad, Abdul, and Ayesha Iqbal. "Modified cosmology through Renyi and logarithmic entropies." International Journal of Geometric Methods in Modern Physics 15, no. 08 (June 22, 2018): 1850130. http://dx.doi.org/10.1142/s021988781850130x.

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We consider two different entropic corrections to Bekenstein entropy, namely Renyi entropy and logarithmic-corrected entropy, and develop the entropic force, heat flow across the horizon and pressure. We also derive the expressions for Newton’s law of gravitation and verify with Bekenstein entropy by taking [Formula: see text] in the case of Renyi entropy and [Formula: see text] for logarithmic entropy. The modified Friedmann equations are also being developed by using Newton’s first law of thermodynamics in both cases. In the presence of these equations, we also analyze the validity of generalized second law of thermodynamics for both entropy corrections on the apparent horizon. It is found that this law remains valid throughout the region under certain assumptions for nonflat FRW universe.

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6

XIAO, CHANGMING, and LIXIN HUANG. "ENTROPIC FORCE IN A CLOSED IDEAL GAS." Modern Physics Letters B 20, no. 09 (April 10, 2006): 495–500. http://dx.doi.org/10.1142/s0217984906010731.

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For a closed thermodynamic system of ideal gas, the entropic force is studied in this paper. The results show that the entropic force arises when the entropy is deviated from its equilibrium maximum value by an external force. This entropic force resists the entropy deviation enlarging, and will drive the entropy back to its maximum value if the external forces disappear.

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7

Silva, Carlos, and Kalyan Annamalai. "Entropy Generation and Human Aging: Lifespan Entropy and Effect of Physical Activity Level." Entropy 10, no. 2 (June 20, 2008): 100–123. http://dx.doi.org/10.3390/entropy-e10020100.

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8

Zhao, Lina, Chengyu Liu, Shoushui Wei, Qin Shen, Fan Zhou, and Jianqing Li. "A New Entropy-Based Atrial Fibrillation Detection Method for Scanning Wearable ECG Recordings." Entropy 20, no. 12 (November 26, 2018): 904. http://dx.doi.org/10.3390/e20120904.

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Entropy-based atrial fibrillation (AF) detectors have been applied for short-term electrocardiogram (ECG) analysis. However, existing methods suffer from several limitations. To enhance the performance of entropy-based AF detectors, we have developed a new entropy measure, named EntropyAF, which includes the following improvements: (1) use of a ranged function rather than the Chebyshev function to define vector distance, (2) use of a fuzzy function to determine vector similarity, (3) replacement of the probability estimation with density estimation for entropy calculation, (4) use of a flexible distance threshold parameter, and (5) use of adjusted entropy results for the heart rate effect. EntropyAF was trained using the MIT-BIH Atrial Fibrillation (AF) database, and tested on the clinical wearable long-term AF recordings. Three previous entropy-based AF detectors were used for comparison: sample entropy (SampEn), fuzzy measure entropy (FuzzyMEn) and coefficient of sample entropy (COSEn). For classifying AF and non-AF rhythms in the MIT-BIH AF database, EntropyAF achieved the highest area under receiver operating characteristic curve (AUC) values of 98.15% when using a 30-beat time window, which was higher than COSEn with AUC of 91.86%. SampEn and FuzzyMEn resulted in much lower AUCs of 74.68% and 79.24% respectively. For classifying AF and non-AF rhythms in the clinical wearable AF database, EntropyAF also generated the largest values of Youden index (77.94%), sensitivity (92.77%), specificity (85.17%), accuracy (87.10%), positive predictivity (68.09%) and negative predictivity (97.18%). COSEn had the second-best accuracy of 78.63%, followed by an accuracy of 65.08% in FuzzyMEn and an accuracy of 59.91% in SampEn. The new proposed EntropyAF also generated highest classification accuracy when using a 12-beat time window. In addition, the results from time cost analysis verified the efficiency of the new EntropyAF. This study showed the better discrimination ability for identifying AF when using EntropyAF method, indicating that it would be useful for the practical clinical wearable AF scanning.

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9

Iqbal, Ayesha, and Abdul Jawad. "Thermodynamics of Ricci-Gauss-Bonnet Dark Energy." Advances in High Energy Physics 2018 (2018): 1–12. http://dx.doi.org/10.1155/2018/6139430.

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We investigate the validity of generalized second law of thermodynamics of a physical system comprising newly proposed dark energy model called Ricci-Gauss-Bonnet and cold dark matter enveloped by apparent horizon and event horizon in flat Friedmann-Robertson-Walker (FRW) universe. For this purpose, Bekenstein entropy, Renyi entropy, logarithmic entropy, and power law entropic corrections are used. It is found that this law exhibits the validity on both apparent and event horizons except for the case of logarithmic entropic correction at apparent horizon. Also, we check the thermodynamical equilibrium condition for all cases of entropy and found its vitality in all cases of entropy.

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10

KAYA, Mehmet Onur, Yunus GÜRAL, and Mehmet GÜRCAN. "Entropy, Information and Entropy Correlation Coefficient." Turkiye Klinikleri Journal of Biostatistics 12, no. 1 (2020): 83–88. http://dx.doi.org/10.5336/biostatic.2020-74305.

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11

Rosser, J. Barkley. "Econophysics and the Entropic Foundations of Economics." Entropy 23, no. 10 (September 30, 2021): 1286. http://dx.doi.org/10.3390/e23101286.

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This paper examines relations between econophysics and the law of entropy as foundations of economic phenomena. Ontological entropy, where actual thermodynamic processes are involved in the flow of energy from the Sun through the biosphere and economy, is distinguished from metaphorical entropy, where similar mathematics used for modeling entropy is employed to model economic phenomena. Areas considered include general equilibrium theory, growth theory, business cycles, ecological economics, urban–regional economics, income and wealth distribution, and financial market dynamics. The power-law distributions studied by econophysicists can reflect anti-entropic forces is emphasized to show how entropic and anti-entropic forces can interact to drive economic dynamics, such as in the interaction between business cycles, financial markets, and income distributions.

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12

Flood, Matthew W., and Bernd Grimm. "EntropyHub: An open-source toolkit for entropic time series analysis." PLOS ONE 16, no. 11 (November 4, 2021): e0259448. http://dx.doi.org/10.1371/journal.pone.0259448.

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An increasing number of studies across many research fields from biomedical engineering to finance are employing measures of entropy to quantify the regularity, variability or randomness of time series and image data. Entropy, as it relates to information theory and dynamical systems theory, can be estimated in many ways, with newly developed methods being continuously introduced in the scientific literature. Despite the growing interest in entropic time series and image analysis, there is a shortage of validated, open-source software tools that enable researchers to apply these methods. To date, packages for performing entropy analysis are often run using graphical user interfaces, lack the necessary supporting documentation, or do not include functions for more advanced entropy methods, such as cross-entropy, multiscale cross-entropy or bidimensional entropy. In light of this, this paper introduces EntropyHub, an open-source toolkit for performing entropic time series analysis in MATLAB, Python and Julia. EntropyHub (version 0.1) provides an extensive range of more than forty functions for estimating cross-, multiscale, multiscale cross-, and bidimensional entropy, each including a number of keyword arguments that allows the user to specify multiple parameters in the entropy calculation. Instructions for installation, descriptions of function syntax, and examples of use are fully detailed in the supporting documentation, available on the EntropyHub website– www.EntropyHub.xyz. Compatible with Windows, Mac and Linux operating systems, EntropyHub is hosted on GitHub, as well as the native package repository for MATLAB, Python and Julia, respectively. The goal of EntropyHub is to integrate the many established entropy methods into one complete resource, providing tools that make advanced entropic time series analysis straightforward and reproducible.

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13

Parker, Michael C., and Chris Jeynes. "A Relativistic Entropic Hamiltonian–Lagrangian Approach to the Entropy Production of Spiral Galaxies in Hyperbolic Spacetime." Universe 7, no. 9 (August 31, 2021): 325. http://dx.doi.org/10.3390/universe7090325.

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Double-spiral galaxies are common in the Universe. It is known that the logarithmic double spiral is a Maximum Entropy geometry in hyperbolic (flat) spacetime that well represents an idealised spiral galaxy, with its central supermassive black hole (SMBH) entropy accounting for key galactic structural features including the stability and the double-armed geometry. Over time the central black hole must accrete mass, with the overall galactic entropy increasing: the galaxy is not at equilibrium. From the associated entropic Euler–Lagrange Equation (enabling the application of Noether’s theorem) we develop analytic expressions for the galactic entropy production of an idealised spiral galaxy showing that it is a conserved quantity, and we also derive an appropriate expression for its relativistic entropic Hamiltonian. We generalise Onsager’s celebrated expression for entropy production and demonstrate that galactic entropy production (entropy production corresponds to the intrinsic dissipation characteristics) is composed of two parts, one many orders of magnitude larger than the other: the smaller is comparable to the Hawking radiation of the central SMBH, while the other is comparable to the high entropy processes occurring within the accretion disks of real SMBHs. We conclude that galaxies cannot be isolated, since even idealised spiral galaxies intrinsically have a non-zero entropy production.

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14

ABDEL-ATY, MAHMOUD, ISSA A. AL-KHAYAT, and SHOUKRY S. HASSAN. "SHANNON INFORMATION AND ENTROPY SQUEEZING OF A SINGLE-MODE CAVITY QED OF A RAMAN INTERACTION." International Journal of Quantum Information 04, no. 05 (October 2006): 807–14. http://dx.doi.org/10.1142/s021974990600216x.

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Entropy squeezing is examined in the framework of Shannon information entropy for a degenerate Raman process involving two degenerate Rydberg energy levels of an atom interacting with a single-mode cavity field. Quantum squeezing in entropy is exhibited via the entropic uncertainty relation.

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15

Swendsen, Robert. "Gibbs’ Paradox and the Definition of Entropy." Entropy 10, no. 1 (March 20, 2008): 15–18. http://dx.doi.org/10.3390/entropy-e10010015.

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16

Naudts, Jan. "Generalised Exponential Families and Associated Entropy Functions." Entropy 10, no. 3 (July 16, 2008): 131–49. http://dx.doi.org/10.3390/entropy-e10030131.

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17

Lechthaler Zdenkovic, M., and A. E. Scheidegger. "Entropy of landscapes." Zeitschrift für Geomorphologie 33, no. 3 (October 5, 1989): 361–71. http://dx.doi.org/10.1127/zfg/33/1989/361.

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18

Yun, Huisung, and Mohammad Modarres. "Measures of Entropy to Characterize Fatigue Damage in Metallic Materials." Entropy 21, no. 8 (August 17, 2019): 804. http://dx.doi.org/10.3390/e21080804.

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This paper presents the entropic damage indicators for metallic material fatigue processes obtained from three associated energy dissipation sources. Since its inception, reliability engineering has employed statistical and probabilistic models to assess the reliability and integrity of components and systems. To supplement the traditional techniques, an empirically-based approach, called physics of failure (PoF), has recently become popular. The prerequisite for a PoF analysis is an understanding of the mechanics of the failure process. Entropy, the measure of disorder and uncertainty, introduced from the second law of thermodynamics, has emerged as a fundamental and promising metric to characterize all mechanistic degradation phenomena and their interactions. Entropy has already been used as a fundamental and scale-independent metric to predict damage and failure. In this paper, three entropic-based metrics are examined and demonstrated for application to fatigue damage. We collected experimental data on energy dissipations associated with fatigue damage, in the forms of mechanical, thermal, and acoustic emission (AE) energies, and estimated and correlated the corresponding entropy generations with the observed fatigue damages in metallic materials. Three entropic theorems—thermodynamics, information, and statistical mechanics—support approaches used to estimate the entropic-based fatigue damage. Classical thermodynamic entropy provided a reasonably constant level of entropic endurance to fatigue failure. Jeffreys divergence in statistical mechanics and AE information entropy also correlated well with fatigue damage. Finally, an extension of the relationship between thermodynamic entropy and Jeffreys divergence from molecular-scale to macro-scale applications in fatigue failure resulted in an empirically-based pseudo-Boltzmann constant equivalent to the Boltzmann constant.

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19

Gao, FuQing, and LiNa Li. "Weak entropy inequalities and entropic convergence." Science in China Series A: Mathematics 51, no. 10 (September 2, 2008): 1798–806. http://dx.doi.org/10.1007/s11425-008-0058-3.

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20

Stahl, D. O. "Entropy control costs and entropic equilibria." International Journal of Game Theory 19, no. 2 (June 1990): 129–38. http://dx.doi.org/10.1007/bf01761072.

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21

Geiger, Davi, and Zvi M. Kedem. "On Quantum Entropy." Entropy 24, no. 10 (September 23, 2022): 1341. http://dx.doi.org/10.3390/e24101341.

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Quantum physics, despite its intrinsically probabilistic nature, lacks a definition of entropy fully accounting for the randomness of a quantum state. For example, von Neumann entropy quantifies only the incomplete specification of a quantum state and does not quantify the probabilistic distribution of its observables; it trivially vanishes for pure quantum states. We propose a quantum entropy that quantifies the randomness of a pure quantum state via a conjugate pair of observables/operators forming the quantum phase space. The entropy is dimensionless, it is a relativistic scalar, it is invariant under canonical transformations and under CPT transformations, and its minimum has been established by the entropic uncertainty principle. We expand the entropy to also include mixed states. We show that the entropy is monotonically increasing during a time evolution of coherent states under a Dirac Hamiltonian. However, in a mathematical scenario, when two fermions come closer to each other, each evolving as a coherent state, the total system’s entropy oscillates due to the increasing spatial entanglement. We hypothesize an entropy law governing physical systems whereby the entropy of a closed system never decreases, implying a time arrow for particle physics. We then explore the possibility that as the oscillations of the entropy must by the law be barred in quantum physics, potential entropy oscillations trigger annihilation and creation of particles.

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22

Plastino, Angelo, Angel Plastino, Evaldo Curado, and Montse Casas. "Incremental Entropy Relation as an Alternative to MaxEnt." Entropy 10, no. 2 (June 24, 2008): 124–30. http://dx.doi.org/10.3390/entropy-e10020124.

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23

Behringer, Hans. "Qualitative Picture of Scaling in the Entropy Formalism." Entropy 10, no. 3 (September 5, 2008): 224–39. http://dx.doi.org/10.3390/entropy-e10030224.

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24

Scarfone, Antonio M. "A Maximal Entropy Distribution Derivation of the Sharma-Taneja-Mittal Entropic Form." Open Systems & Information Dynamics 25, no. 01 (March 2018): 1850002. http://dx.doi.org/10.1142/s1230161218500026.

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In this letter we derive the distribution maximizing the Sharma-Taneja-Mittal entropy under certain constrains by using an information inequality satisfied by the Br`egman divergence associated to this entropic form. The resulting maximal entropy distribution coincides with the one derived from the calculus according to the maximal entropy principle à la Jaynes.

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25

Kozhemyakina, Olga, Vladimir Barakhnin, Natalia Shashok, and Elina Kozhemyakina. "The Question of Studying Information Entropy in Poetic Texts." Applied Sciences 13, no. 20 (October 13, 2023): 11247. http://dx.doi.org/10.3390/app132011247.

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One of the approaches to quantitative text analysis is to represent a given text in the form of a time series, which can be followed by an information entropy study for different text representations, such as “symbolic entropy”, “phonetic entropy” and “emotional entropy” of various orders. Studying authors’ styles based on such entropic characteristics of their works seems to be a promising area in the field of information analysis. In this work, the calculations of entropy values of the first, second and third order for the corpus of poems by A.S. Pushkin and other poets from the Golden Age of Russian Poetry were carried out. The values of “symbolic entropy”, “phonetic entropy” and “emotional entropy” and their mathematical expectations and variances were calculated for given corpora using the software application that automatically extracts statistical information, which is potentially applicable to tasks that identify features of the author’s style. The statistical data extracted could become the basis of the stylometric classification of authors by entropy characteristics.

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26

Zhang, J., and H. Matsuzoe. "Entropy, cross-entropy, relative entropy: Deformation theory (a)." EPL (Europhysics Letters) 134, no. 1 (April 1, 2021): 18001. http://dx.doi.org/10.1209/0295-5075/134/18001.

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27

Weilenmann, Mirjam, and Roger Colbeck. "Non-Shannon inequalities in the entropy vector approach to causal structures." Quantum 2 (March 14, 2018): 57. http://dx.doi.org/10.22331/q-2018-03-14-57.

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A causal structure is a relationship between observed variables that in general restricts the possible correlations between them. This relationship can be mediated by unobserved systems, modelled by random variables in the classical case or joint quantum systems in the quantum case. One way to differentiate between the correlations realisable by two different causal structures is to use entropy vectors, i.e., vectors whose components correspond to the entropies of each subset of the observed variables. To date, the starting point for deriving entropic constraints within causal structures are the so-called Shannon inequalities (positivity of entropy, conditional entropy and conditional mutual information). In the present work we investigate what happens when non-Shannon entropic inequalities are included as well. We show that in general these lead to tighter outer approximations of the set of realisable entropy vectors and hence enable a sharper distinction of different causal structures. Since non-Shannon inequalities can only be applied amongst classical variables, it might be expected that their use enables an entropic distinction between classical and quantum causal structures. However, this remains an open question. We also introduce techniques for deriving inner approximations to the allowed sets of entropy vectors for a given causal structure. These are useful for proving tightness of outer approximations or for finding interesting regions of entropy space. We illustrate these techniques in several scenarios, including the triangle causal structure.

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28

VAKARIN, E. V., and J. P. BADIALI. "A LINK BETWEEN THE MAXIMUM ENTROPY APPROACH AND THE VARIATIONAL ENTROPY FORM." Modern Physics Letters B 25, no. 22 (August 30, 2011): 1821–28. http://dx.doi.org/10.1142/s0217984911027054.

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The maximum entropy approach operating with quite general entropy measure and constraint is considered. It is demonstrated that for a conditional or parametrized probability distribution f(x|μ), there is a "universal" relation among the entropy rate and the functions appearing in the constraint. This relation allows one to translate the specificities of the observed behavior θ(μ) into the amount of information on the relevant random variable x at different values of the parameter μ. It is shown that the recently proposed variational formulation of the entropic functional can be obtained as a consequence of this relation, that is from the maximum entropy principle. This resolves certain puzzling points that appeared in the variational approach.

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29

GULKO, LES. "THE ENTROPIC MARKET HYPOTHESIS." International Journal of Theoretical and Applied Finance 02, no. 03 (July 1999): 293–329. http://dx.doi.org/10.1142/s0219024999000170.

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Information theory teaches that entropy is the fundamental limit for data compression, and electrical engineers routinely use entropy as a criterion for efficient storage and transmission of information. Since modern financial theory teaches that competitive market prices store and transmit information with some efficiency, should financial economists be concerned with entropy? This paper presents a market model in which entropy emerges endogenously as a condition for the operational efficiency of price discovery while entropy maximization emerges as a condition for the informational efficiency of market prices. The maximum-entropy formalism makes the efficient market hypothesis operational and testable. This formalism is used to establish that entropic markets admit no arbitrage and support both the Ross arbitrage pricing theory and the Black–Scholes stock option pricing model.

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30

Michalowicz, Joseph, Jonathan Nichols, and Frank Bucholtz. "Calculation of Differential Entropy for a Mixed Gaussian Distribution." Entropy 10, no. 3 (August 25, 2008): 200–206. http://dx.doi.org/10.3390/entropy-e10030200.

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31

Lejček, Pavel, Siegfried Hofmann, and Václav Paidar. "The Significance of Entropy in Grain Boundary Segregation." Materials 12, no. 3 (February 5, 2019): 492. http://dx.doi.org/10.3390/ma12030492.

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The role of entropy in materials science is demonstrated in this report in order to establish its importance for the example of solute segregation at the grain boundaries of bcc iron. We show that substantial differences in grain boundary chemistry arise if their composition is calculated with or without consideration of the entropic term. Another example which clearly documents the necessity of implementing the entropic term in materials science is the enthalpy-entropy compensation effect. Entropy also plays a decisive role in the anisotropy of grain boundary segregation and in interface characterization. The consequences of the ambiguous determination of grain boundary segregation on the prediction of materials behavior are also briefly discussed. All the mentioned examples prove the importance of entropy in the quantification of grain boundary segregation and consequently of other materials properties.

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32

Wand, A. Joshua, and Kim A. Sharp. "Measuring Entropy in Molecular Recognition by Proteins." Annual Review of Biophysics 47, no. 1 (May 20, 2018): 41–61. http://dx.doi.org/10.1146/annurev-biophys-060414-034042.

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Molecular recognition by proteins is fundamental to the molecular basis of biology. Dissection of the thermodynamic landscape governing protein–ligand interactions has proven difficult because determination of various entropic contributions is quite challenging. Nuclear magnetic resonance relaxation measurements, theory, and simulations suggest that conformational entropy can be accessed through a dynamical proxy. Here, we review the relationship between measures of fast side-chain motion and the underlying conformational entropy. The dynamical proxy reveals that the contribution of conformational entropy can range from highly favorable to highly unfavorable and demonstrates the potential of this key thermodynamic variable to modulate protein–ligand interactions. The dynamical so-called entropy meter also refines the role of solvent entropy and directly determines the loss in rotational–translational entropy that occurs upon formation of high-affinity complexes. The ability to quantify the roles of entropy through an entropy meter based on measurable dynamical properties promises to highlight its role in protein function.

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33

ZHAO, HUI-HUA, GUANG-LIANG LI, REN ZHAO, MENG-SEN MA, and LI-CHUN ZHANG. "ENTANGLEMENT ENTROPY OF d-DIMENSIONAL BLACK HOLE AND QUANTUM ISOLATED HORIZON." Modern Physics Letters A 28, no. 32 (October 6, 2013): 1350129. http://dx.doi.org/10.1142/s0217732313501290.

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Based on the works of Ghosh et al. who view the black hole entropy as the logarithm of the number of quantum states on the Quantum Isolated Horizon (QIH), the entropy of d-dimensional black hole is studied. According to the Unruh–Verlinde temperature deduced from the concept of entropic force, the statistical entropy of quantum fields under the background of d-dimensional spacetime is calculated by means of quantum statistics. The results reveal the relation between the entanglement entropy of black hole and the logarithm of the number of quantum states and display the effects of dimensions on the correction terms of the entanglement entropy.

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34

BEN ABDALLAH, NAOUFEL, HEDIA CHAKER, and CHRISTIAN SCHMEISER. "THE HIGH FIELD ASYMPTOTICS FOR A FERMIONIC BOLTZMANN EQUATION: ENTROPY SOLUTIONS AND KINETIC SHOCK PROFILES." Journal of Hyperbolic Differential Equations 04, no. 04 (December 2007): 679–704. http://dx.doi.org/10.1142/s0219891607001318.

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The high field approximation of a fermionic Boltzmann equation of semiconductors is performed after the formation of shocks. By employing a new entropy, whose dissipation measures the departure from the high field equilibrium, convergence towards the entropic solution of the limiting conservation law is proven. The entropy is also used to construct kinetic shock profiles for entropic shocks and to prove non-existence of non-entropic shock profiles.

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DOOLEY, A. H., V. YA GOLODETS, D. J. RUDOLPH, and S. D. SINEL’SHCHIKOV. "Non-Bernoulli systems with completely positive entropy." Ergodic Theory and Dynamical Systems 28, no. 1 (February 2008): 87–124. http://dx.doi.org/10.1017/s014338570700034x.

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AbstractA new approach to actions of countable amenable groups with completely positive entropy (cpe), allowing one to answer some basic questions in this field, was recently developed. The question of the existence of cpe actions which are not Bernoulli was raised. In this paper, we prove that every countable amenable groupG, which contains an element of infinite order, has non-Bernoulli cpe actions. In fact we can produce, for any$h \in (0, \infty ]$, an uncountable family of cpe actions of entropyh, which are pairwise automorphically non-isomorphic. These actions are given by a construction which we call co-induction. This construction is related to, but different from the standard induced action. We study the entropic properties of co-induction, proving that ifαGis co-induced from an actionαΓof a subgroup Γ, thenh(αG)=h(αΓ). We also prove that ifαΓis a non-Bernoulli cpe action of Γ, thenαGis also non-Bernoulli and cpe. Hence the problem of finding an uncountable family of pairwise non-isomorphic cpe actions of the same entropy is reduced to one of finding an uncountable family of non-Bernoulli cpe actions of$\mathbb Z$, which pairwise satisfy a property we call ‘uniform somewhat disjointness’. We construct such a family using refinements of the classical cutting and stacking methods.

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Guel-Cortez, Adrian-Josue, and Eun-Jin Kim. "Relations between entropy rate, entropy production and information geometry in linear stochastic systems." Journal of Statistical Mechanics: Theory and Experiment 2023, no. 3 (March 1, 2023): 033204. http://dx.doi.org/10.1088/1742-5468/acbc24.

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Abstract In this work, we investigate the relation between the concept of ‘information rate’, an information geometric method for measuring the speed of the time evolution of the statistical states of a stochastic process, and stochastic thermodynamics quantities like entropy rate and entropy production. Then, we propose the application of entropy rate and entropy production to different practical applications such as abrupt event detection, correlation analysis, and control engineering. Specifically, by utilising the Fokker–Planck equation of multi-variable linear stochastic processes described by Langevin equations, we calculate the exact value for information rate, entropy rate, and entropy production and derive various inequalities among them. Inspired by classical correlation coefficients and control techniques, we create entropic-informed correlation coefficients as abrupt event detection methods and information geometric cost functions as optimal thermodynamic control policies, respectively. The methods are analysed via the numerical simulations of common prototypical systems.

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Kremer, Gilberto M. "Entropy, entropy flux and entropy rate of granular materials." Physica A: Statistical Mechanics and its Applications 389, no. 19 (October 2010): 4018–25. http://dx.doi.org/10.1016/j.physa.2010.06.004.

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Li, Shu-Nan, and Bing-Yang Cao. "Fractional-order heat conduction models from generalized Boltzmann transport equation." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 378, no. 2172 (May 11, 2020): 20190280. http://dx.doi.org/10.1098/rsta.2019.0280.

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The relationship between fractional-order heat conduction models and Boltzmann transport equations (BTEs) lacks a detailed investigation. In this paper, the continuity, constitutive and governing equations of heat conduction are derived based on fractional-order phonon BTEs. The underlying microscopic regimes of the generalized Cattaneo equation are thereafter presented. The effective thermal conductivity κ eff converges in the subdiffusive regime and diverges in the superdiffusive regime. A connection between the divergence and mean-square displacement 〈|Δ x | 2 〉 ∼ t γ is established, namely, κ eff ∼ t γ −1 , which coincides with the linear response theory. Entropic concepts, including the entropy density, entropy flux and entropy production rate, are studied likewise. Two non-trivial behaviours are observed, including the fractional-order expression of entropy flux and initial effects on the entropy production rate. In contrast with the continuous time random walk model, the results involve the non-classical continuity equations and entropic concepts. This article is part of the theme issue ‘Advanced materials modelling via fractional calculus: challenges and perspectives’.

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Serpa, Nilo, and Gisele Alves Fernandes. "The Way of Entropy: from Lagrangian Modelling to Thermal Engineering." CALIBRE - Revista Brasiliense de Engenharia e Física Aplicada 5 (December 20, 2020): 1. http://dx.doi.org/10.17648/calibre.v5.1476.

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<p>This article discusses the concept of entropy in an alternative thermodynamic view, demonstrating dialectically that the reversibility illustrated in common laboratory practice is only a local technical effect resulting from anthropic processes that slow down the irreversible advance of the disorder. Then, negative entropy is only a fiction stemming from the imaginationist idealism. The Lagrangian formalism is applied from the introduction of the idea of temporal confinement of thermal energy states, with time being interpreted as the basis of an evolutionary variable. The acceleration of entropy is formally presented independently of statistical mechanics.</p><p><br /><strong>Key words</strong>: thermodynamics, entropy, entropy acceleration, irreversibility.</p><p>=================================================================</p><p>O presente artigo discute o conceito de entropia numa visão termodinâmica alternativa, demonstrando dialeticamente que a reversibilidade ilustrada na prática laboratorial comum é apenas um efeito técnico local decorrente de processos antrópicos que desaceleram o avanço irreversível da desordem. Dessa forma, entropia negativa é uma ficção decorrente do idealismo imaginacionista. O formalismo Lagrangeano é aplicado a partir da introdução da ideia de confinamento temporal dos estados de energia térmica, com o tempo sendo interpretado como base de uma variável evolutiva. A aceleração da entropia é formalmente apresentada de modo independente da mecânica estatística.</p><p><br /><strong>Palavras-chave</strong>: termodinâmica, entropia, aceleração da entropia, irreversibilidade.</p>

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Pinal, Rodolfo. "Entropy of Mixing and the Glass Transition of Amorphous Mixtures." Entropy 10, no. 3 (August 26, 2008): 207–23. http://dx.doi.org/10.3390/entropy-e10030207.

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Guchenko, S. A., V. M. Yurov, V. I. Goncharenko, and V. S. Oleshko. "High-Entropy ZrTiCrNiCu Coating." METALLOFIZIKA I NOVEISHIE TEKHNOLOGII 43, no. 10 (December 29, 2021): 1365–75. http://dx.doi.org/10.15407/mfint.43.10.1365.

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Lin, Shu-Kun. "Gibbs Paradox and the Concepts of Information, Symmetry, Similarity and Their Relationship." Entropy 10, no. 1 (March 17, 2008): 1–5. http://dx.doi.org/10.3390/entropy-e10010001.

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43

Ratsaby, Joel. "An Algorithmic Complexity Interpretation of Lin's Third Law of Information Theory." Entropy 10, no. 1 (March 20, 2008): 6–14. http://dx.doi.org/10.3390/entropy-e10010006.

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Khrennikov, Andrei. "Bell-Boole Inequality: Nonlocality or Probabilistic Incompatibility of Random Variables?" Entropy 10, no. 2 (March 19, 2008): 19–32. http://dx.doi.org/10.3390/entropy-e10020019.

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Doyle, Laurance, Brenda McCowan, Sean Hanser, Christopher Chyba, Taylor Bucci, and J. Blue. "Applicability of Information Theory to the Quantification of Responses to Anthropogenic Noise by Southeast Alaskan Humpback Whales." Entropy 10, no. 2 (May 14, 2008): 33–46. http://dx.doi.org/10.3390/entropy-e10020033.

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Lin, Shu-Kun. "Asymmetry: The Foundation of Information. By Scott Muller. Springer: Berlin. 2007. VIII, 165 p. 33 illus., Hardcover. CHF 139.50. ISBN: 978-3-540-69883-8." Entropy 10, no. 2 (June 13, 2008): 47–48. http://dx.doi.org/10.3390/entropy-e10020047.

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Nosonovsky, Michael, and Sven Esche. "A Paradox of Decreasing Entropy in Multiscale Monte Carlo Grain Growth Simulations." Entropy 10, no. 2 (June 16, 2008): 49–54. http://dx.doi.org/10.3390/entropy-e10020049.

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Lin, Shu-Kun. "Symmetry Rules: How Science and Nature Are Founded on Symmetry. By Joe Rosen. Springer: Berlin. 2008, XIV, 305 p. 86 illus., Hardcover. CHF 70. ISBN: 978-3-540-75972-0." Entropy 10, no. 2 (June 16, 2008): 55–57. http://dx.doi.org/10.3390/entropy-e10020055.

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Kirwan, A. "Quantum and Ecosystem Entropies." Entropy 10, no. 2 (June 17, 2008): 58–70. http://dx.doi.org/10.3390/entropy-e10020058.

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Gao, Yun, Ioannis Kontoyiannis, and Elie Bienenstock. "Estimating the Entropy of Binary Time Series: Methodology, Some Theory and a Simulation Study." Entropy 10, no. 2 (June 17, 2008): 71–99. http://dx.doi.org/10.3390/entropy-e10020071.

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