Статті в журналах: "Entropic Potential"

1

Coffey, M. W. "Semiclassical position and momentum information entropy for sech2 and a family of rational potentials." Canadian Journal of Physics 85, no. 7 (July 1, 2007): 733–43. http://dx.doi.org/10.1139/p07-062.

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The classical and semiclassical position and momentum information entropies for the reflectionless sech2 potential and a family of rational potentials are obtained explicitly. The sum of these entropies is of interest for the entropic uncertainty principle that is stronger than the Heisenberg uncertainty relation. The analytic results relate the classical period of the motion, total energy, position and momentum entropy, and dependence upon the principal quantum number n. The logarithmic energy dependence of the entropies is presented. The potentials considered include as special cases the attractive delta function and square well. PACS Nos.: 03.67–a, 03.65.Sq, 03.65.Ge, 03.65.–w

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2

Rastegin, Alexey E. "Tests for quantum contextuality in terms of Q-entropies." Quantum Information and Computation 14, no. 11&12 (September 2014): 996–1013. http://dx.doi.org/10.26421/qic14.11-12-7.

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The information-theoretic approach to Bell's theorem is developed with use of the conditional $q$-entropies. The $q$-entropic measures fulfill many similar properties to the standard Shannon entropy. In general, both the locality and noncontextuality notions are usually treated with use of the so-called marginal scenarios. These hypotheses lead to the existence of a joint probability distribution, which marginalizes to all particular ones. Assuming the existence of such a joint probability distribution, we derive the family of inequalities of Bell's type in terms of conditional $q$-entropies for all $q\geq1$. Quantum violations of the new inequalities are exemplified within the Clauser--Horne--Shimony--Holt (CHSH) and Klyachko--Can--Binicio\v{g}lu--Shumovsky (KCBS) scenarios. An extension to the case of $n$-cycle scenario is briefly mentioned. The new inequalities with conditional $q$-entropies allow to expand a class of probability distributions, for which the nonlocality or contextuality can be detected within entropic formulation. The $q$-entropic inequalities can also be useful in analyzing cases with detection inefficiencies. Using two models of such a kind, we consider some potential advantages of the $q$-entropic formulation.

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3

Gavriil, Vassilios, Margarita Chatzichristidi, Zoe Kollia, Alkiviadis-Constantinos Cefalas, Nikolaos Spyropoulos-Antonakakis, Vadim Semashko, and Evangelia Sarantopoulou. "Photons Probe Entropic Potential Variation during Molecular Confinement in Nanocavities." Entropy 20, no. 8 (July 24, 2018): 545. http://dx.doi.org/10.3390/e20080545.

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In thin polymeric layers, external molecular analytes may well be confined within tiny surface nano/microcavities, or they may be attached to ligand adhesion binding sites via electrical dipole forces. Even though molecular trapping is followed by a variation of the entropic potential, the experimental evidence of entropic energy variation from molecular confinement is scarce because tiny thermodynamic energy density diverseness can be tracked only by sub-nm surface strain. Here, it is shown that water confinement within photon-induced nanocavities in Poly (2-hydroxyethyl methacrylate), (PHEMA) layers could be trailed by an entropic potential variation that competes with a thermodynamic potential from electric dipole attachment of molecular adsorbates in polymeric ligands. The nano/microcavities and the ligands were fabricated on a PHEMA matrix by vacuum ultraviolet laser photons at 157 nm. The entropic energy variation during confinement of water analytes on the photon processed PHEMA layer was monitored via sub-nm surface strain by applying white light reflectance spectroscopy, nanoindentation, contact angle measurements, Atomic Force Microscopy (AFM) imaging, and surface and fractal analysis. The methodology has the potency to identify entropic energy density variations less than 1 pJm−3 and to monitor dipole and entropic fields on biosurfaces.

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4

Bousnane, Z. "Entropic potential as manifold for the reduced entropy representations in superconductivity." Semiconductor physics, quantum electronics and optoelectronics 10, no. 1 (June 1, 2007): 101–5. http://dx.doi.org/10.15407/spqeo10.01.101.

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5

Chen, Hao, Yifan Sun, Shize Yang, Hui Wang, Wojciech Dmowski, Takeshi Egami, and Sheng Dai. "Self-regenerative noble metal catalysts supported on high-entropy oxides." Chemical Communications 56, no. 95 (2020): 15056–59. http://dx.doi.org/10.1039/d0cc05860b.

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A reversible temperature-dependent dissolution–exsolution process was discovered for noble metal species supported on high-entropy oxides, which indicates the potential to exploit the enhanced entropic effects to access self-regenerative catalysts.

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6

Morales, Rafael, Noé Hernández, Ricardo Cruz, Victor D. Cruz, and Luis A. Pineda. "Entropic associative memory for manuscript symbols." PLOS ONE 17, no. 8 (August 4, 2022): e0272386. http://dx.doi.org/10.1371/journal.pone.0272386.

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Manuscript symbols can be stored, recognized and retrieved from an entropic digital memory that is associative and distributed but yet declarative; memory retrieval is a constructive operation, memory cues to objects not contained in the memory are rejected directly without search, and memory operations can be performed through parallel computations. Manuscript symbols, both letters and numerals, are represented in Associative Memory Registers that have an associated entropy. The memory recognition operation obeys an entropy trade-off between precision and recall, and the entropy level impacts on the quality of the objects recovered through the memory retrieval operation. The present proposal is contrasted in several dimensions with neural networks models of associative memory. We discuss the operational characteristics of the entropic associative memory for retrieving objects with both complete and incomplete information, such as severe occlusions. The experiments reported in this paper add evidence on the potential of this framework for developing practical applications and computational models of natural memory.

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7

Korablev, Grigory A. "COVID-19 ENTROPIC CHARACTERISTICS." IZVESTIYA VYSSHIKH UCHEBNYKH ZAVEDENII KHIMIYA KHIMICHESKAYA TEKHNOLOGIYA 63, no. 9 (August 5, 2020): 101–7. http://dx.doi.org/10.6060/ivkkt.20206309.6284.

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It is demonstrated that according to the first law of thermodynamics the equality of entropic and negentropic components is the condition of resonance stationary state of systems. In the systems in which the interaction proceeds along the potential gradient (positive work), the resultant potential energy is found based on the principle of adding reciprocals of corresponding values of subsystems. This is the corpuscular process, in which entropy can serve as the theoretical concept. In the systems in which the interactions proceed against the potential gradient (negative work) the algebraic addition of their masses, as well as the corresponding energies of subsystems is performed. This is the wave process, in which negentropy can serve as the theoretical concept. The resonance stationary state of the systems is fulfilled under the condition of equality of degrees of their corpuscular and wave interactions. The entropy products in stationary state are completely compensated by the negentropy flow. Mathematically and graphically (by nomograms) the stationary state in microsystems is found by the following equation containing the tangent of the geodesic angel. The geodesic angle numerically defines the ratio of two legs of the right triangle whose values characterize energy dependencies through axial and circumferential stresses in the system with corpuscular-wave processes. This condition corresponds to the most optimal technological options and is widely present in nature, as well as in fractal systems. The initial nomograms of entropic and negentropic characteristics for many processes and phenomena in nature, engineering and physical chemistry are given. The entopic technique for forming fractal systems is presented. The coronavirus scenario in Russia is analyzed. The accuracy of forecast regarding the maximum number of diseases at the given moment and plateau duration is 96.5 % and 98.5%, respectively.

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8

Zhang, Zi-qiang, De-fu Hou, and Gang Chen. "The effect of chemical potential on imaginary potential and entropic force." Physics Letters B 768 (May 2017): 180–86. http://dx.doi.org/10.1016/j.physletb.2017.02.055.

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9

Curado, Evaldo M. F., and Fernando D. Nobre. "Non-Additive Entropic Forms and Evolution Equations for Continuous and Discrete Probabilities." Entropy 25, no. 8 (July 27, 2023): 1132. http://dx.doi.org/10.3390/e25081132.

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Increasing interest has been shown in the subject of non-additive entropic forms during recent years, which has essentially been due to their potential applications in the area of complex systems. Based on the fact that a given entropic form should depend only on a set of probabilities, its time evolution is directly related to the evolution of these probabilities. In the present work, we discuss some basic aspects related to non-additive entropies considering their time evolution in the cases of continuous and discrete probabilities, for which nonlinear forms of Fokker–Planck and master equations are considered, respectively. For continuous probabilities, we discuss an H-theorem, which is proven by connecting functionals that appear in a nonlinear Fokker–Planck equation with a general entropic form. This theorem ensures that the stationary-state solution of the Fokker–Planck equation coincides with the equilibrium solution that emerges from the extremization of the entropic form. At equilibrium, we show that a Carnot cycle holds for a general entropic form under standard thermodynamic requirements. In the case of discrete probabilities, we also prove an H-theorem considering the time evolution of probabilities described by a master equation. The stationary-state solution that comes from the master equation is shown to coincide with the equilibrium solution that emerges from the extremization of the entropic form. For this case, we also discuss how the third law of thermodynamics applies to equilibrium non-additive entropic forms in general. The physical consequences related to the fact that the equilibrium-state distributions, which are obtained from the corresponding evolution equations (for both continuous and discrete probabilities), coincide with those obtained from the extremization of the entropic form, the restrictions for the validity of a Carnot cycle, and an appropriate formulation of the third law of thermodynamics for general entropic forms are discussed.

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10

Ikot, A. N., G. J. Rampho, P. O. Amadi, U. S. Okorie, M. J. Sithole, and M. L. Lekala. "Quantum information-entropic measures for exponential-type potential." Results in Physics 18 (September 2020): 103150. http://dx.doi.org/10.1016/j.rinp.2020.103150.

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11

Zhang, Jialin. "Entropic Statistics: Concept, Estimation, and Application in Machine Learning and Knowledge Extraction." Machine Learning and Knowledge Extraction 4, no. 4 (September 30, 2022): 865–87. http://dx.doi.org/10.3390/make4040044.

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The demands for machine learning and knowledge extraction methods have been booming due to the unprecedented surge in data volume and data quality. Nevertheless, challenges arise amid the emerging data complexity as significant chunks of information and knowledge lie within the non-ordinal realm of data. To address the challenges, researchers developed considerable machine learning and knowledge extraction methods regarding various domain-specific challenges. To characterize and extract information from non-ordinal data, all the developed methods pointed to the subject of Information Theory, established following Shannon’s landmark paper in 1948. This article reviews recent developments in entropic statistics, including estimation of Shannon’s entropy and its functionals (such as mutual information and Kullback–Leibler divergence), concepts of entropic basis, generalized Shannon’s entropy (and its functionals), and their estimations and potential applications in machine learning and knowledge extraction. With the knowledge of recent development in entropic statistics, researchers can customize existing machine learning and knowledge extraction methods for better performance or develop new approaches to address emerging domain-specific challenges.

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12

Sarswat, Shruti, Aiswarya R, and Jobin Jose. "Shannon entropy of resonant scattered state in the e–C₆₀ elastic collision." Journal of Physics B: Atomic, Molecular and Optical Physics 55, no. 5 (March 2, 2022): 055003. http://dx.doi.org/10.1088/1361-6455/ac5719.

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Abstract Resonance is a remarkable feature in elastic scattering and the resonant states of e–C60 scattering are benchmarked using Shannon entropy in the present work. The resonant wavefunction, total cross-section, partial cross-sections, and scattering phase shifts are calculated for the e–C60 scattering to review the localization properties owing to resonance. Three different model interaction potentials are used in the paper to simulate the environment of the C60 shell; annular square well, Gaussian annular square well, and Lorentzian potential. This paper aims to establish a relationship between the Shannon entropy and resonant properties linked with e + C60 scattering. This work introduces the Shannon entropy as an indicator of resonance in elastic scattering and it unveils the susceptibility of entropic properties to the nature of the model potential.

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13

Herwig, Heinz. "How to Teach Heat Transfer More Systematically by Involving Entropy." Entropy 20, no. 10 (October 15, 2018): 791. http://dx.doi.org/10.3390/e20100791.

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In order to teach heat transfer systematically and with a clear physical background, it is recommended that entropy should not be ignored as a fundamental quantity. Heat transfer processes are characterized by introducing the so-called “entropic potential” of the transferred energy, and an assessment number is based on this new quantity.

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14

Liu, Yang, and Bao-Quan Ai. "Diffusion in a tilted periodic potential with entropic barriers." Journal of Physics: Condensed Matter 21, no. 46 (October 26, 2009): 465102. http://dx.doi.org/10.1088/0953-8984/21/46/465102.

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15

Grassi, A. "An entropic form for NLFP with coulombic-like potential." Physics Letters A 376, no. 6-7 (January 2012): 803–8. http://dx.doi.org/10.1016/j.physleta.2012.01.021.

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16

Zhang, Zi-qiang, Xiangrong Zhu, and Ping-ping Wu. "Imaginary potential and entropic force in non-commutative plasma." Nuclear Physics B 945 (August 2019): 114689. http://dx.doi.org/10.1016/j.nuclphysb.2019.114689.

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17

Majumder, Barun. "The Effects of Minimal Length in Entropic Force Approach." Advances in High Energy Physics 2013 (2013): 1–8. http://dx.doi.org/10.1155/2013/296836.

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With Verlinde’s recent proposal which says that gravity can be identified with an entropic force and considering the effects of generalized uncertainty principle in the black hole entropy-area relation we derive the modified equations for Newton’s law of gravitation, modified Newtonian dynamics, and Einstein’s general relativity. The corrections to the Newtonian potential is compared with the corrections that come from Randall-Sundrum II model and an effective field theoretical model of quantum general relativity. The effect of the generalized uncertainty principle introduces aareatype correction term in the entropy-area relation whose consequences in different scenarios are discussed.

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18

CATTUTO, C., G. COSTANTINI, and F. MARCHESONI. "NOISE RECTIFICATION AS AN ENTROPIC EFFECT." Fluctuation and Noise Letters 01, no. 02 (June 2001): L97—L103. http://dx.doi.org/10.1142/s0219477501000263.

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Asymmetric kinks bridging two adjacent potential valleys of equal depth but different curvature are predicted to drift with velocity proportional to their temperature, in close agreement with numerical simulation. Such a (white) noise rectification phenomenon, not to be mistaken for a ratchet-like effect, is an entropic mechanism with potential impact on noise-sustained signal propagation in linear bistable arrays, of both biological and microelectronic nature.

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19

Daguerre, L., G. Torroba, R. Medina, and M. Solís. "NON RELATIVISTIC QUANTUM FIELD THEORY: DYNAMICS AND IRREVERSIBILITY." Anales AFA 32, no. 4 (January 15, 2022): 93–98. http://dx.doi.org/10.31527/analesafa.2021.32.4.93.

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We study aspects of quantum field theory at finite density using techniques and concepts from quantum information theory. We focus on massive Dirac fermions with chemical potential in 1+1 space-time dimensions. Using the entanglement entropy on an interval, we construct an entropic c-function that is finite. This c-function is not monotonous,and incorporates the long-range entanglement from the Fermi surface. Motivated by previous works on lattice models,we next compute the Renyi entropies numerically, and find Friedel-type oscillations. Next, we analyze the mutual in-formation as a measure of correlation functions between different regions. Using a long-distance expansion developed by Cardy, we show how the mutual information detects the Fermi surface correlations already at leading order in the expansion. Finally, we analyze the relative entropy and its Renyi generalizations in order to distinguish states with different charge. We find that states in different superselection sectors give rise to a super-extensive behavior in the relative entropy.

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20

Loukidis, Andronikos, Dimos Triantis, and Ilias Stavrakas. "Non-Extensive Statistical Analysis of Acoustic Emissions: The Variability of Entropic Index q during Loading of Brittle Materials Until Fracture." Entropy 23, no. 3 (February 25, 2021): 276. http://dx.doi.org/10.3390/e23030276.

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Non-extensive statistical mechanics (NESM), introduced by Tsallis based on the principle of non-additive entropy, is a generalisation of the Boltzmann–Gibbs statistics. NESM has been shown to provide the necessary theoretical and analytical implementation for studying complex systems such as the fracture mechanisms and crack evolution processes that occur in mechanically loaded specimens of brittle materials. In the current work, acoustic emission (AE) data recorded when marble and cement mortar specimens were subjected to three distinct loading protocols until fracture, are discussed in the context of NESM. The NESM analysis showed that the cumulative distribution functions of the AE interevent times (i.e., the time interval between successive AE hits) follow a q-exponential function. For each examined specimen, the corresponding Tsallis entropic q-indices and the parameters βq and τq were calculated. The entropic index q shows a systematic behaviour strongly related to the various stages of the implemented loading protocols for all the examined specimens. Results seem to support the idea of using the entropic index q as a potential pre-failure indicator for the impending catastrophic fracture of the mechanically loaded specimens.

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21

Kumar, Kirtee, and Vinod Prasad. "Entropic measures of an atom confined in modified Hulthen potential." Results in Physics 21 (February 2021): 103796. http://dx.doi.org/10.1016/j.rinp.2020.103796.

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22

Kaplan, P. D., Luc P. Faucheux, and Albert J. Libchaber. "Direct Observation of the Entropic Potential in a Binary Suspension." Physical Review Letters 73, no. 21 (November 21, 1994): 2793–96. http://dx.doi.org/10.1103/physrevlett.73.2793.

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23

De Cristofaro, R., M. Picozzi, E. De Candia, B. Rocca, and R. Landolfi. "Thrombin-thrombomodulin interaction: energetics and potential role of water as an allosteric effector." Biochemical Journal 310, no. 1 (August 15, 1995): 49–53. http://dx.doi.org/10.1042/bj3100049.

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The interaction of rabbit lung thrombomodulin (TM) and C-terminal hirudin 54-65 fragment (Hir54-65) with human alpha-thrombin were investigated by exploiting their competitive inhibition of thrombin-fibrinogen interaction. Measurements of Ki values for TM and Hir54-65 interactions with human alpha-thrombin performed over a temperature range spanning from 10 to 40 degrees C showed a constant enthalpy for both ligands. The enthalpic and entropic contributions to the free energy of binding, however, are different for TM and the hirudin peptide. The calculated values of delta H and delta S, in fact, were -47.3 +/- 2.51 kJ (-11.3 +/- 0.6 kcal)/mol and -42.7 +/- 7.9 J (-10.2 +/- 1.9 cal)/mol.K for the hirudin peptide, while being -22.9 +/- 2.09 kJ (-5.47 +/- 0.5 kcal)/mol and 102.50 +/- 6.69 J (24.5 +/- 1.6 cal)/mol.K respectively for TM binding. These findings indicate that the interaction between thrombin and Hir54-65 is largely driven by the enthalpic contribution, whereas the positive entropy change is the driving force for the formation of the thrombin-TM complex. In other experiments performed in the presence of various concentrations of either sorbitol or sucrose it could be demonstrated that the value of the equilibrium association constant for thrombin-TM interaction increases as a function of the osmotic pressure, while the thrombin-Hir54-65 interaction was not affected by the same conditions. Moreover, control experiments showed that no major conformational changes are produced on TM by osmotic pressures used in the present study. From these experiments it was calculated that roughly 35 water molecules are released into the bulk water upon TM binding. Such a phenomenon, which is likely to be responsible for the entropic change described above, indicates the relevance of hydration processes for the formation of the thrombin-TM adduct.

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24

Gavriil, Vassilios, Margarita Chatzichristidi, Dimitrios Christofilos, Gerasimos A. Kourouklis, Zoe Kollia, Evangelos Bakalis, Alkiviadis-Constantinos Cefalas, and Evangelia Sarantopoulou. "Entropy and Random Walk Trails Water Confinement and Non-Thermal Equilibrium in Photon-Induced Nanocavities." Nanomaterials 10, no. 6 (June 2, 2020): 1101. http://dx.doi.org/10.3390/nano10061101.

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Molecules near surfaces are regularly trapped in small cavitations. Molecular confinement, especially water confinement, shows intriguing and unexpected behavior including surface entropy adjustment; nevertheless, observations of entropic variation during molecular confinement are scarce. An experimental assessment of the correlation between surface strain and entropy during molecular confinement in tiny crevices is difficult because strain variances fall in the nanometer scale. In this work, entropic variations during water confinement in 2D nano/micro cavitations were observed. Experimental results and random walk simulations of water molecules inside different size nanocavitations show that the mean escaping time of molecular water from nanocavities largely deviates from the mean collision time of water molecules near surfaces, crafted by 157 nm vacuum ultraviolet laser light on polyacrylamide matrixes. The mean escape time distribution of a few molecules indicates a non-thermal equilibrium state inside the cavity. The time differentiation inside and outside nanocavities reveals an additional state of ordered arrangements between nanocavities and molecular water ensembles of fixed molecular length near the surface. The configured number of microstates correctly counts for the experimental surface entropy deviation during molecular water confinement. The methodology has the potential to identify confined water molecules in nanocavities with life science importance.

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25

Gaberle, Julian, David Z. Gao, and Alexander L. Shluger. "Calculating free energies of organic molecules on insulating substrates." Beilstein Journal of Nanotechnology 8 (March 21, 2017): 667–74. http://dx.doi.org/10.3762/bjnano.8.71.

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The challenges and limitations in calculating free energies and entropies of adsorption and interaction of organic molecules on an insulating substrate are discussed. The adhesion of 1,3,5-tri(4'-cyano-[1,1'-biphenyl]-4-yl)benzene (TCB) and 1,4-bis(4-cyanophenyl)-2,5-bis(decyloxy)benzene (CDB) molecules to step edges on the KCl(001) surface and the formation of molecular dimers were studied using classical molecular dynamics. Both molecules contain the same anchoring groups and benzene ring structures, yet differ in their flexibility. Therefore, the entropic contributions to their free energy differ, which affects surface processes. Using potential of mean force and thermodynamic integration techniques, free energy profiles and entropy changes were calculated for step adhesion and dimer formation of these molecules. However, converging these calculations is nontrivial and comes at large computational cost. We illustrate the difficulties as well as the possibilities of applying these methods towards understanding dynamic processes of organic molecules on insulating substrates.

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26

Keshmiri, Soheil. "Conditional Entropy: A Potential Digital Marker for Stress." Entropy 23, no. 3 (February 26, 2021): 286. http://dx.doi.org/10.3390/e23030286.

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Recent decades have witnessed a substantial progress in the utilization of brain activity for the identification of stress digital markers. In particular, the success of entropic measures for this purpose is very appealing, considering (1) their suitability for capturing both linear and non-linear characteristics of brain activity recordings and (2) their direct association with the brain signal variability. These findings rely on external stimuli to induce the brain stress response. On the other hand, research suggests that the use of different types of experimentally induced psychological and physical stressors could potentially yield differential impacts on the brain response to stress and therefore should be dissociated from more general patterns. The present study takes a step toward addressing this issue by introducing conditional entropy (CE) as a potential electroencephalography (EEG)-based resting-state digital marker of stress. For this purpose, we use the resting-state multi-channel EEG recordings of 20 individuals whose responses to stress-related questionnaires show significantly higher and lower level of stress. Through the application of representational similarity analysis (RSA) and K-nearest-neighbor (KNN) classification, we verify the potential that the use of CE can offer to the solution concept of finding an effective digital marker for stress.

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27

Wiesner, K., J. Teles, M. Hartnor, and C. Peterson. "Haematopoietic stem cells: entropic landscapes of differentiation." Interface Focus 8, no. 6 (October 19, 2018): 20180040. http://dx.doi.org/10.1098/rsfs.2018.0040.

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The metaphor of a potential epigenetic differentiation landscape broadly suggests that during differentiation a stem cell approaches a stable equilibrium state from a higher free energy towards a stable equilibrium state which represents the final cell type. It has been conjectured that there is an analogy to the concept of entropy in statistical mechanics. In this context, in the undifferentiated state, the entropy would be large since fewer constraints exist on the gene expression programmes of the cell. As differentiation progresses, gene expression programmes become more and more constrained and thus the entropy would be expected to decrease. In order to assess these predictions, we compute the Shannon entropy for time-resolved single-cell gene expression data in two different experimental set-ups of haematopoietic differentiation. We find that the behaviour of this entropy measure is in contrast to these predictions. In particular, we find that the Shannon entropy is not a decreasing function of developmental pseudo-time but instead it increases towards the time point of commitment before decreasing again. This behaviour is consistent with an increase in gene expression disorder observed in populations sampled at the time point of commitment. Single cells in these populations exhibit different combinations of regulator activity that suggest the presence of multiple configurations of a potential differentiation network as a result of multiple entry points into the committed state.

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28

Löhr, Thomas, Pietro Sormanni, and Michele Vendruscolo. "Conformational Entropy as a Potential Liability of Computationally Designed Antibodies." Biomolecules 12, no. 5 (May 18, 2022): 718. http://dx.doi.org/10.3390/biom12050718.

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In silico antibody discovery is emerging as a viable alternative to traditional in vivo and in vitro approaches. Many challenges, however, remain open to enabling the properties of designed antibodies to match those produced by the immune system. A major question concerns the structural features of computer-designed complementarity determining regions (CDRs), including the role of conformational entropy in determining the stability and binding affinity of the designed antibodies. To address this problem, we used enhanced-sampling molecular dynamics simulations to compare the free energy landscapes of single-domain antibodies (sdAbs) designed using structure-based (DesAb-HSA-D3) and sequence-based approaches (DesAbO), with that of a nanobody derived from llama immunization (Nb10). Our results indicate that the CDR3 of DesAbO is more conformationally heterogeneous than those of both DesAb-HSA-D3 and Nb10, and the CDR3 of DesAb-HSA-D3 is slightly more dynamic than that of Nb10, which is the original scaffold used for the design of DesAb-HSA-D3. These differences underline the challenges in the rational design of antibodies by revealing the presence of conformational substates likely to have different binding properties and to generate a high entropic cost upon binding.

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29

Gasper, Paul M., Phineus R. Markwick, and J. Andrew McCammon. "Accelerated Molecular Dynamics Simulations of Thrombin-Thrombomodulin Reveal Potential for Entropic Allostery." Biophysical Journal 102, no. 3 (January 2012): 735a—736a. http://dx.doi.org/10.1016/j.bpj.2011.11.3992.

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30

Le Blanc, Richard. "Jaynes-Gibbs Entropic Convex Duals and Orthogonal Polynomials." Entropy 24, no. 5 (May 16, 2022): 709. http://dx.doi.org/10.3390/e24050709.

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The univariate noncentral distributions can be derived by multiplying their central distributions with translation factors. When constructed in terms of translated uniform distributions on unit radius hyperspheres, these translation factors become generating functions for classical families of orthogonal polynomials. The ultraspherical noncentral t, normal N, F, and χ2 distributions are thus found to be associated with the Gegenbauer, Hermite, Jacobi, and Laguerre polynomial families, respectively, with the corresponding central distributions standing for the polynomial family-defining weights. Obtained through an unconstrained minimization of the Gibbs potential, Jaynes’ maximal entropy priors are formally expressed in terms of the empirical densities’ entropic convex duals. Expanding these duals on orthogonal polynomial bases allows for the expedient determination of the Jaynes–Gibbs priors. Invoking the moment problem and the duality principle, modelization can be reduced to the direct determination of the prior moments in parametric space in terms of the Bayes factor’s orthogonal polynomial expansion coefficients in random variable space. Genomics and geophysics examples are provided.

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31

Keshmiri, Soheil. "Entropy and the Brain: An Overview." Entropy 22, no. 9 (August 21, 2020): 917. http://dx.doi.org/10.3390/e22090917.

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Entropy is a powerful tool for quantification of the brain function and its information processing capacity. This is evident in its broad domain of applications that range from functional interactivity between the brain regions to quantification of the state of consciousness. A number of previous reviews summarized the use of entropic measures in neuroscience. However, these studies either focused on the overall use of nonlinear analytical methodologies for quantification of the brain activity or their contents pertained to a particular area of neuroscientific research. The present study aims at complementing these previous reviews in two ways. First, by covering the literature that specifically makes use of entropy for studying the brain function. Second, by highlighting the three fields of research in which the use of entropy has yielded highly promising results: the (altered) state of consciousness, the ageing brain, and the quantification of the brain networks’ information processing. In so doing, the present overview identifies that the use of entropic measures for the study of consciousness and its (altered) states led the field to substantially advance the previous findings. Moreover, it realizes that the use of these measures for the study of the ageing brain resulted in significant insights on various ways that the process of ageing may affect the dynamics and information processing capacity of the brain. It further reveals that their utilization for analysis of the brain regional interactivity formed a bridge between the previous two research areas, thereby providing further evidence in support of their results. It concludes by highlighting some potential considerations that may help future research to refine the use of entropic measures for the study of brain complexity and its function. The present study helps realize that (despite their seemingly differing lines of inquiry) the study of consciousness, the ageing brain, and the brain networks’ information processing are highly interrelated. Specifically, it identifies that the complexity, as quantified by entropy, is a fundamental property of conscious experience, which also plays a vital role in the brain’s capacity for adaptation and therefore whose loss by ageing constitutes a basis for diseases and disorders. Interestingly, these two perspectives neatly come together through the association of entropy and the brain capacity for information processing.

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32

MAGOULAS, GEORGE D., and ARISTOKLIS ANASTASIADIS. "APPROACHES TO ADAPTIVE STOCHASTIC SEARCH BASED ON THE NONEXTENSIVE q-DISTRIBUTION." International Journal of Bifurcation and Chaos 16, no. 07 (July 2006): 2081–91. http://dx.doi.org/10.1142/s0218127406015921.

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This paper explores the use of the nonextensive q-distribution in the context of adaptive stochastic searching. The proposed approach consists of generating the "probability" of moving from one point of the search space to another through a probability distribution characterized by the q entropic index of the nonextensive entropy. The potential benefits of this technique are investigated by incorporating it in two different adaptive search algorithmic models to create new modifications of the diffusion method and the particle swarm optimizer. The performance of the modified search algorithms is evaluated in a number of nonlinear optimization and neural network training benchmark problems.

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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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34

D'Aniello, Raffaele, Karsten Knobloch, and Carolin Kissner. "Analysis of Combustion Noise Sources Using Doak's Momentum Potential Theory." INTER-NOISE and NOISE-CON Congress and Conference Proceedings 265, no. 6 (February 1, 2023): 1061–72. http://dx.doi.org/10.3397/in_2022_0148.

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Noise emissions of modern lean combustors are related to different sources. Direct combustion noise is generated by heat release fluctuations, while indirect noise sources include the acceleration of entropy and vorticity inhomogeneities through the nozzle-guide-vane or at the combustor exit. The latter noise source is characterized by the coupling of fluctuations convected in non-uniform mean flow, which can e.g. cause vortical or entropic fluctuations to be partly transferred into acoustics. Due to the complexity of the sources, a clear and quantitative separation of the different phenomena in terms of primitive variables presents a significant challenge. This study therefore proposes an alternative framework for the description of combustion noise based on Doak's Momentum Potential Theory (MPT). The MPT defines a Generalized Acoustic Field (GAF) and describes the sound production in terms of mean energy fluxes carried by the respective acoustic, thermal and turbulent fluctuating momentum components. To confirm the ability to identify the different combustion noise sources, the method was applied to Large-Eddy Simulation data of a non-reacting swirl-combustor simulator. Finally, the coherent character and spectral behavior of the GAF were investigated using a Spectral Proper Orthogonal Decomposition (SPOD) analysis and correlated to the source distributions.

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35

Zhu, Zhongfan, and Jie Dou. "An Extended Entropic Model for Cohesive Sediment Flocculation in a Piecewise Varied Shear Environment." Entropy 23, no. 10 (September 28, 2021): 1263. http://dx.doi.org/10.3390/e23101263.

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In this study, an extended model for describing the temporal evolution of a characteristic floc size of cohesive sediment particles when the flocculation system is subject to a piecewise varied turbulent shear rate was derived by the probability methods based on the Shannon entropy theory following Zhu (2018). This model only contained three important parameters: initial and steady-state values of floc size, and a parameter characterizing the maximum capacity for floc size increase (or decay), and it can be adopted to capture well a monotonic pattern in which floc size increases (or decays) with flocculation time. Comparison with 13 literature experimental data sets regarding floc size variation to a varied shear rate showed the validity of the entropic model with a high correlation coefficient and few errors. Furthermore, for the case of tapered shear flocculation, it was found that there was a power decay of the capacity parameter with the shear rate, which is similar to the dependence of the steady-state floc size on the shear rate. The entropic model was further parameterized by introducing these two empirical relations into it, and the finally obtained model was found to be more sensitive to two empirical coefficients that have been incorporated into the capacity parameter than those in the steady-state floc size. The proposed entropic model could have the potential, as an addition to existing flocculation models, to be coupled into present mature hydrodynamic models to model the cohesive sediment transport in estuarine and coastal regions.

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36

Dehesa, Jesús S. "Rényi Entropies of Multidimensional Oscillator and Hydrogenic Systems with Applications to Highly Excited Rydberg States." Entropy 24, no. 11 (November 2, 2022): 1590. http://dx.doi.org/10.3390/e24111590.

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The various facets of the internal disorder of quantum systems can be described by means of the Rényi entropies of their single-particle probability density according to modern density functional theory and quantum information techniques. In this work, we first show the lower and upper bounds for the Rényi entropies of general and central-potential quantum systems, as well as the associated entropic uncertainty relations. Then, the Rényi entropies of multidimensional oscillator and hydrogenic-like systems are reviewed and explicitly determined for all bound stationary position and momentum states from first principles (i.e., in terms of the potential strength, the space dimensionality and the states’s hyperquantum numbers). This is possible because the associated wavefunctions can be expressed by means of hypergeometric orthogonal polynomials. Emphasis is placed on the most extreme, non-trivial cases corresponding to the highly excited Rydberg states, where the Rényi entropies can be amazingly obtained in a simple, compact, and transparent form. Powerful asymptotic approaches of approximation theory have been used when the polynomial’s degree or the weight-function parameter(s) of the Hermite, Laguerre, and Gegenbauer polynomials have large values. At present, these special states are being shown of increasing potential interest in quantum information and the associated quantum technologies, such as e.g., quantum key distribution, quantum computation, and quantum metrology.

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37

Funkhouser, Scott, William Suski, and Andrew Winn. "Waveform information from quantum mechanical entropy." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 472, no. 2190 (June 2016): 20160033. http://dx.doi.org/10.1098/rspa.2016.0033.

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Although the entropy of a given signal-type waveform is technically zero, it is nonetheless desirable to use entropic measures to quantify the associated information. Several such prescriptions have been advanced in the literature but none are generally successful. Here, we report that the Fourier-conjugated ‘total entropy’ associated with quantum-mechanical probabilistic amplitude functions (PAFs) is a meaningful measure of information in non-probabilistic real waveforms, with either the waveform itself or its (normalized) analytic representation acting in the role of the PAF. Detailed numerical calculations are presented for both adaptations, showing the expected informatic behaviours in a variety of rudimentary scenarios. Particularly noteworthy are the sensitivity to the degree of randomness in a sequence of pulses and potential for detection of weak signals.

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38

Zhang, Zhanli. "Coupling entropy of co-processing model on social networks." Modern Physics Letters B 29, no. 25 (September 20, 2015): 1550149. http://dx.doi.org/10.1142/s0217984915501493.

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Coupling entropy of co-processing model on social networks is investigated in this paper. As one crucial factor to determine the processing ability of nodes, the information flow with potential time lag is modeled by co-processing diffusion which couples the continuous time processing and the discrete diffusing dynamics. Exact results on master equation and stationary state are achieved to disclose the formation. In order to understand the evolution of the co-processing and design the optimal routing strategy according to the maximal entropic diffusion on networks, we propose the coupling entropy comprehending the structural characteristics and information propagation on social network. Based on the analysis of the co-processing model, we analyze the coupling impact of the structural factor and information propagating factor on the coupling entropy, where the analytical results fit well with the numerical ones on scale-free social networks.

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39

Polson, James M. "Entropic collapse transition of a polymer in a solvent with a nonadditive potential." Physical Review E 60, no. 3 (September 1, 1999): 3429–31. http://dx.doi.org/10.1103/physreve.60.3429.

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40

Wenterodt, Tammo, and Heinz Herwig. "The Entropic Potential Concept: a New Way to Look at Energy Transfer Operations." Entropy 16, no. 4 (April 14, 2014): 2071–84. http://dx.doi.org/10.3390/e16042071.

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41

Wenterodt, Tammo, Christoph Redecker, and Heinz Herwig. "Second law analysis for sustainable heat and energy transfer: The entropic potential concept." Applied Energy 139 (February 2015): 376–83. http://dx.doi.org/10.1016/j.apenergy.2014.10.073.

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42

Isonguyo, C. N., K. J. Oyewumi, O. S. Oyun, and I. B. Okon. "Entropic uncertainty relations and the fisher information for the Generalized radial Yukawa potential." World Journal of Applied Science & Technology 14, no. 1b (June 19, 2023): 44–50. http://dx.doi.org/10.4314/wojast.v14i1b.44.

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The Heisenberg uncertainty relation as well as the Fisher information are presented analytically and numerically for the Generalized radial Yukawa potential. The probability density for the ground and first excited state has been analyzed via the Fisher information for this potential model. Some numerical results are obtained. From the numerical results obtained, we observed that, for n = 0, 1, the position-space Fisher information Ir increases with increasing potential parameter a, while the momentum-space Fisher information Iρ initially increases, and later decreases with increasing potential parameter a. The Fisher-information-based uncertainty relation and the Heisenberg uncertainty relation have been verified to hold for this atomic model. In addition, we observed a squeezed phenomenon in some of the results in position r and momentum ρ for the ground and first excited states.

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43

Plastino, Angelo, and M. C. Rocca. "Statistical Mechanics-Based Schrödinger Treatment of Gravity." Entropy 21, no. 7 (July 12, 2019): 682. http://dx.doi.org/10.3390/e21070682.

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The entropic gravity conception proposes that what has been traditionally interpreted as unobserved dark matter might be merely the product of quantum effects. These effects would produce a novel sort of positive energy that translates into dark matter via E = m c 2 . In the case of axions, this perspective has been shown to yield quite sensible, encouraging results [DOI:10.13140/RG.2.2.17894.88641]. Therein, a simple Schrödinger mechanism was utilized, in which his celebrated equation is solved with a potential function based on the microscopic Verlinde’s entropic force advanced in [Physica A 511 (2018) 139]. In this paper, we revisit this technique with regards to fermions’ behavior (specifically, baryons).

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44

Marquet, Pascal, and Bjorn Stevens. "On Moist Potential Temperatures and Their Ability to Characterize Differences in the Properties of Air Parcels." Journal of the Atmospheric Sciences 79, no. 4 (April 2022): 1089–103. http://dx.doi.org/10.1175/jas-d-21-0095.1.

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Abstract A framework is introduced to compare moist “potential” temperatures. The equivalent potential temperature θe, the liquid water potential temperature θℓ, and the entropy potential temperature θs are all shown to be potential temperatures, in the sense that they measure the temperatures of certain reference-state systems whose entropy is the same as that of the air parcel. They only differ in the choice of reference-state composition—θℓ describes the temperature a condensate-free state, θe a vapor-free state, and θs a water-free state—required to have the same entropy as the given state. Although in this sense θe, θℓ, and θs are all different flavors of the same thing, only θℓ satisfies the stricter definition of a “potential temperature,” as corresponding to a reference temperature accessible by an isentropic and closed transformation of a system in equilibrium; both θe and θℓ measure the “relative” enthalpy of an air parcel at their respective reference states, but only θs measures air-parcel entropy. None mix linearly, but all do so approximately, and all reduce to the dry potential temperature θ in the limit as the water mass fraction goes to zero. As is well known, θ does mix linearly and inherits all the favorable (entropic, enthalpic, and potential temperature) properties of its various—but descriptively less rich—moist counterparts. All involve quite complex expressions, but admit relatively simple and useful approximations. Of the three moist “potential” temperatures, θs is the least familiar, but the most well mixed in the broader tropics, a property that merits further study as a possible basis for constraining mixing processes.

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45

Fattahi, Abolfazl, Ebrahim Rahmani, Nader Karimi, and S. Mostafa Hosseinalipour. "On the decay of entropic-compositional sources of indirect noise in combustors." INTER-NOISE and NOISE-CON Congress and Conference Proceedings 265, no. 2 (February 1, 2023): 5167–78. http://dx.doi.org/10.3397/in_2022_0750.

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For nearly half a century, indirect combustion noise in gas turbine combustors was entirely attributed to entropy waves, as the convecting hot spots. However, recent studies identified another source of indirect noise called compositional waves, which consists of convecting chemical blobs. Understanding the evolution of this new source during its journey throughout the combustor requires attention due to the unknown physics of the turbulent, heat transferring flow in which it moves. In the current study, a hot chemical blob including a mixture of combustion products is introduced at the channel inlet. During its convection along the channel, degeneration of various thermal and chemical components of the entropic-compositional wave is investigated in the frequency domain using large-eddy simulations. It is shown that the wave annihilation due to wall cooling, as found in real combustors, can exceed those imposed by the flow hydrodynamics. Through a coherence analysis, it is found that mixture fraction is mainly responsible for deteriorating the chemical sources and that the contribution of potential function is comparatively smaller. Overall, it is concluded that compared to entropy waves, compositional waves are up to 20% more prone to decay.

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46

Persinger, Michael A., and Robert M. Lafrenie. "The Cancer Cell Plasma Membrane Potentials as Energetic Equivalents to Astrophysical Properties." International Letters of Chemistry, Physics and Astronomy 36 (July 2014): 67–77. http://dx.doi.org/10.18052/www.scipress.com/ilcpa.36.67.

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The primary physical and chemical parameters that define the hypopolarized plasma cell membrane of malignant (cancer) cells compared to non-malignant cells reflect universal characteristics. The median value for the resting membrane potential is the constant for the Nernst equation without reference to discrepancies in ion concentrations and is identical to Boltzmann energies at 37 °C. The threshold energy defining space-time converges with access to entropic processes that are reflected in the morphology of cancer cells and tumors. Slowing of growth in cancer cell lines but not normal cells following exposure to weak (~1 to 10 μT) patterned magnetic fields occurs when the energy induced within the cell corresponds to the energy equivalent of the hypopolarized membrane potential. The optimal temporal parameters for the efficacy of these fields can be derived from Hubble‟s parameter and the transform function for “noise” or “random” patterns within the system. Quantitative solutions and experimental data indicate that the cancer cell may be dominated by entropic process that can be attenuated or blocked by temporally-structured applied magnetic fields whose intensity matches the increment of energy associated with this threshold.

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47

Persinger, Michael A., and Robert M. Lafrenie. "The Cancer Cell Plasma Membrane Potentials as Energetic Equivalents to Astrophysical Properties." International Letters of Chemistry, Physics and Astronomy 36 (July 15, 2014): 67–77. http://dx.doi.org/10.56431/p-1jp553.

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The primary physical and chemical parameters that define the hypopolarized plasma cell membrane of malignant (cancer) cells compared to non-malignant cells reflect universal characteristics. The median value for the resting membrane potential is the constant for the Nernst equation without reference to discrepancies in ion concentrations and is identical to Boltzmann energies at 37 °C. The threshold energy defining space-time converges with access to entropic processes that are reflected in the morphology of cancer cells and tumors. Slowing of growth in cancer cell lines but not normal cells following exposure to weak (~1 to 10 μT) patterned magnetic fields occurs when the energy induced within the cell corresponds to the energy equivalent of the hypopolarized membrane potential. The optimal temporal parameters for the efficacy of these fields can be derived from Hubble‟s parameter and the transform function for “noise” or “random” patterns within the system. Quantitative solutions and experimental data indicate that the cancer cell may be dominated by entropic process that can be attenuated or blocked by temporally-structured applied magnetic fields whose intensity matches the increment of energy associated with this threshold.

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48

Burr, Jordan. "Entropy’s Enemies: Postmodern Fission and Transhuman Fusion in the Post-War Era." Humanities 9, no. 1 (March 5, 2020): 23. http://dx.doi.org/10.3390/h9010023.

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In the early to mid-twentieth century, thermodynamic entropy—the inevitable diffusion of usable energy in the Universe—became a ubiquitous metaphor for the dissolution of Western values and cultural energy. Many Golden Age science fiction writers portrayed twentieth century technological progress as anti-entropic, a sign of Universal progress and unity which might postpone or negate both cultural and thermodynamic forms of entropy. Following the evolutionary metaphysics of Georg Hegel and Pierre Teilhard de Chardin, Golden Age science fiction writers like Arthur C. Clarke and Isaac Asimov imagined the creation of powerful collective beings whose unitary existence signified the defeat of entropy. In contrast, later literary postmodernists like Thomas Pynchon and Pamela Zoline often accepted and even exalted in the chaotic, liberating potential of entropy. In postmodern fiction, the disorder of entropy was often compared favorably to the stifling hegemony of cultural universalism. More broadly, these two responses might be understood to represent two societal stages of grief-- denial and acceptance—to the new trauma introduced to the world by the parallel concepts of cultural entropy and a Universal “heat death.”

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49

Adams, Stefan, Nicolas Dirr, Mark Peletier, and Johannes Zimmer. "Large deviations and gradient flows." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 371, no. 2005 (December 28, 2013): 20120341. http://dx.doi.org/10.1098/rsta.2012.0341.

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In recent work we uncovered intriguing connections between Otto’s characterization of diffusion as an entropic gradient flow on the one hand and large-deviation principles describing the microscopic picture (Brownian motion) on the other. In this paper, we sketch this connection, show how it generalizes to a wider class of systems and comment on consequences and implications. Specifically, we connect macroscopic gradient flows with large-deviation principles, and point out the potential of a bigger picture emerging: we indicate that, in some non-equilibrium situations, entropies and thermodynamic free energies can be derived via large-deviation principles. The approach advocated here is different from the established hydrodynamic limit passage but extends a link that is well known in the equilibrium situation.

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50

TKACHENKO, Ivan, Vitalii SHARKO, and Tatiana ZAVHORODNIA. "ENTROPIC EVALUATION OF INNOVATIVE SYSTEMS ENTERPRISE DEVELOPMENT." Herald of Khmelnytskyi National University. Economic sciences 304, no. 2(1) (March 18, 2022): 44–52. http://dx.doi.org/10.31891/2307-5740-2022-304-2(1)-5.

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The model of the production complex always includes the object of management and the subject of management in the form of appropriate systems. The method of realization of relations between them depends on the level of development of industrial relations. At the present stage of development of machinery and technology to the method of implementation of these relations requires their integration into a single corporate governance system. In recent years, several approaches have been used to identify the mechanisms underlying the development and operation of complex systems. Particularly useful results were obtained in their study by methods of random matrix theory, mono- and multifractal analysis, chaos theory with reconstruction of the system trajectory in phase space and determination of its parameters such as correlation dimension, spectrum of Lyapunov indicators, recurrent maps. However, the use of some of the methods requires the stationary nature of the studied data, requires long time series and a comprehensive calculation of several parameters. Another approach to considering the features of complex systems is to calculate the characteristics of entropy. The paper considers problematic issues related to the innovative development of machine-building enterprises. An algorithm for increasing the innovation potential of an industrial enterprise is proposed. The authors present a variant of assessing the systemic nature of innovative development of machine-building enterprises. The indicators of evaluation and increase of the level of innovative development of industrial enterprises are systematized. The integral index and the system entropy index are determined.

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