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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…
Inference and learning are commonly cast in terms of optimisation, yet the fundamental constraints governing uncertainty reduction remain unclear. This work presents a first-principles framework inherent to Bayesian updating, termed…
The general idea of information entropy provided by C.E. Shannon "hangs over everything we do" and can be applied to a great variety of problems once the connection between a distribution and the quantities of interest is found. The Shannon…
Even if a probability distribution is properly normalizable, its associated Shannon (or von Neumann) entropy can easily be infinite. We carefully analyze conditions under which this phenomenon can occur. Roughly speaking, this happens when…
The introduced entropy functional's (EF) information measure of random process integrates multiple information contributions along the process trajectories, evaluating both the states' and between states' bound information connections. This…
It is not obvious how to extend Shannon's original information entropy to higher dimensions, and many different approaches have been tried. We replace the English text symbol sequence originally used to illustrate the theory by a discrete,…
Shannon information was defined for characterizing the uncertainty information of classical probabilistic distributions. As an uncertainty measure it is generally believed to be positive. This holds for any information quantity from two…
When an experimentalist measures a time series of qubits, the outcomes generate a classical stochastic process. We show that measurement induces high complexity in these processes in two specific senses: they are inherently unpredictable…
Information flow analysis is a powerful technique for reasoning about the sensitive information exposed by a program during its execution. While past work has proposed information theoretic metrics (e.g., Shannon entropy, min-entropy,…
Entropic uncertainty relations are interesting in their own rights as well as for a lot of applications. Keeping this in mind, we try to make the corresponding inequalities as tight as possible. The use of parametrized entropies also allows…
In this paper, the time dynamics of the daily means of wind speed measured in complex mountainous regions are investigated. For 293 measuring stations distributed over all Switzerland, the Fisher information measure and the Shannon entropy…
In this work we determine and discuss the entropic uncertainty measures of Shannon type for all the discrete stationary states of the multidimensional harmonic systems directly in terms of the states' hyperquantum numbers, the…
The problem of the insensitivity of the macroscopic behavior of any thermodynamical system to partitioning generates a bias between the reproducibility of its macroscopic behavior viewed as the simplest form of causality and its long-term…
Shannon Information theory has achieved great success in not only communication technology where it was originally developed for but also many other science and engineering fields such as machine learning and artificial intelligence.…
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…
Complementarity relations between various characterizations of a probability distribution are at the core of information theory. In particular, lower and upper bounds for the entropic function are of great importance. In applied topics, we…
We analyze the Shannon and Fisher information measures for systems subjected to quartic and symmetric potential wells. The wave functions are obtained by solving the time-independent Schr\"{o}dinger equation, using aspects of perturbation…
We describe how to analyze the wide class of non stationary processes with stationary centered increments using Shannon information theory. To do so, we use a practical viewpoint and define ersatz quantities from time-averaged probability…
Information and uncertainty are closely related and extensively studied concepts in a number of scientific disciplines such as communication theory, probability theory, and statistics. Increasing the information arguably reduces the…
Climate is known for being characterised by strong non-linearity and chaotic behaviour. Nevertheless, few studies in climate science adopt statistical methods specifically designed for non-stationary or non-linear systems. Here we show how…