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Journal articles on the topic 'Prigogine'

Author: Grafiati
Published: 4 June 2021
Last updated: 21 February 2023

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1

Rice, Stuart A. "Ilya Prigogine." Physics Today 57, no. 4 (April 2004): 102–3. http://dx.doi.org/10.1063/1.1752434.

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2

Akhmediev, N., J. M. Soto-Crespo, Peter Vouzas, N. Devine, and Wonkeun Chang. "Dissipative solitons with extreme spikes in the normal and anomalous dispersion regimes." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 376, no. 2124 (June 11, 2018): 20180023. http://dx.doi.org/10.1098/rsta.2018.0023.

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Prigogine’s ideas of systems far from equilibrium and self-organization (Prigogine & Lefever. 1968 J. Chem. Phys. 48 , 1695–1700 ( doi:10.1063/1.1668896 ); Glansdorff & Prigogine. 1971 Thermodynamic theory of structures, stability and fluctuations . New York, NY/London, UK: Wiley) deeply influenced physics, and soliton science in particular. These ideas allowed the notion of solitons to be extended from purely integrable cases to the concept of dissipative solitons. The latter are qualitatively different from the solitons in integrable and Hamiltonian systems. The variety in their forms is huge. In this paper, one recent example is considered—dissipative solitons with extreme spikes (DSESs). It was found that DSESs exist in large regions of the parameter space of the complex cubic–quintic Ginzburg–Landau equation. A continuous variation in any of its parameters results in a rich structure of bifurcations. This article is part of the theme issue ‘Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (part 1)’.
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3

Lombardi, Olimpia. "Prigogine: ciencia y realidad." Crítica (México D. F. En línea) 30, no. 90 (December 12, 1998): 47–75. http://dx.doi.org/10.22201/iifs.18704905e.1998.730.

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4

Balescu, Radu. "Ilya Prigogine (1917–2003)." Nature 424, no. 6944 (July 2003): 30. http://dx.doi.org/10.1038/424030a.

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5

Guo, Minyong, Yu Tian, Xiaoning Wu, and Hongbao Zhang. "From Prigogine to Raychaudhuri." Classical and Quantum Gravity 34, no. 3 (January 10, 2017): 035013. http://dx.doi.org/10.1088/1361-6382/aa54a0.

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6

Nicolis, Gregoire. "Ilya Prigogine 1917–2003." Physics World 16, no. 7 (July 2003): 12. http://dx.doi.org/10.1088/2058-7058/16/7/17.

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7

Goldbeter, Albert. "Ilya Prigogine (1917–2003)." Journal of Biosciences 28, no. 6 (December 2003): 657–59. http://dx.doi.org/10.1007/bf02708424.

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8

Antoniou, Ioannis. "Farewell to Ilya Prigogine." International Journal of Quantum Chemistry 98, no. 2 (2004): 60–61. http://dx.doi.org/10.1002/qua.10881.

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9

Белощенко, D. Beloshchenko, Пахомов, A. Pakhomov, Козлова, V. Kozlova, Умаров, and B. Umarov. "Entropic approach in assessment of seasonal dynamics of neuromuscular system’s parameters in human under exposure to local cooling." Complexity. Mind. Postnonclassic 4, no. 2 (September 25, 2015): 38–47. http://dx.doi.org/10.12737/12010.

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The paper presents an experimental verification of Prigogine-Glansdorff’s theorem for evolution of complex biological systems and verification of Prigogine´s theorem for an open nonequilibrium thermodynamic (biological) systems. Entropy can be represented as a value that indicates how many different states are in the system, but it does not represent if they are stable, i.e. it is not linked to the concept of chaos, order and disorder act as deterministic and non-deterministic state of the system. Thus, we found that the conditions of Prigogine-Glansdorff’s theorem for studying the biosystems don’t suite because it is common (except for tremorogramm’s parameters of the spring period) that the entropy of parameters of tremorogramms and myograms statistically doesn’t change.
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10

Juarrero, Alicia. "Downward Causation: Polanyi and Prigogine." Tradition and Discovery: The Polanyi Society Periodical 40, no. 3 (2013): 4–15. http://dx.doi.org/10.5840/traddisc2013/201440330.

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11

Schmelzer, Jürn W. P., and Ivan Gutzow. "The Prigogine-Defay ratio revisited." Journal of Chemical Physics 125, no. 18 (November 14, 2006): 184511. http://dx.doi.org/10.1063/1.2374894.

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12

Angell, C. Austen, and Iolanda Santana Klein. "Prigogine and Defay say relax." Nature Physics 7, no. 10 (October 2011): 750–51. http://dx.doi.org/10.1038/nphys2113.

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13

Elkaïm, Mony. "En hommage à Ilya Prigogine." Cahiers critiques de thérapie familiale et de pratiques de réseaux 30, no. 1 (2003): 150. http://dx.doi.org/10.3917/ctf.030.0150.

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14

Novaes, Marcel. "Ilya Prigogine: uma visão crítica." Revista Brasileira de Ensino de Física 32, no. 1 (March 2010): 1306–4. http://dx.doi.org/10.1590/s1806-11172010000100006.

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A obra de divulgação científica de Ilya Prigogine é avaliada de forma crítica. Com relação à sua suposta teoria que encontraria na dinâmica caótica uma explicação determinista para a tendência irreversível ao equilíbrio, argumento que suas motivações são infundadas, suas contribuições inexistentes e suas conclusões exageradas. As áreas da física para as quais ele busca chamar atenção são de fato interessantes, mas ele presta um desserviço ao público ao mistificá-las.
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15

Antoniou, Ioannis, and Vladimir Gontar. "In memory of Ilya Prigogine." Discrete Dynamics in Nature and Society 2004, no. 1 (2004): 1–2. http://dx.doi.org/10.1155/s1026022604004005.

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16

Maruani, Jean. "Obituary: Ilya Prigogine (1917-2003)." International Journal of Quantum Chemistry 99, no. 4 (June 3, 2004): 183–84. http://dx.doi.org/10.1002/qua.20059.

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17

Bravo, R., M. Pintos, and A. Amigo. "Dependence upon temperature of the excess molar volumes of tetrahydropyran + n-alkane mixtures." Canadian Journal of Chemistry 73, no. 3 (March 1, 1995): 375–79. http://dx.doi.org/10.1139/v95-049.

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Excess molar volumes VE, at 288.15 and 308.15 K and normal atmospheric pressure, are reported for the binary mixtures tetrahydropyran + n-alkanes (C7–C9). From the results, the differential coefficient (∂VE/∂T)p was estimated over the entire range of mole fractions. The Prigogine–Flory–Patterson theory and its applicability in predicting VE is tested. Keywords: Excess molar volumes, digital densimeter, tetrahydropyran, n-heptane, n-octane, n-nonane, Prigogine–Flory–Patterson theory.
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18

Buchanan, James M., and Viktor J. Vanberg. "The Market as a Creative Process." Economics and Philosophy 7, no. 2 (October 1991): 167–86. http://dx.doi.org/10.1017/s0266267100001383.

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Contributions in modern theoretical physics and chemistry on the behavior of nonlinear systems, exemplified by Ilya Prigogine's work on the thermodynamics of open systems (Prigogine and Stengers, 1984), attract growing attention in economics (Anderson, Arrow, and Pines, 1988; Arthur, 1990; Baumol and Benhabib, 1989; Mirowski, 1990; Radzicki, 1990). Our purpose here is to relate the new orientation in the natural sciences to a particular nonorthodox strand of thought within economics. All that is needed for this purpose is some appreciation of the general thrust of the enterprise, which involves a shift of perspective from the determinism of conventional physics (which presumably inspired the neoclassical research program in economics) to the nonteleological open-endedness, creative, and nondetermined nature of evolutionary processes.
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19

Haila, Yrjö. "Isabelle Stengers: tieteenanalyysin ja -kritiikin moniulotteinen käytännöllisyys." Tiede & edistys, no. 4 (February 7, 2022): 235–48. http://dx.doi.org/10.51809/te.114361.

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Chuck Dyke1: ”Maailmassa on kahdenlaisia ihmisiä, ystävä hyvä: ne, jotka ajattelevat, että jos he eivät keksi yhtä kanonisoitua tapaa sanoa se, he eivät ymmärrä sitä; ja ne, jotka ajattelevat, että jos he eivät kykene sanomaan sitä usealla tusinalla eri tavalla, he eivät ymmärrä sitä. Edelliset ovat teologeja; ja jälkimmäiset ovat opettajia. Tajuatko?” (Lähde [soveltaen]: Sergio Leone et al. Hyvät, pahat ja rumat). Isabelle Stengers (s. 1948) on laaja-alainen tieteen analyytikko, filosofi sekä ajankohtaisten kulttuuristen ja poliittisten teemojen arvioitsija, johon voi hyvin perustein soveltaa attribuuttia ”moderni klassikko”. Stengers on peruskoulutukseltaan luonnontieteilijä; hänen tausta-alansa on kemia. Hän ei sopeutunut laboratoriotutkijan uralle vaan kiinnostui jo varhain tieteen historiasta ja filosofiasta ja tuli kansainvälisesti tunnetuksi yhdessä kemian Nobelilla vuonna 1977 palkitun Ilya Prigoginen (1917–2003) kanssa kirjoittamastaan teoksesta Order Out Of Chaos. Man’s New Dialogue with Nature (Prigogine & Stengers 1984).
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20

Ito, Sosuke. "Information geometry, trade-off relations, and generalized Glansdorff–Prigogine criterion for stability." Journal of Physics A: Mathematical and Theoretical 55, no. 5 (January 17, 2022): 054001. http://dx.doi.org/10.1088/1751-8121/ac3fc2.

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Abstract We discuss a relationship between information geometry and the Glansdorff–Prigogine criterion for stability. For the linear master equation, we found a relation between the line element and the excess entropy production rate. This relation leads to a new perspective of stability in a nonequilibrium steady-state. We also generalize the Glansdorff–Prigogine criterion for stability based on information geometry. Our information-geometric criterion for stability works well for the nonlinear master equation, where the Glansdorff–Prigogine criterion for stability does not work well. We derive a trade-off relation among the fluctuation of the observable, the mean change of the observable, and the intrinsic speed. We also derive a novel thermodynamic trade-off relation between the excess entropy production rate and the intrinsic speed. These trade-off relations provide a physical interpretation of our information-geometric criterion for stability. We illustrate our information-geometric criterion for stability by an autocatalytic reaction model, where dynamics are driven by a nonlinear master equation.
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21

de Palma, André. "In Memoriam: Ilya Prigogine (1917–2003)." Transportation Science 37, no. 3 (August 2003): 255–56. http://dx.doi.org/10.1287/trsc.37.3.255.16048.

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22

Ibáñez, Eduardo. "Historicidad e irreversibilidad en la concepción prigoginiana y agustiniana del tiempo." Tópicos. Revista de Filosofía de Santa Fe, no. 11 (June 21, 2018): 107–24. http://dx.doi.org/10.14409/topicos.v0i11.7442.

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El trabajo compara las nociones de “historicidad” e “irreversibilidad” en la concepción del tiempo de Prigogine y de San Agustín, estableciendo semejanzas y diferencias. Analiza primero la idea agustiniana de la temporalidad siguiendo el Libro Undécimo de las Confesiones, y las interpretaciones de dicha idea efectuadas por Paul Ricoeur y por Jean Guitton. A continuación, analiza la redefinición del tiempo llevada a cabo por Ilya Prigogine, diferenciándola fundamentalmente de la concepción estática o geométrica de la dinámica newtoniana. Muestra que esta reconceptualización lo diferencia de la física clásica y lo acerca a la idea agustiniana del tiempo, en tanto y en cuanto, en ambos autores, las nociones de “irreversibilidad”, “historicidad”, “novedad”, “acontecimiento” y “creatividad”, son cruciales para entender la temporalidad. Finalmente, pone de manifiesto las diferencias entre los dos autores: mientras que San Agustín se refiere fundamentalmente a un tiempo humano o existencial, en el que está presente un claro sentido de la trascendencia, Prigogine alude al tiempo de la dinámica y la termodinámica de los procesos irreversibles alejados del equilibrio, en un sentido ciertamente inmanente y físico.
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23

Maïsseu, André. "ECOLOGIST UTOPIA FACING REALITY: MALTHUS AGAINST PRIGOGINE." Вестник НИЯУ МИФИ 10, no. 5 (2021): 459–76. http://dx.doi.org/10.1134/s2304487x21050035.

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24

Sandoval-Villalbazo, Alfredo, and L. S. García-Colín. "Meixner-Prigogine scheme in relativistic transport theory." Physica A: Statistical Mechanics and its Applications 234, no. 1-2 (December 1996): 358–70. http://dx.doi.org/10.1016/s0378-4371(96)00268-3.

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25

Nicolis, G., L. E. Reichl, and A. van der Merwe. "For Ilya Prigogine on his seventieth birthday." Foundations of Physics 17, no. 5 (May 1987): 459–60. http://dx.doi.org/10.1007/bf01559697.

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26

Suchanecki, Z., I. Antoniou, and S. Tasaki. "Nonlocality of the Misra-Prigogine-Courbage semigroup." Journal of Statistical Physics 75, no. 5-6 (June 1994): 919–28. http://dx.doi.org/10.1007/bf02186750.

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27

Sicardi Schifino, A. C., A. Costa, and C. Ferro Fontán. "Generalization of the Glansdorff–Prigogine stability criterion." Journal of Mathematical Physics 32, no. 5 (May 1991): 1350–53. http://dx.doi.org/10.1063/1.529286.

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28

Lombardi, Olimpia. "Prigogine and the many voices of nature." Foundations of Chemistry 14, no. 3 (November 18, 2011): 205–19. http://dx.doi.org/10.1007/s10698-011-9140-y.

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29

Brändas, Erkki. "A tribute to Ilya Prigogine (1917-2003)." International Journal of Quantum Chemistry 98, no. 2 (2004): 59. http://dx.doi.org/10.1002/qua.10880.

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30

Szendrei, Eric V. "Bergson, Prigogine and the Rediscovery of Time." Process Studies 18, no. 3 (October 1, 1989): 181–93. http://dx.doi.org/10.2307/44798547.

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31

Courbage, Maurice. "Time in dynamical systems." Discrete Dynamics in Nature and Society 2004, no. 1 (2004): 85–90. http://dx.doi.org/10.1155/s102602260440301x.

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32

Gustafson, Karl. "Microscopic irreversibility." Discrete Dynamics in Nature and Society 2004, no. 1 (2004): 155–68. http://dx.doi.org/10.1155/s1026022604310034.

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First, I will recount the substance of several important conversations I had with Ilya Prigogine over the years. There is no doubt in my mind that Professor Prigogine firmly believed in the underlying stochasticity of the universe. Second, I will summarize my curiosity about the principle of detailed balance. In my opinion, so far it has always been put in by hand. Third, I will advance my own theory of microscopic irreversibility, that is, irreversibility at the quantum level. This involves new concepts of probability preference and probability violation. A manifestation of this irreversibility may be seen during emission of bound-free photons during field-matter interactions. Entropy increase is tied to radiation increase, and the notion of heat bath becomes light bath.
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33

Day, Richard H. "Physics and the foundations of economic science: comments in memory of Ilya Prigogine." Discrete Dynamics in Nature and Society 2004, no. 1 (2004): 91–99. http://dx.doi.org/10.1155/s1026022604312045.

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This paper discusses how the concepts of nonlinearity, discrete dynamics, chaos, and emergent order that Ilya Prigogine advanced correspond to similar ideas involved in the adaptive, evolutionary branch of economics.
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34

Хадарцев, А. А., О. Е. Филатова, И. А. Мандрыка, and В. В. Еськов. "The Entropy-Based Approach to Physics of Living Systems and the Chaos and Self-Organization Theory." Успехи кибернетики / Russian Journal of Cybernetics, no. 3(3) (September 30, 2020): 41–49. http://dx.doi.org/10.51790/2712-9942-2020-1-3-5.

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Рассматриваются фундаментальные законы поведения живых систем с позиций классической термодинамики Р. Клаузиуса и Л. Больцмана и термодинамики неравновесных систем I.R. Prigogine. Показывается с позиций новой теории хаоса-самоорганизации, что законы термодинамики невозможно применять к живым гомеостатическим системам на уровне организации этих систем (т. е. на системном уровне), хотя на молекулярном уровне все работает. Одновременно мы не можем использовать и законы термодинамики неравновесных систем. Для гомеостатических (живых) систем неприменима теорема Гленсдорфа–Пригожина о минимуме прироста энтропии P=dE/dt в области (окрестности), где энтропия E имеет максимум (в точках равновесия). Более того, само понятие равновесия в границах термодинамики неприменимо к медико-биологическим системам – системам третьего типа. The fundamental living system behavior patterns are considered in terms of classical Clausius and Boltzmann thermodynamics, and I. R. Prigogine nonequilibrium system thermodynamics. The new theory of chaos and selforganization shows that the laws of thermodynamics are inapplicable to live homeostatic systems at their level of organization (i.e., the system level), although they are perfectly applicable at the molecular level. We cannot use the laws of nonequilibrium system thermodynamics, either. The Glensdorff–Prigogine theorem stating the minimum entropy increase P=dE/dt in the area (vicinity) where the entropy E has a maximum (at the equilibrium points) is inapplicable to homeostatic (living) systems. Moreover, the very concept of nonequilibrium as used in thermodynamics is inapplicable to the systems of the 3rd kind (medical and biological systems).
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35

Massoni, Neusa Teresinha. "Ilya Prigogine: uma contribuição à filosofia da ciência." Revista Brasileira de Ensino de Física 30, no. 2 (2008): 2308.1–2308.8. http://dx.doi.org/10.1590/s0102-47442008000200009.

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Este trabalho tem o objetivo de trazer para o debate epistemológico algumas das principais idéias filosóficas de Ilya Prigogine enquanto cientista e um pequeno resumo de suas teorias científicas enquanto filósofo. Queremos crer que ele próprio, um eminente físico-químico ganhador do Prêmio Nobel de Química em 1977, não se dizia filósofo da ciência. Mas sua inovadora interpretação do tempo, do caos e da instabilidade, fontes de desordem e também de ordem, nos proporciona uma excursão por uma ciência em evolução, nas palavras de Prigogine, e não deixa dúvidas de suas profundas contribuições para uma renovada visão de inter-relação entre ciência e filosofia. As idéias aqui sumarizadas, no entanto, não devem ser tomadas como generalizações indevidas, pois as pesquisas nessa área ainda estão em curso, mas tão somente como uma instigante contribuição às visões epistemológicas contemporâneas.
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36

Stasiulis, Nerijus. "ON THE CONCEPTION OF THE CREATIVE IN NATURAL SCIENCE AND PHILOSOPHICAL REFLECTIONS THEREOF." Creativity Studies 9, no. 1 (December 13, 2015): 42–52. http://dx.doi.org/10.3846/23450479.2015.1114041.

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The article discusses creativity as an ontological principle as it is presented in scientific-philosophical attitudes of a Nobel Prize winner for chemistry Ilya Prigogine and Werner Heisenberg’s pupil and a former director of the Max Planck Institute for Physics Hans-Peter Dürr. These attitudes are assessed in the light of Heideggerian notions of Being, subiectum, ousia and time and thus they themselves shed light on the potentiality of Heideggerian mode of thinking on the conception of the creative in the postmodern society and science. Bergsonian notion of creativity is also invoked. It is presented as a philosophical basis of the postmodern techno-scientific creativity and is discussed in terms of Heideggerian ecstatic temporality. The juxtaposition of the notions presented by Henri Bergson and Martin Heidegger provides the clue to compare and assess the science-based attitudes of Prigogine and Dürr.
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37

Massoni, Neusa Teresinha. "Ilya Prigogine: uma contribuição à filosofia da ciência." Revista Brasileira de Ensino de Física 30, no. 2 (2008): 2308.1–2308.8. http://dx.doi.org/10.1590/s1806-11172008000200009.

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38

Nicolis, Grégoire. "Ilya Prigogine (1917–2003): Strukturbildung fernab des Gleichgewichts." Angewandte Chemie 115, no. 29 (July 28, 2003): 3446–47. http://dx.doi.org/10.1002/ange.200390559.

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39

El-Banna, Mohamed M., and Mervette M. El-Batouti. "Article." Canadian Journal of Chemistry 76, no. 12 (December 1, 1998): 1860–66. http://dx.doi.org/10.1139/v98-200.

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Excess molar volumes, VE, for three binary liquid mixtures of cyclohexane + n-dodecane, n-tetradecane, and n-hexadecane were determined from density measurements at seven different temperatures in the range from 283.15 to 313.15 K and atmospheric pressure, over the entire range of mole fractions. The VE values were derived and the results show a regular negative pattern of behaviour for each of the three sets of the binary system. For cyclohexane, the magnitude of VE increases with the alkane chain length. The Prigogine-Flory-Patterson theory was applied to analyze the experimental behaviour by calculating three different contributions to VE, i.e., interactional, free volume, and internal pressure. The theory gives a representation of the main feature of the systems studied by using a fitted parameter to describe the behaviour throughout the composition range.Key words: excess molar volumes, binary mixtures, cyclohexane, n-dodecane, n-tetradecane, n-hexadecane, Prigogine-Flory-Patterson theory.
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40

Kolesnichenko, Aleksandr Vladimirovich, and Michail Yakovlevich Marov. "Toward the construction of the entropic-force model of the expansion of the Universe due to the gravitationally-induced production of dark matter and the influence of exchange entropy on the event horizon." Keldysh Institute Preprints, no. 4 (2023): 1–39. http://dx.doi.org/10.20948/prepr-2023-4.

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Within the framework of Prigogin's gravitational theory of the geometry-matter connection that ensures the production of particles in a cosmological fluid, a single-fluid model of the evolution of a spatially flat, homogeneous and isotropic Universe is thermodynamically constructed. In order to obtain it, the continuity equation (energy conservation equation) was derived from the first law of thermodynamics taking into account the gravity-induced creation of matter and energy exchange processes on the visible horizon of the Universe. Based on this equation and the fundamental Friedman equation describing the expansion of the Universe, in the context of the entropic formalitу modified Friedman-Robertson-Walker equations were constructed to model various scenarios of the evolution of the flat Universe with matter production. In their derivation, several forms of exchangeable phenomenological entropies associated by assumption with the region of the visible cosmological horizon were used. The resulting generalized Prigogine model agrees well with the standard cosmological ?-model for cold dark matter and allows us to explain the accelerated expansion of the late Universe, providing its cosmological history without the introduction of new fields.
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41

Almeida, Maria da Conceição de. "A ciência como bifurcação: uma homenagem à Ilya Prigogine." Revista FAMECOS 11, no. 23 (April 12, 2008): 77. http://dx.doi.org/10.15448/1980-3729.2004.23.3251.

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A Universidade Livre de Bruxelas e o Instituto de Química, em particular, perderam um professor que honrava a instituição por suas pesquisas nas fronteiras da química, da física e da filosofia. A comunidade científica mundial conta agora com a ausência de um dos cientistas mais brilhantes do século XX.
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42

Casalini, R., R. F. Gamache, and C. M. Roland. "Density-scaling and the Prigogine–Defay ratio in liquids." Journal of Chemical Physics 135, no. 22 (December 14, 2011): 224501. http://dx.doi.org/10.1063/1.3664180.

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43

Gilstrap, Donald L. "Dissipative structures in educational change: Prigogine and the academy." International Journal of Leadership in Education 10, no. 1 (January 2007): 49–69. http://dx.doi.org/10.1080/13603120600933758.

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44

Sandoval-Villalbazo, Alfredo, and L. S. García-Colín. "Relativistic Navier-Stokes equations in the Meixner-Prigogine scheme." Physica A: Statistical Mechanics and its Applications 240, no. 3-4 (June 1997): 480–90. http://dx.doi.org/10.1016/s0378-4371(97)00013-7.

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45

Doll, William E. "Prigogine: A new sense of order, a new curriculum." Theory Into Practice 25, no. 1 (January 1986): 10–16. http://dx.doi.org/10.1080/00405848609543192.

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46

Nicolis, Grégoire. "Ilya Prigogine (1917–2003): Structure Formation Far from Equilibrium." Angewandte Chemie International Edition 42, no. 29 (July 28, 2003): 3324–25. http://dx.doi.org/10.1002/anie.200390530.

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47

Ederer, Michael, Ernst Dieter Gilles, and Oliver Sawodny. "The Glansdorff–Prigogine stability criterion for biochemical reaction networks." Automatica 47, no. 6 (June 2011): 1097–104. http://dx.doi.org/10.1016/j.automatica.2011.01.072.

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48

Волов and V. Volov. "Fractal-cluster theory of thermodynamic principles of analysis of resources distribution in hierarchical self-organizing systems." Complexity. Mind. Postnonclassic 3, no. 3 (June 10, 2014): 56–69. http://dx.doi.org/10.12737/6724.

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Abstract:
The tenets of the fractal-cluster theory including fractal-cluster ratios, the dynamic equations of the evolution of fractal-cluster system and criteria of the complex systems control are presented. On the basis of the synthesis of main tenets of thermodynamics structure by I. Prigogine, we conducted the analysis of control by economic systems and development of living organisms
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49

Zhang, Li-Chun, and Ren Zhao. "The universal Ehrenfest scheme on black holes." Modern Physics Letters A 30, no. 36 (November 3, 2015): 1550187. http://dx.doi.org/10.1142/s0217732315501874.

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By use of the Jacobi determinant, we verify that, for a thermodynamic system which satisfies the first law of thermodynamics, if only there is second-order phase transition in the system, the Prigogine–Defay ratio is the constant 1. This conclusion is universal and independent of the concrete forms of the thermodynamic functions and also apply to black holes.
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50

Gauthier, Yvon. "Ilya Prigogine. La fin des certitudes. Odile Jacob, Paris, 1996." Horizons philosophiques 7, no. 1 (1996): 129. http://dx.doi.org/10.7202/801035ar.

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