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  1. Article ; Online: Necessary Condition of Self-Organisation in Nonextensive Open Systems.

    Afsar, Ozgur / Tirnakli, Ugur

    Entropy (Basel, Switzerland)

    2023  Volume 25, Issue 3

    Abstract: In this paper, we focus on evolution from an equilibrium state in a power law form by means ... ...

    Abstract In this paper, we focus on evolution from an equilibrium state in a power law form by means of
    Language English
    Publishing date 2023-03-17
    Publishing country Switzerland
    Document type Journal Article
    ZDB-ID 2014734-X
    ISSN 1099-4300 ; 1099-4300
    ISSN (online) 1099-4300
    ISSN 1099-4300
    DOI 10.3390/e25030517
    Database MEDical Literature Analysis and Retrieval System OnLINE

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  2. Article ; Online: Necessary Condition of Self-Organisation in Nonextensive Open Systems

    Ozgur Afsar / Ugur Tirnakli

    Entropy, Vol 25, Iss 517, p

    2023  Volume 517

    Abstract: In this paper, we focus on evolution from an equilibrium state in a power law form by means of q -exponentials to an arbitrary one. Introducing new q -Gibbsian equalities as the necessary condition of self-organization in nonextensive open systems, we ... ...

    Abstract In this paper, we focus on evolution from an equilibrium state in a power law form by means of q -exponentials to an arbitrary one. Introducing new q -Gibbsian equalities as the necessary condition of self-organization in nonextensive open systems, we theoretically show how to derive the connections between q -renormalized entropies ( <semantics> Δ S ˜ q </semantics> ) and q -relative entropies ( <semantics> K L q </semantics> ) in both Bregman and Csiszar forms after we clearly explain the connection between renormalized entropy by Klimantovich and relative entropy by Kullback-Leibler without using any predefined effective Hamiltonian. This function, in our treatment, spontaneously comes directly from the calculations. We also explain the difference between using ordinary and normalized q -expectations in mean energy calculations of the states. To verify the results numerically, we use a toy model of complexity, namely the logistic map defined as <semantics> X t + 1 = 1 − a X t 2 </semantics> , where <semantics> a ∈ [ 0 , 2 ] </semantics> is the map parameter. We measure the level of self-organization using two distinct forms of the q -renormalized entropy through period doublings and chaotic band mergings of the map as the number of periods/chaotic-bands increase/decrease. We associate the behaviour of the q -renormalized entropies with the emergence/disappearance of complex structures in the phase space as the control parameter of the map changes. Similar to Shiner-Davison-Landsberg (SDL) complexity, we categorize the tendencies of the q -renormalized entropies for the evaluation of the map for the whole control parameter space. Moreover, we show that any evolution between two states possesses a unique <semantics> q = q * </semantics> value (not a range for q values) for which the q -Gibbsian equalities hold and the values are the same for the Bregmann and Csiszar forms. Interestingly, if the evolution is from <semantics> a = 0 ...
    Keywords S-theorem ; q-renormalized entropy ; complexity measures ; logistic map ; Science ; Q ; Astrophysics ; QB460-466 ; Physics ; QC1-999
    Subject code 511
    Language English
    Publishing date 2023-03-01T00:00:00Z
    Publisher MDPI AG
    Document type Article ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  3. Article ; Online: A generalization of the standard map and its statistical characterization.

    Cetin, Kivanc / Tirnakli, Ugur / Boghosian, Bruce M

    Scientific reports

    2022  Volume 12, Issue 1, Page(s) 8575

    Abstract: From the statistical mechanical point of view, area-preserving maps have great potential and importance. These maps exhibit chaotic and regular behavior separately or together in the available phase space as the control parameter changes. Several works ... ...

    Abstract From the statistical mechanical point of view, area-preserving maps have great potential and importance. These maps exhibit chaotic and regular behavior separately or together in the available phase space as the control parameter changes. Several works on these maps, e.g., the standard map and the web map, have shown that ergodicity breakdown causes the statistical mechanical framework that describes the dynamics of the system to change. In this paper, for a novel generalization of the standard map, which we define by generalizing the periodic function used in its definition, we verify that a q-Gaussian with [Formula: see text] for the probability distribution of sum of the iterates of the system with initial conditions chosen from the nonergodic stability islands is robust. We also show that the probability distributions become more complicated and unexpected limiting behavior occurs for some parameter regimes.
    MeSH term(s) Probability
    Language English
    Publishing date 2022-05-20
    Publishing country England
    Document type Journal Article ; Research Support, Non-U.S. Gov't
    ZDB-ID 2615211-3
    ISSN 2045-2322 ; 2045-2322
    ISSN (online) 2045-2322
    ISSN 2045-2322
    DOI 10.1038/s41598-022-12213-5
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  4. Article ; Online: A generalization of the standard map and its statistical characterization

    Kivanc Cetin / Ugur Tirnakli / Bruce M. Boghosian

    Scientific Reports, Vol 12, Iss 1, Pp 1-

    2022  Volume 17

    Abstract: Abstract From the statistical mechanical point of view, area-preserving maps have great potential and importance. These maps exhibit chaotic and regular behavior separately or together in the available phase space as the control parameter changes. ... ...

    Abstract Abstract From the statistical mechanical point of view, area-preserving maps have great potential and importance. These maps exhibit chaotic and regular behavior separately or together in the available phase space as the control parameter changes. Several works on these maps, e.g., the standard map and the web map, have shown that ergodicity breakdown causes the statistical mechanical framework that describes the dynamics of the system to change. In this paper, for a novel generalization of the standard map, which we define by generalizing the periodic function used in its definition, we verify that a q-Gaussian with $$q\simeq 1.935$$ q ≃ 1.935 for the probability distribution of sum of the iterates of the system with initial conditions chosen from the nonergodic stability islands is robust. We also show that the probability distributions become more complicated and unexpected limiting behavior occurs for some parameter regimes.
    Keywords Medicine ; R ; Science ; Q
    Subject code 515
    Language English
    Publishing date 2022-05-01T00:00:00Z
    Publisher Nature Portfolio
    Document type Article ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  5. Article ; Online: Predicting COVID-19 Peaks Around the World

    Tsallis, Constantino / Tirnakli, Ugur

    Frontiers in Physics

    2020  Volume 8

    Keywords covid19
    Publisher Frontiers Media SA
    Publishing country ch
    Document type Article ; Online
    ZDB-ID 2721033-9
    ISSN 2296-424X
    ISSN 2296-424X
    DOI 10.3389/fphy.2020.00217
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  6. Article ; Online: Predicting COVID-19 Peaks Around the World

    Constantino Tsallis / Ugur Tirnakli

    Frontiers in Physics, Vol

    2020  Volume 8

    Abstract: The official data for the time evolution of active cases of COVID-19 pandemics around the world are available online. For all countries, a peak has been either observed (China and South Korea) or is expected in the near future. The approximate dates and ... ...

    Abstract The official data for the time evolution of active cases of COVID-19 pandemics around the world are available online. For all countries, a peak has been either observed (China and South Korea) or is expected in the near future. The approximate dates and heights of those peaks have important epidemiological implications. Inspired by similar complex behavior of volumes of transactions of stocks at the NYSE and NASDAQ, we propose a q-statistical functional form that appears to describe satisfactorily the available data for all countries. Consistently, predictions of the dates and heights of those peaks in severely affected countries become possible unless efficient treatments or vaccines, or sensible modifications of the adopted epidemiological strategies, emerge.
    Keywords COVID-19 ; pandemics ; complex systems ; non-extensive statistical mechanics ; epidemiology ; Physics ; QC1-999 ; covid19
    Language English
    Publishing date 2020-05-01T00:00:00Z
    Publisher Frontiers Media S.A.
    Document type Article ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  7. Article ; Online: Predicting COVID-19 peaks around the world

    TSALLIS, Constantino / TIRNAKLI, Ugur

    Abstract: The official data for the time evolution of active cases of COVID-19 pandemics around the world are available online. For all countries, a peak has been either observed (China and South Korea) or is expected in near future. The approximate dates and ... ...

    Abstract The official data for the time evolution of active cases of COVID-19 pandemics around the world are available online. For all countries, a peak has been either observed (China and South Korea) or is expected in near future. The approximate dates and heights of those peaks imply in important epidemiological issues. Inspired by similar complex behaviour of volumes of transactions of stocks at NYSE and NASDAQ, we propose a q-statistical functional form which appears to describe satisfactorily the available data of all countries. Consistently, predictions become possible of the dates and heights of those peaks in severely affected countries unless efficient treatments or vaccines, or sensible modifications of the adopted epidemiological strategies, emerge.
    Keywords covid19
    Publisher MedRxiv; WHO
    Document type Article ; Online
    DOI 10.1101/2020.04.24.20078154
    Database COVID19

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  8. Article ; Online: Predicting COVID-19 peaks around the world

    TSALLIS, Constantino / TIRNAKLI, Ugur

    medRxiv

    Abstract: The official data for the time evolution of active cases of COVID-19 pandemics around the world are available online. For all countries, a peak has been either observed (China and South Korea) or is expected in near future. The approximate dates and ... ...

    Abstract The official data for the time evolution of active cases of COVID-19 pandemics around the world are available online. For all countries, a peak has been either observed (China and South Korea) or is expected in near future. The approximate dates and heights of those peaks imply in important epidemiological issues. Inspired by similar complex behaviour of volumes of transactions of stocks at NYSE and NASDAQ, we propose a q-statistical functional form which appears to describe satisfactorily the available data of all countries. Consistently, predictions become possible of the dates and heights of those peaks in severely affected countries unless efficient treatments or vaccines, or sensible modifications of the adopted epidemiological strategies, emerge.
    Keywords covid19
    Language English
    Publishing date 2020-04-29
    Publisher Cold Spring Harbor Laboratory Press
    Document type Article ; Online
    DOI 10.1101/2020.04.24.20078154
    Database COVID19

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  9. Article ; Online: Epidemiological model with anomalous kinetics - The Covid-19 pandemics

    TIRNAKLI, Ugur / Tsallis, Constantino

    medRxiv

    Abstract: We generalize the phenomenological, law of mass action-like, SIR and SEIR epidemiological models to situations with anomalous kinetics. Specifically, the contagion and removal terms, normally linear in the fraction $I$ of infecteds, are taken to depend ... ...

    Abstract We generalize the phenomenological, law of mass action-like, SIR and SEIR epidemiological models to situations with anomalous kinetics. Specifically, the contagion and removal terms, normally linear in the fraction $I$ of infecteds, are taken to depend on $I^{\,q_{up}}$ and $I^{\,q_{down}}$, respectively. These dependencies can be understood as highly reduced effective descriptions of contagion via anomalous diffusion of susceptibles and infecteds in fractal geometries, and removal (i.e., recovery or death) via complex mechanisms leading to slowly decaying removal-time distributions. We obtain rather convincing fits to time series for both active cases and mortality with the same values of $(q_{up},q_{down})$ for a given country, suggesting that such aspects may in fact be present in the evolution of the Covid-19 pandemic. We also obtain approximate values for the effective population $N_{eff}$, which turns out to be a small percentage of the entire population $N$ for each country.
    Keywords covid19
    Language English
    Publishing date 2020-06-26
    Publisher Cold Spring Harbor Laboratory Press
    Document type Article ; Online
    DOI 10.1101/2020.06.24.20139287
    Database COVID19

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  10. Article ; Online: The standard map: From Boltzmann-Gibbs statistics to Tsallis statistics.

    Tirnakli, Ugur / Borges, Ernesto P

    Scientific reports

    2016  Volume 6, Page(s) 23644

    Abstract: As well known, Boltzmann-Gibbs statistics is the correct way of thermostatistically approaching ergodic systems. On the other hand, nontrivial ergodicity breakdown and strong correlations typically drag the system into out-of-equilibrium states where ... ...

    Abstract As well known, Boltzmann-Gibbs statistics is the correct way of thermostatistically approaching ergodic systems. On the other hand, nontrivial ergodicity breakdown and strong correlations typically drag the system into out-of-equilibrium states where Boltzmann-Gibbs statistics fails. For a wide class of such systems, it has been shown in recent years that the correct approach is to use Tsallis statistics instead. Here we show how the dynamics of the paradigmatic conservative (area-preserving) stan-dard map exhibits, in an exceptionally clear manner, the crossing from one statistics to the other. Our results unambiguously illustrate the domains of validity of both Boltzmann-Gibbs and Tsallis statistical distributions. Since various important physical systems from particle confinement in magnetic traps to autoionization of molecular Rydberg states, through particle dynamics in accelerators and comet dynamics, can be reduced to the standard map, our results are expected to enlighten and enable an improved interpretation of diverse experimental and observational results.
    Language English
    Publishing date 2016-03-23
    Publishing country England
    Document type Journal Article ; Research Support, Non-U.S. Gov't
    ZDB-ID 2615211-3
    ISSN 2045-2322 ; 2045-2322
    ISSN (online) 2045-2322
    ISSN 2045-2322
    DOI 10.1038/srep23644
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