相关论文: The use of spatial information in entropy measures
We produce a probabilistic space from logic, both classical and quantum, which is in addition partially ordered in such a way that entropy is monotone. In particular do we establish the following equation: Quantitative Probability = Logic +…
The R{\'e}nyi entropy is one of the important information measures that generalizes Shannon's entropy. The quantum R{\'e}nyi entropy has a fundamental role in quantum information theory, therefore, bounding this quantity is of vital…
Thermodynamic uncertainty relations reveal a fundamental trade-off between the precision of a trajectory observable and entropy production, where the uncertainty of the observable is quantified by its variance. In information theory,…
It is shown that for any ensemble, whether classical or quantum, continuous or discrete, there is only one measure of the "volume" of the ensemble that is compatible with several basic geometric postulates. This volume measure is thus a…
Information diagram and the I-measure are useful mnemonics where random variables are treated as sets, and entropy and mutual information are treated as a signed measure. Although the I-measure has been successful in machine proofs of…
Markov categories are a novel framework to describe and treat problems in probability and information theory. In this work we combine the categorical formalism with the traditional quantitative notions of entropy, mutual information, and…
Most psychophysical experiments discard half the data collected. Specifically, experiments discard reaction time data, and use binary responses (e.g. yes/no) to measure performance. Here, Shannon's information theory is used to define…
Entropy has been a common index to quantify the complexity of time series in a variety of fields. Here, we introduce increment entropy to measure the complexity of time series in which each increment is mapped into a word of two letters,…
While most useful information theoretic inequalities can be deduced from the basic properties of entropy or mutual information, Shannon's entropy power inequality (EPI) seems to be an exception: available information theoretic proofs of the…
The Shannon entropy of a random variable $X$ has much behaviour analogous to a signed measure. Previous work has concretized this connection by defining a signed measure $\mu$ on an abstract information space $\tilde{X}$, which is taken to…
The statistical analysis of data stemming from dynamical systems, including, but not limited to, time series, routinely relies on the estimation of information theoretical quantities, most notably Shannon entropy. To this purpose, possibly…
A two parameter generalization of Boltzmann-Gibbs-Shannon entropy based on natural logarithm is introduced. The generalization of the Shannon-Kinchinn axioms corresponding to the two parameter entropy is proposed and verified. We present…
The data for many classification problems, such as pattern and speech recognition, follow mixture distributions. To quantify the optimum performance for classification tasks, the Shannon mutual information is a natural information-theoretic…
The Shannon entropy is used as a basis for applying different lemmas and conjectures concerning the set of gaps between prime numbers G_p , thus estimating several measures of it. The same procedures are applied to artificially created…
Shannon's metric of "Entropy" of information is a foundational concept of information theory. This article is a primer for novices that presents an intuitive way of understanding, remembering, and/or reconstructing Shannon's Entropy metric…
Entropic uncertainty relations place nontrivial lower bounds to the sum of Shannon information entropies for noncommuting observables. Here we obtain a novel lower bound on the entropy sum for general pairs of observables in…
Shannon and Renyi entropies are quantitative measures of uncertainty in a data set. They are developed by Renyi in the context of entropy theory. These measures have been studied in the case of the multivariate t-distributions. We extend…
It is shown that the standard expression for the information entropy, originally due to Shannon, is only valid for a particular set of states. For the general case of statistical mechanics, one needs to include an additional term in the…
The paper analyzes the probability distribution of the occupancy numbers and the entropy of a system at the equilibrium composed by an arbitrary number of non-interacting bosons. The probability distribution is derived both by tracing out…
I consider the effect of a finite sample size on the entropy of a sample of independent events. I propose formula for entropy which satisfies Shannon's axioms, and which reduces to Shannon's entropy when sample size is infinite. I discuss…