The Experts below are selected from a list of 11451 Experts worldwide ranked by ideXlab platform

Ya A Sultanov - One of the best experts on this subject based on the ideXlab platform.

Karoly Urmossy - One of the best experts on this subject based on the ideXlab platform.

  • statistical power law due to reservoir fluctuations and the universal thermostat independence principle
    Entropy, 2014
    Co-Authors: T S Biro, Gergely Gabor Barnafoldi, Karoly Urmossy
    Abstract:

    Certain fluctuations in particle number, \(n\), at fixed total energy, \(E\), lead exactly to a cut-power law distribution in the one-particle energy, \(\omega\), via the induced fluctuations in the phase-space volume ratio, \(\Omega_n(E-\omega)/\Omega_n(E)=(1-\omega/E)^n\). The only parameters are \(1/T=\langle \beta \rangle=\langle n \rangle/E\) and \(q=1-1/\langle n \rangle + \Delta n^2/\langle n \rangle^2\). For the binomial distribution of \(n\) one obtains \(q=1-1/k\), for the negative binomial \(q=1+1/(k+1)\). These results also represent an approximation for general particle number distributions in the reservoir up to second order in the Canonical Expansion \(\omega \ll E\). For general systems the average phase-space volume ratio \(\langle e^{S(E-\omega)}/e^{S(E)}\rangle\) to second order delivers \(q=1-1/C+\Delta \beta^2/\langle \beta \rangle^2\) with \(\beta=S^{\prime}(E)\) and \(C=dE/dT\) heat capacity. However, \(q \ne 1\) leads to non-additivity of the Boltzmann–Gibbs entropy, \(S\). We demonstrate that a deformed entropy, \(K(S)\), can be constructed and used for demanding additivity, i.e., \(q_K=1\). This requirement leads to a second order differential equation for \(K(S)\). Finally, the generalized \(q\)-entropy formula, \(K(S)=\sum p_i K(-\ln p_i)\), contains the Tsallis, Renyi and Boltzmann–Gibbs–Shannon expressions as particular cases. For diverging variance, \(\Delta\beta^2\) we obtain a novel entropy formula.

  • statistical power law due to reservoir fluctuations and the universal thermostat independence principle
    Entropy, 2014
    Co-Authors: T S Biro, Gergely Gabor Barnafoldi, Peter Van, Karoly Urmossy
    Abstract:

    Certain fluctuations in particle number, \(n\), at fixed total energy, \(E\), lead exactly to a cut-power law distribution in the one-particle energy, \(\omega\), via the induced fluctuations in the phase-space volume ratio, \(\Omega_n(E-\omega)/\Omega_n(E)=(1-\omega/E)^n\). The only parameters are \(1/T=\langle \beta \rangle=\langle n \rangle/E\) and \(q=1-1/\langle n \rangle + \Delta n^2/\langle n \rangle^2\). For the binomial distribution of \(n\) one obtains \(q=1-1/k\), for the negative binomial \(q=1+1/(k+1)\). These results also represent an approximation for general particle number distributions in the reservoir up to second order in the Canonical Expansion \(\omega \ll E\). For general systems the average phase-space volume ratio \(\langle e^{S(E-\omega)}/e^{S(E)}\rangle\) to second order delivers \(q=1-1/C+\Delta \beta^2/\langle \beta \rangle^2\) with \(\beta=S^{\prime}(E)\) and \(C=dE/dT\) heat capacity. However, \(q \ne 1\) leads to non-additivity of the Boltzmann–Gibbs entropy, \(S\). We demonstrate that a deformed entropy, \(K(S)\), can be constructed and used for demanding additivity, i.e., \(q_K=1\). This requirement leads to a second order differential equation for \(K(S)\). Finally, the generalized \(q\)-entropy formula, \(K(S)=\sum p_i K(-\ln p_i)\), contains the Tsallis, Renyi and Boltzmann–Gibbs–Shannon expressions as particular cases. For diverging variance, \(\Delta\beta^2\) we obtain a novel entropy formula.

  • statistical power law due to reservoir fluctuations and the universal thermostat independence principle
    arXiv: Statistical Mechanics, 2014
    Co-Authors: T S Biro, Gergely Gabor Barnafoldi, Peter Van, Karoly Urmossy
    Abstract:

    Certain fluctuations in particle number at fixed total energy lead exactly to a cut-power law distribution in the one-particle energy, via the induced fluctuations in the phase-space volume ratio. The temperature parameter is expressed automatically by an equipartition relation, while the q-parameter is related to the scaled variance and to the expectation value of the particle number. For the binomial distribution q is smaller, for the negative binomial q is larger than one. These results also represent an approximation for general particle number distributions in the reservoir up to second order in the Canonical Expansion. For general systems the average phase-space volume ratio expanded to second order delivers a q parameter related to the heat capacity and to the variance of the temperature. However, q differing from one leads to non-additivity of the Boltzmann-Gibbs entropy. We demonstrate that a deformed entropy, K(S), can be constructed and used for demanding additivity. This requirement leads to a second order differential equation for K(S). Finally, the generalized q-entropy formula contains the Tsallis, Renyi and Boltzmann-Gibbs-Shannon expressions as particular cases. For diverging temperature variance we obtain a novel entropy formula.

  • statistical power law spectra due to reservoir fluctuations
    arXiv: High Energy Physics - Phenomenology, 2014
    Co-Authors: T S Biro, Karoly Urmossy, Peter Van, Gergely Gabor Barnafoldi
    Abstract:

    distributions also can be viewed as an approximation for arbitrary particle number distributions in the reservoir up to s ubleading (second) order in the Canonical Expansion ! ≪ E. For non-ideal systems the general Expansion up to second order delivers q = 1−1/C +�T 2 /T 2 , a combined result with the heat capacity and the variance of the temperature of finit e heat bath. These quantities seem to act against each other. Here the variance of the temperature is meant for the estimator 1/S ′ (E) of the thermodynamical temperature, the latter defined by 1/T = hS ′ (E)i. This way in the Gaussian ap

T S Biro - One of the best experts on this subject based on the ideXlab platform.

  • statistical power law due to reservoir fluctuations and the universal thermostat independence principle
    Entropy, 2014
    Co-Authors: T S Biro, Gergely Gabor Barnafoldi, Karoly Urmossy
    Abstract:

    Certain fluctuations in particle number, \(n\), at fixed total energy, \(E\), lead exactly to a cut-power law distribution in the one-particle energy, \(\omega\), via the induced fluctuations in the phase-space volume ratio, \(\Omega_n(E-\omega)/\Omega_n(E)=(1-\omega/E)^n\). The only parameters are \(1/T=\langle \beta \rangle=\langle n \rangle/E\) and \(q=1-1/\langle n \rangle + \Delta n^2/\langle n \rangle^2\). For the binomial distribution of \(n\) one obtains \(q=1-1/k\), for the negative binomial \(q=1+1/(k+1)\). These results also represent an approximation for general particle number distributions in the reservoir up to second order in the Canonical Expansion \(\omega \ll E\). For general systems the average phase-space volume ratio \(\langle e^{S(E-\omega)}/e^{S(E)}\rangle\) to second order delivers \(q=1-1/C+\Delta \beta^2/\langle \beta \rangle^2\) with \(\beta=S^{\prime}(E)\) and \(C=dE/dT\) heat capacity. However, \(q \ne 1\) leads to non-additivity of the Boltzmann–Gibbs entropy, \(S\). We demonstrate that a deformed entropy, \(K(S)\), can be constructed and used for demanding additivity, i.e., \(q_K=1\). This requirement leads to a second order differential equation for \(K(S)\). Finally, the generalized \(q\)-entropy formula, \(K(S)=\sum p_i K(-\ln p_i)\), contains the Tsallis, Renyi and Boltzmann–Gibbs–Shannon expressions as particular cases. For diverging variance, \(\Delta\beta^2\) we obtain a novel entropy formula.

  • statistical power law due to reservoir fluctuations and the universal thermostat independence principle
    Entropy, 2014
    Co-Authors: T S Biro, Gergely Gabor Barnafoldi, Peter Van, Karoly Urmossy
    Abstract:

    Certain fluctuations in particle number, \(n\), at fixed total energy, \(E\), lead exactly to a cut-power law distribution in the one-particle energy, \(\omega\), via the induced fluctuations in the phase-space volume ratio, \(\Omega_n(E-\omega)/\Omega_n(E)=(1-\omega/E)^n\). The only parameters are \(1/T=\langle \beta \rangle=\langle n \rangle/E\) and \(q=1-1/\langle n \rangle + \Delta n^2/\langle n \rangle^2\). For the binomial distribution of \(n\) one obtains \(q=1-1/k\), for the negative binomial \(q=1+1/(k+1)\). These results also represent an approximation for general particle number distributions in the reservoir up to second order in the Canonical Expansion \(\omega \ll E\). For general systems the average phase-space volume ratio \(\langle e^{S(E-\omega)}/e^{S(E)}\rangle\) to second order delivers \(q=1-1/C+\Delta \beta^2/\langle \beta \rangle^2\) with \(\beta=S^{\prime}(E)\) and \(C=dE/dT\) heat capacity. However, \(q \ne 1\) leads to non-additivity of the Boltzmann–Gibbs entropy, \(S\). We demonstrate that a deformed entropy, \(K(S)\), can be constructed and used for demanding additivity, i.e., \(q_K=1\). This requirement leads to a second order differential equation for \(K(S)\). Finally, the generalized \(q\)-entropy formula, \(K(S)=\sum p_i K(-\ln p_i)\), contains the Tsallis, Renyi and Boltzmann–Gibbs–Shannon expressions as particular cases. For diverging variance, \(\Delta\beta^2\) we obtain a novel entropy formula.

  • statistical power law due to reservoir fluctuations and the universal thermostat independence principle
    arXiv: Statistical Mechanics, 2014
    Co-Authors: T S Biro, Gergely Gabor Barnafoldi, Peter Van, Karoly Urmossy
    Abstract:

    Certain fluctuations in particle number at fixed total energy lead exactly to a cut-power law distribution in the one-particle energy, via the induced fluctuations in the phase-space volume ratio. The temperature parameter is expressed automatically by an equipartition relation, while the q-parameter is related to the scaled variance and to the expectation value of the particle number. For the binomial distribution q is smaller, for the negative binomial q is larger than one. These results also represent an approximation for general particle number distributions in the reservoir up to second order in the Canonical Expansion. For general systems the average phase-space volume ratio expanded to second order delivers a q parameter related to the heat capacity and to the variance of the temperature. However, q differing from one leads to non-additivity of the Boltzmann-Gibbs entropy. We demonstrate that a deformed entropy, K(S), can be constructed and used for demanding additivity. This requirement leads to a second order differential equation for K(S). Finally, the generalized q-entropy formula contains the Tsallis, Renyi and Boltzmann-Gibbs-Shannon expressions as particular cases. For diverging temperature variance we obtain a novel entropy formula.

  • statistical power law spectra due to reservoir fluctuations
    arXiv: High Energy Physics - Phenomenology, 2014
    Co-Authors: T S Biro, Karoly Urmossy, Peter Van, Gergely Gabor Barnafoldi
    Abstract:

    distributions also can be viewed as an approximation for arbitrary particle number distributions in the reservoir up to s ubleading (second) order in the Canonical Expansion ! ≪ E. For non-ideal systems the general Expansion up to second order delivers q = 1−1/C +�T 2 /T 2 , a combined result with the heat capacity and the variance of the temperature of finit e heat bath. These quantities seem to act against each other. Here the variance of the temperature is meant for the estimator 1/S ′ (E) of the thermodynamical temperature, the latter defined by 1/T = hS ′ (E)i. This way in the Gaussian ap

Igor Atamanyuk - One of the best experts on this subject based on the ideXlab platform.

  • Identification of the Optimal Parameters for Forecasting the State of Technical Objects Based on the Canonical Random Sequence Decomposition
    2020 IEEE 11th International Conference on Dependable Systems Services and Technologies (DESSERT), 2020
    Co-Authors: Igor Atamanyuk, Vyacheslav Shebanin, Yuriy Kondratenko, Valerii Havrysh, Vadim Lykhach, Sergey Kramarenko
    Abstract:

    Method of calculation of the optimal parameters of a predictive model on the basis of a power polynomial Canonical Expansion of a random sequence of state changes of a technical object or system is offered. The interval between measurements and number of sampling points, the duration of aftereffect and also the order of probabilistic relation are calculated parameters. The flow chart of the algorithm for determining specified parameters is presented in the work as well. The use of optimal characteristics will allow to take into full consideration the properties of an investigated random sequence and consequently to maximize the quality of solving the problem of individual forecasting the reliability of technical objects.

  • Predictive Control of Electrical Equipment Reliability on the Basis of the Non-linear Canonical Model of a Vector Random Sequence
    2019 IEEE International Conference on Modern Electrical and Energy Systems (MEES), 2019
    Co-Authors: Igor Atamanyuk, Vyacheslav Shebanin, Yuriy Volosyuk, Oleksii Sheptylevskyi, Yuriy Kondratenko, Valeriia Atamaniuk
    Abstract:

    Method of individual prediction of electrical equipment reliability on the basis of the analysis of the probability of no-failure operation at future moments of time is offered. A posteriori probability of no-failure operation is calculated using the statistical modeling of the realizations of a vector random sequence of the change of the parameters of electrical device in the prediction area. Relative frequency of the number of realizations belonging to the area of allowable values of the parameters of an electrical device is taken as the estimation of a sought a posteriori probability. Statistical modeling is performed on the basis of non-linear Canonical Expansion of a random sequence. Taking into full account of stochastic relations and properties of electric equipment parameters is a substantial advantage of this mathematical model which will allow to achieve maximum accuracy of the solving of the problem of predictive control of reliability.

  • computer s analysis method and reliability assessment of fault tolerance operation of information systems
    ICTERI, 2015
    Co-Authors: Igor Atamanyuk, Yuriy P Kondratenko
    Abstract:

    In this paper there was obtained an calculation method of the assessment of the probability of fail-safe operation of information systems in the future instants of time. The method is based on the algorithm for modeling a posteriori nonlinear random sequence of change of values of the controlled parameters which is imposed a limitation of belonging to a certain range of possible values. The probability of fail-safe operation is defined as the ratio of the number of realizations that fell in the allowable range to the total number of them, formed as a result of the numerical experiment. The realization of an a posteriori random sequence is an additive mixture of optimal from the point of view of mean-square nonlinear estimate of the future value of the parameter analyzed and of the value of a random variable, which may not be predicted due to the stochastic nature of the parameters. The model of a posteriori random sequence is based on the Pugachev's Canonical Expansion. The calculation method offered does not impose any significant constraints on the class of random sequences analyzed (linearity, stationarity, Markov behavior, monotoneness, etc.).

Gergely Gabor Barnafoldi - One of the best experts on this subject based on the ideXlab platform.

  • statistical power law due to reservoir fluctuations and the universal thermostat independence principle
    Entropy, 2014
    Co-Authors: T S Biro, Gergely Gabor Barnafoldi, Karoly Urmossy
    Abstract:

    Certain fluctuations in particle number, \(n\), at fixed total energy, \(E\), lead exactly to a cut-power law distribution in the one-particle energy, \(\omega\), via the induced fluctuations in the phase-space volume ratio, \(\Omega_n(E-\omega)/\Omega_n(E)=(1-\omega/E)^n\). The only parameters are \(1/T=\langle \beta \rangle=\langle n \rangle/E\) and \(q=1-1/\langle n \rangle + \Delta n^2/\langle n \rangle^2\). For the binomial distribution of \(n\) one obtains \(q=1-1/k\), for the negative binomial \(q=1+1/(k+1)\). These results also represent an approximation for general particle number distributions in the reservoir up to second order in the Canonical Expansion \(\omega \ll E\). For general systems the average phase-space volume ratio \(\langle e^{S(E-\omega)}/e^{S(E)}\rangle\) to second order delivers \(q=1-1/C+\Delta \beta^2/\langle \beta \rangle^2\) with \(\beta=S^{\prime}(E)\) and \(C=dE/dT\) heat capacity. However, \(q \ne 1\) leads to non-additivity of the Boltzmann–Gibbs entropy, \(S\). We demonstrate that a deformed entropy, \(K(S)\), can be constructed and used for demanding additivity, i.e., \(q_K=1\). This requirement leads to a second order differential equation for \(K(S)\). Finally, the generalized \(q\)-entropy formula, \(K(S)=\sum p_i K(-\ln p_i)\), contains the Tsallis, Renyi and Boltzmann–Gibbs–Shannon expressions as particular cases. For diverging variance, \(\Delta\beta^2\) we obtain a novel entropy formula.

  • statistical power law due to reservoir fluctuations and the universal thermostat independence principle
    Entropy, 2014
    Co-Authors: T S Biro, Gergely Gabor Barnafoldi, Peter Van, Karoly Urmossy
    Abstract:

    Certain fluctuations in particle number, \(n\), at fixed total energy, \(E\), lead exactly to a cut-power law distribution in the one-particle energy, \(\omega\), via the induced fluctuations in the phase-space volume ratio, \(\Omega_n(E-\omega)/\Omega_n(E)=(1-\omega/E)^n\). The only parameters are \(1/T=\langle \beta \rangle=\langle n \rangle/E\) and \(q=1-1/\langle n \rangle + \Delta n^2/\langle n \rangle^2\). For the binomial distribution of \(n\) one obtains \(q=1-1/k\), for the negative binomial \(q=1+1/(k+1)\). These results also represent an approximation for general particle number distributions in the reservoir up to second order in the Canonical Expansion \(\omega \ll E\). For general systems the average phase-space volume ratio \(\langle e^{S(E-\omega)}/e^{S(E)}\rangle\) to second order delivers \(q=1-1/C+\Delta \beta^2/\langle \beta \rangle^2\) with \(\beta=S^{\prime}(E)\) and \(C=dE/dT\) heat capacity. However, \(q \ne 1\) leads to non-additivity of the Boltzmann–Gibbs entropy, \(S\). We demonstrate that a deformed entropy, \(K(S)\), can be constructed and used for demanding additivity, i.e., \(q_K=1\). This requirement leads to a second order differential equation for \(K(S)\). Finally, the generalized \(q\)-entropy formula, \(K(S)=\sum p_i K(-\ln p_i)\), contains the Tsallis, Renyi and Boltzmann–Gibbs–Shannon expressions as particular cases. For diverging variance, \(\Delta\beta^2\) we obtain a novel entropy formula.

  • statistical power law due to reservoir fluctuations and the universal thermostat independence principle
    arXiv: Statistical Mechanics, 2014
    Co-Authors: T S Biro, Gergely Gabor Barnafoldi, Peter Van, Karoly Urmossy
    Abstract:

    Certain fluctuations in particle number at fixed total energy lead exactly to a cut-power law distribution in the one-particle energy, via the induced fluctuations in the phase-space volume ratio. The temperature parameter is expressed automatically by an equipartition relation, while the q-parameter is related to the scaled variance and to the expectation value of the particle number. For the binomial distribution q is smaller, for the negative binomial q is larger than one. These results also represent an approximation for general particle number distributions in the reservoir up to second order in the Canonical Expansion. For general systems the average phase-space volume ratio expanded to second order delivers a q parameter related to the heat capacity and to the variance of the temperature. However, q differing from one leads to non-additivity of the Boltzmann-Gibbs entropy. We demonstrate that a deformed entropy, K(S), can be constructed and used for demanding additivity. This requirement leads to a second order differential equation for K(S). Finally, the generalized q-entropy formula contains the Tsallis, Renyi and Boltzmann-Gibbs-Shannon expressions as particular cases. For diverging temperature variance we obtain a novel entropy formula.

  • statistical power law spectra due to reservoir fluctuations
    arXiv: High Energy Physics - Phenomenology, 2014
    Co-Authors: T S Biro, Karoly Urmossy, Peter Van, Gergely Gabor Barnafoldi
    Abstract:

    distributions also can be viewed as an approximation for arbitrary particle number distributions in the reservoir up to s ubleading (second) order in the Canonical Expansion ! ≪ E. For non-ideal systems the general Expansion up to second order delivers q = 1−1/C +�T 2 /T 2 , a combined result with the heat capacity and the variance of the temperature of finit e heat bath. These quantities seem to act against each other. Here the variance of the temperature is meant for the estimator 1/S ′ (E) of the thermodynamical temperature, the latter defined by 1/T = hS ′ (E)i. This way in the Gaussian ap