The information generating function of a probability distribution (Corresp.)

Golomb, S. W.

doi:10.1109/tit.1966.1053843

Cited by 65 publications

(33 citation statements)

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“…19). It is convenient to introduce the characteristic function or the information-generating function 20,21 , the Fourier transform of the probability distribution function, dJe iξJ P SA (J) = n p 1−iξ n , which may be regarded as the Rényi entropy of order α = 1 − iξ 22,23 . As we will see later in Eq.…”

Section: Figmentioning

confidence: 99%

Optimum capacity and full counting statistics of information content and heat quantity in the steady state

Utsumi

2019

Phys. Rev. B

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We consider a bipartite quantum conductor and analyze fluctuations of heat quantity in a subsystem as well as self-information associated with the reduced-density matrix of the subsystem. By exploiting the multi-contour Keldysh technique, we calculate the Rényi entropy, or the information generating function, subjected to the constraint of the local heat quantity of the subsystem, from which the probability distribution of conditional self-information is derived. We present an equality that relates the optimum capacity of information transmission and the Rényi entropy of order 0, which is the number of integer partitions into distinct parts. We apply our formalism to a twoterminal quantum dot. We point out that in the steady state, the reduced-density matrix and the operator of the local heat quantity of the subsystem may be commutative.

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Section: Figmentioning

confidence: 99%

Optimum capacity and full counting statistics of information content and heat quantity in the steady state

Utsumi

2019

Phys. Rev. B

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“…We will relate this to the information generating function 31,32 , which is the Fourier transform of the joint probability distribution of self-information and particle number (11). We will extend the multi-contour Keldysh Green function technique 30,33,34 to account for the particle number constraint.…”

Section: D R a Bmentioning

confidence: 99%

Full counting statistics of information content and particle number

Utsumi

2017

Phys. Rev. B

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We consider a bipartite quantum conductor and discuss the joint probability distribution of particle number in a subsystem and the self-information associated with the reduced density matrix of the subsystem. By extending the multi-contour Keldysh Green function technique, we calculate the R\'enyi entropy of a positive integer order $M$ subjected to the particle number constraint, from which we derive the joint probability distribution. For energy-independent transmission, we derive the time dependence of the accessible entanglement entropy, or the conditional entropy. We analyze the joint probability distribution for energy-dependent transmission probability at the steady state under the coherent resonant tunneling and the incoherent sequential tunneling conditions. We also discuss the probability distribution of the efficiency, which measures the information content transfered by a single electron.Comment: 20 pages, 8 figure

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“…The information potential is actually the Information Generating Function defined in [26]. It is called information potential since each term in its kernel estimator can be interpreted as a potential between two particles [4].…”

Section: Remarkmentioning

confidence: 99%

“…In the following, we show, however, that similar results hold for finite samples case. Consider again the kernel density estimator Equation (26). For simplicity we assume that the kernel function is Gaussian with covariance matrix Σ Z " I, where I is a dˆd identity matrix.…”

Section: Multivariate Entropy Estimators With Finite Samplesmentioning

confidence: 99%

Insights into Entropy as a Measure of Multivariate Variability

Chen

Wang

Zhao

et al. 2016

Entropy

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Entropy has been widely employed as a measure of variability for problems, such as machine learning and signal processing. In this paper, we provide some new insights into the behaviors of entropy as a measure of multivariate variability. The relationships between multivariate entropy (joint or total marginal) and traditional measures of multivariate variability, such as total dispersion and generalized variance, are investigated. It is shown that for the jointly Gaussian case, the joint entropy (or entropy power) is equivalent to the generalized variance, while total marginal entropy is equivalent to the geometric mean of the marginal variances and total marginal entropy power is equivalent to the total dispersion. The smoothed multivariate entropy (joint or total marginal) and the kernel density estimation (KDE)-based entropy estimator (with finite samples) are also studied, which, under certain conditions, will be approximately equivalent to the total dispersion (or a total dispersion estimator), regardless of the data distribution.

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The information generating function of a probability distribution (Corresp.)

Cited by 65 publications

References 0 publications

Optimum capacity and full counting statistics of information content and heat quantity in the steady state

Optimum capacity and full counting statistics of information content and heat quantity in the steady state

Full counting statistics of information content and particle number

Insights into Entropy as a Measure of Multivariate Variability

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