相关论文: Gibbs-Shannon Entropy and Related Measures: Tsalli…

Fundamental properties for the Tsallis relative entropy in both classical and quantum systems are studied. As one of our main results, we give the parametric extension of the trace inequality between the quantum relative entropy and the…

We revisit the derivation of a formula for the $q$-generalised multinomial coefficient rooted in the $q$-deformed algebra, a foundational framework in the study of nonextensive statistics. Previous approximate expressions in the literature…

A general investigation is made into the intrinsic Riemannian geometry for complex systems, from the perspective of statistical mechanics. The entropic formulation of statistical mechanics is the ingredient which enables a connection…

We numerically investigate entropic Bell inequalities for a pair of entangled qutrits using information-theoretic distances. We show that for this class of inequalities Tsallis entropy is more suitable than Shannon as it reveals…

In this paper, we investigate the asymptotic stability of finite-dimensional stochastic integrable Hamiltonian systems via information entropy. Specifically, we establish the asymptotic vanishing of Shannon entropy difference (with…

We have studied finite $N$-body $D$-dimensional nonextensive ideal gases and harmonic oscillators, by using the maximum-entropy methods with the $q$- and normal averages ($q$: the entropic index). The validity range, specific heat and…

The quantum relative Renyi entropy of two density matrices was recently extended when the two do not commute, from which a conditional entropy is identified. This is here extended to the corresponding Tsallis relative entropy and to its…

We consider the problem of finite sample corrections for entropy estimation. New estimates of the Shannon entropy are proposed and their systematic error (the bias) is computed analytically. We find that our results cover correction…

We examine the entropy of non-equilibrium stationary states of boundary driven totally asymmetric simple exclusion processes. As a consequence, we obtain that the Gibbs-Shannon entropy of the non equilibrium stationary state converges to…

From the output produced by a memoryless deletion channel from a uniformly random input of known length $n$, one obtains a posterior distribution on the channel input. The difference between the Shannon entropy of this distribution and that…

We propose a method to derive the stationary size distributions of a system, and the degree distributions of networks, using maximisation of the Gibbs-Shannon entropy. We apply this to a preferential attachment-type algorithm for systems of…

The paper extends the analysis of the entropies of the Poisson distribution with parameter $\lambda$. It demonstrates that the Tsallis and Sharma-Mittal entropies exhibit monotonic behavior with respect to $\lambda$, whereas two generalized…

The Tsallis and R\'enyi entropies are important quantities in the information theory, statistics and related fields because the Tsallis entropy is an one parameter generalization of the Shannon entropy and the R\'enyi entropy includes…

We prove an entropic uncertainty relation for two quantum channels, extending the work of Frank and Lieb for quantum measurements. This is obtained via a generalized strong super-additivity (SSA) of quantum entropy. Motivated by Petz's…

We consider information-theoretic inequalities of the Bell type in the presence of decoherence. It is natural that too strong coupling with the environment can prevent an observation of quantum correlations. In this regard, the use of…

We discuss the relationship between entropic uncertainty relations and entanglement. We present two methods for deriving separability criteria in terms of entropic uncertainty relations. Especially we show how any entropic uncertainty…

Entropic uncertainty relations for the position and momentum within the generalized uncertainty principle are examined. Studies of this principle are motivated by the existence of a minimal observable length. Then the position and momentum…

We give a new proof of the theorems on the maximum entropy principle in Tsallis statistics. That is, we show that the $q$-canonical distribution attains the maximum value of the Tsallis entropy, subject to the constraint on the…

We derive a family of entanglement criteria for continuous variable systems based on the R\'enyi entropy of complementary distributions. We show that these entanglement witnesses can be more sensitive than those based on second-order…

We derive several entanglement criteria for bipartite continuous variable quantum systems based on the Shannon entropy. These criteria are more sensitive than those involving only second-order moments, and are equivalent to well-known…