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Shannon based his information theory on the notion of probability measures as it we developed by Kolmogorov. In this paper we study some fundamental problems in information theory based on expectation measures. In the theory of expectation…
Stimulated by the need of describing useful notions related to information measures, we introduce the `pdf-related distributions'. These are defined in terms of transformation of absolutely continuous random variables through their own…
Entropic measures provide analytic tools to help us understand correlation in quantum systems. In our previous work, we calculated linear entropy and von Neumann entropy as entanglement measures for the ground state and lower lying excited…
Heisenberg-like and Fisher-information-based uncertainty relations which extend and generalize previous similar expressions are obtained for $N$-fermion $d$-dimensional systems. The contributions of both spatial and spin degrees of freedom…
We review the introduction of likelihood functions and Fisher information in classical estimation theory, and we show how they can be defined in a very similar manner within quantum measurement theory. We show that the stochastic master…
The notion of information pervades informal descriptions of biological systems, but formal treatments face the problem of defining a quantitative measure of information rooted in a concept of fitness, which is itself an elusive notion.…
A measure called Physical Complexity is established and calculated for a population of sequences, based on statistical physics, automata theory, and information theory. It is a measure of the quantity of information in an organism's genome.…
The importance of Fisher information is increasing in nonequilibrium thermodynamics, as it has played a fundamental role in trade-off relations such as thermodynamic uncertainty relations and speed limits. In this work, we investigate…
A surrogate data analysis is presented, which is based on the fluctuations of the ``entropy'' $S$ defined in the natural time-domain [Phys. Rev. E {\bf 68}, 031106, 2003]. This entropy is not a static one as, for example, the Shannon…
We study the Shannon entropy of the probability distribution resulting from the ground-state wave function of a one-dimensional quantum model. This entropy is related to the entanglement entropy of a Rokhsar-Kivelson-type wave function…
Position and momentum information measures are evaluated for the ground state of the \emph{relativistic} hydrogen-like atoms. Consequences of the fact that the radial momentum operator is not self-adjoint are explicitly studied, exhibiting…
In this paper, we present a new multi-scale information content calculation method based on Shannon information (and Shannon entropy). The original method described by Claude E. Shannon and based on the logarithm of the probability of…
Newtonian dynamics is derived from prior information codified into an appropriate statistical model. The basic assumption is that there is an irreducible uncertainty in the location of particles so that the state of a particle is defined by…
This paper introduces time into information theory, gives a more accurate definition of information, and unifies the information in cognition and Shannon information theory. Specially, we consider time as a measure of information, giving a…
Reliable data-driven estimation of Shannon entropy from small data sets, where the number of examples is potentially smaller than the number of possible outcomes, is a critical matter in several applications. In this paper, we introduce a…
Ecological and evolutionary processes show various population dynamics depending on internal interactions and environmental changes. While crucial in predicting biological processes, discovering general relations for such nonlinear dynamics…
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…
The Shannon entropy of a collection of random variables is subject to a number of constraints, the best-known examples being monotonicity and strong subadditivity. It remains an open question to decide which of these "laws of information…
Transfer entropy is capable of capturing nonlinear source-destination relations between multi-variate time series. It is a measure of association between source data that are transformed into destination data via a set of linear…
We present a quantum information theory that allows for a consistent description of entanglement. It parallels classical (Shannon) information theory but is based entirely on density matrices (rather than probability distributions) for the…