The recently developed TECNO schemes for hyperbolic conservation laws are designed to be high-order accurate and entropy stable, but are, as of yet, only semi-discrete. We perform an explicit discretization of the temporal derivative to obtain a fully discrete scheme, and derive a non-strict CFL condition that ensures global entropy stability. The scheme is tested in a series of numerical exper...

In this paper, we propose a novel method for increasing the entropy of a sequence of independent, discrete random variables with arbitrary distributions. The method uses an auxiliary table and a novel theorem that concerns the entropy of a sequence in which the elements are a bitwise exclusive-or sum of independent discrete random variables.

We have presented a new axiomatic derivation of Shannon entropy for a discrete probability distribution on the basis of the postulates of additivity and concavity of the entropy function. We have then modified Shannon entropy to take account of observational uncertainty.The modified entropy reduces, in the limiting case, to the form of Shannon differential entropy. As an application, we have de...

For discrete-time stochastic processes, there is a close connection between return/waiting times and entropy. Such a connection cannot be straightforwardly extended to the continuous-time setting. Contrarily to the discrete-time case one does need a reference measure and so the natural object is relative entropy rather than entropy. In this paper we elaborate on this in the case of continuous-t...

Entropy and information are common measures of probabilistic models of data, frequently used for discrete and discretized but more rarely for continuous data. We employ finite mixture models, which handle continuous and discrete data simultaneously, to construct a probabilistic model whose entropy can be estimated. Analytic estimates of entropy are intractable for some models, so an approximate...

Abstract. In this paper, we propose an entropy satisfying conservative method to solve the Fokker–Planck equation of the finitely extensible nonlinear elastic dumbbell model for polymers, subject to homogeneous fluids. Both semidiscrete and fully discrete schemes satisfy all three desired properties—(i) mass conservation, (ii) positivity preserving, and (iii) entropy satisfying—in the sense tha...

In this work we establish conditions for an approximate simple Riemann solver to satisfy a semi-discrete entropy inequality. The semi-discrete approach is less restrictive than the fully-discrete case and allows to grant some other good properties for numerical schemes. First, conditions are established in an abstract framework for simple Riemann solvers to satisfy a semi-discrete entropy inequ...

The uniqueness theorem for the relative entropy was proven by A.Hobson. Recently, the Tsallis entropy was characterized by H.Suyari in terms of the generalized ShannonKhinchin’s axiom. In this short paper, we characterize the Tsallis relative entropy in the finite discrete system by generalizing the conditions in Hobson’s axiom.

In this paper, the influence of four key issues on wavelet-based analysis of hydrologic series’ complexity under multi-temporal scales, including the choice of mother wavelet, noise, estimation of probability density function and trend of series data, was first studied. Then, the complexities of several representative hydrologic series data were quantified and described, based on which the perf...

X dP dμ ln dP dμ dμ on a measure space (X,M, μ), does not qualify itself as an information measure (it is not a natural extension of the discrete case), maximum entropy (ME) prescriptions in the measure-theoretic case are consistent with that of discrete case. In this paper, we study the measure-theoretic definitions of generalized information measures and discuss the ME prescriptions. We prese...