Related papers: Procedural Mixture Sets
Thermodynamics can be formulated in either of two approaches, the phenomenological approach, which refers to the macroscopic properties of systems, and the statistical approach, which describes systems in terms of their microscopic…
Upper and lower bounds are obtained for the joint entropy of a collection of random variables in terms of an arbitrary collection of subset joint entropies. These inequalities generalize Shannon's chain rule for entropy as well as…
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…
Mountain river torrents and snow avalanches generate human and material damages with dramatic consequences. Knowledge about natural phenomenona is often lacking and expertise is required for decision and risk management purposes using…
Seifert derived an exact fluctuation relation for diffusion processes using the concept of "stochastic system entropy". In this note we extend his formalism to entropic transport. We introduce the notion of relative stochastic entropy, or…
A general theory for computing information transfers in nonlinear stochastic systems driven by deterministic forcing and additive and/or multiplicative noises, is presented. It extends the Liang-Kleeman framework of causality inference to…
Probability theory is fundamental for modeling uncertainty, with traditional probabilities being real and non-negative. Complex probability extends this concept by allowing complex-valued probabilities, opening new avenues for analysis in…
The Shannon entropy is a fundamental measure for quantifying diversity and model complexity in fields such as information theory, ecology, and genetics. However, many existing studies assume that the number of species is known, an…
This article introduces the physics of information in the context of molecular biology and genomics. Entropy and information, the two central concepts of Shannon's theory of information and communication, are often confused with each other…
There are numerous characterizations of Shannon entropy and Tsallis entropy as measures of information obeying certain properties. Using work by Faddeev and Furuichi, we derive a very simple characterization. Instead of focusing on the…
We review a new form of entropy suggested by us, with origin in mixing of states of systems due to interactions and deformations of phase cells. It is demonstrated that this nonextensive form also leads to asymmetric maximal entropy…
In 2002, in a seminal article, Christoph Bandt and Bernd Pompe proposed a new methodology for the analysis of complex time series, now known as Ordinal Analysis. The ordinal methodology is based on the computation of symbols (known as…
We introduce a computational method to discover polymorphs in molecular crystals at finite temperature. The method is based on reproducing the crystallization process starting from the liquid and letting the system discover the relevant…
According to E.T. Jaynes and E.P. Wigner, entropy is an anthropomorphic concept in the sense that in a physical system correspond many thermodynamic systems. The physical system can be examined from many points of view each time examining…
An "entropy increasing to the maximum" result analogous to the entropic central limit theorem (Barron 1986; Artstein et al. 2004) is obtained in the discrete setting. This involves the thinning operation and a Poisson limit. Monotonic…
In this paper, some general properties of Shannon information measures are investigated over sets of probability distributions with restricted marginals. Certain optimization problems associated with these functionals are shown to be…
Permutation entropy measures the complexity of deterministic time series via a data symbolic quantization consisting of rank vectors called ordinal patterns or just permutations. The reasons for the increasing popularity of this entropy in…
Information plays an important role in our understanding of the physical world. We hence propose an entropic measure of information for any physical theory that admits systems, states and measurements. In the quantum and classical world,…
Many complex systems are characterized by non-Boltzmann distribution functions of their statistical variables. If one wants to -- justified or not -- hold on to the maximum entropy principle for complex statistical systems (non-Boltzmann)…
We propose a unifying picture where the notion of generalized entropy is related to information theory by means of a group-theoretical approach. The group structure comes from the requirement that an entropy be well defined with respect to…