("It takes an infinite amount of information to pin-point a continuous variable".) It is shown, however, that a "law of diminishing returns" operates. The information content of a distribution over a narrow interval as decreasing with the range of the variable and this decrease exactly ...
Fisk, C., Brown, G.R. (1975): A Note on the Entropy Formulation of Distribution Models. Operational Research Quarterly 26, 755-758Fisk C, Brown G R, 1975, "A note on the entropy formulation of distribution models" Operational Research Quarterly 26 755-758...
The Shannon entropy of a distribution p∈P̄(Ω) is defined as (3)H(p)≔−∑ω∈supppp(ω)lnp(ω). It measures the uncertainty about the outcome of an experiment governed by p. A related quantity which can be interpreted as a ‘distance’ on the space of probability distributions...
The goal of quantum key distribution (QKD) is to establish a secure key between two parties connected by an insecure quantum channel. To use a QKD protocol in practice, one has to prove that a finite size key is secure against general attacks: no matter the adversary’s attack, they canno...
Ken A. Dill Nature Reviews Physics6,382–393 (2024)Cite this article 4648Accesses 7Citations 3Altmetric Metrics Abstract Statistical physics relates the properties of macroscale systems to the distributions of their microscale agents. Its central tool has been the maximization of entropy, an equilibri...
–But I can feel, that finally, it is still a distribution question, just a more complex one and non-average one. And finally, it will still comes to the case, the equilibrium case, and of course, the maximum S. Because that is the definition of the entropy. Thus though I can not...
Many unique properties of complex networks result from heterogeneity. The measure and analysis of heterogeneity are important and desirable to the research of the properties and functions of complex networks. In this paper, the rank distribution is proposed as a new statistic feature of complex networ...
Using the maximum-entropy method, we calculate the end-to-end distance distribution of the force-stretched chain from the moments of the distribution, which can be obtained from the extension-force curves measured in single-molecule experiments. If one knows the force expansion of the extension th...
The cultural and geographical properties of the environment have been shown to deeply influence cognition and mental health1–6. Living near green spaces has been found to be strongly beneficial7–11, and urban residence has been associated with a h
we first provide explicit formulas for the central moments of both binomial and multinomial distributions describing the distribution of the sample entropy. Second, we identify the optimal rolling window length to estimate time-varying Shannon entropy. We optimize this choice using a novel self-consiste...