Shannon entropy of a probability measure P, defined as -∫X(dP/dμ)ln(dP/dμ)dμ on a measure space (X,M,μ), is not a natural extension from the discrete case. However, maximum entropy (ME) prescriptions of Shannon entropy functional in the measure-theoretic case are consistent with those for...

It is suggested that thermodynamical equilibrium equals game theoretical equilibrium. Aspects of this thesis are discussed. The philosophy is consistent with maximum entropy thinking of Jaynes, but goes one step deeper by deriving the maximum entropy principle from an underlying game theoretical...

We propose a one-parameter family Rq of deformations of the reals, which is motivated by the generalized additivity of the Tsallis entropy. We introduce a generalized multiplication which is distributive with respect to the generalized addition of the Tsallis entropy. These operations establish...

We investigate the behavior of the Shannon entropy, S(T), and the time generalized q-entropy, Sq(T), at increasing aggregation intervals, T, using series of 15-min and hourly rainfall records in the tropical Andes of Colombia, spanning from 21 months to 40 years, as well as average daily...

Physiologic complexity is an important concept to characterize time series from biological systems, which associated to multiscale analysis can contribute to comprehension of many complex phenomena. Although multiscale entropy has been applied to physiological time series, it measures...

A measure of redundancy inherent in the layouts of water distribution networks is developed using the Tsallis entropy. Both the local redundancy at a node and the global redundancy due to the redundancies at adjacent nodes are derived. The redundancy measure is applied to layouts reported in the...

We develop a dynamic framework to identify aggregate market fears ahead of a major market crash through the skewness premium of European options. Our methodology is based on measuring the distribution of a skewness premium through a q-Gaussian density and a maximum entropy principle. Our...