Related papers: A complete characterisation of conditional entropi…
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…
The principle of maximum entropy is a broadly applicable technique for computing a distribution with the least amount of information possible while constrained to match empirically estimated feature expectations. However, in many real-world…
A generalization of the entropy production rate is proposed $\Pi_q$ in non-equilibrium systems by extending the formalism of classical stochastic thermodynamics to regimes with non-Gaussian fluctuations. Through the R\'enyi entropy $S_q$ ,…
We study the notion of approximate entropy within the framework of network theory. Approximate entropy is an uncertainty measure originally proposed in the context of dynamical systems and time series. We firstly define a purely structural…
The conditional entropy power inequality is a fundamental inequality in information theory, stating that the conditional entropy of the sum of two conditionally independent vector-valued random variables each with an assigned conditional…
Entropy production is a key quantity in any finite-time thermodynamic process. It is intimately tied with the fundamental laws of thermodynamics, embodying a tool to extend thermodynamic considerations all the way to non-equilibrium…
Separability conditions for a bipartite quantum system of finite-dimensional subsystems are formulated in terms of R\'{e}nyi and Tsallis entropies. Entropic uncertainty relations often lead to entanglement criteria. We propose new approach…
A new combinatorial-probabilistic diagnostic entropy has been introduced. It describes the pair-wise sum of probabilities of system conditions that have to be distinguished during the diagnosing process. The proposed measure describes the…
Shannon entropy, a cornerstone of information theory, statistical physics and inference methods, is uniquely identified by the Shannon-Khinchin or Shore-Johnson axioms. Generalizations of Shannon entropy, motivated by the study of…
Subshifts of deterministic substitutions are ubiquitous objects in dynamical systems and aperiodic order (the mathematical theory of quasicrystals). Two of their most striking features are that they have low complexity (zero topological…
When at equilibrium, large-scale systems obey conventional thermodynamics because they belong to microscopic configurations (or states) that are typical. Crucially, the typical states usually represent only a small fraction of the total…
Heisenberg's uncertainty principle has recently led to general measurement uncertainty relations for quantum systems: incompatible observables can be measured jointly or in sequence only with some unavoidable approximation, which can be…
This dissertation investigates relative entropies, also called generalized divergences, and how they can be used to characterize information-theoretic tasks in quantum information theory. The main goal is to further refine characterizations…
We address an information-theoretic approach to noise and disturbance in quantum measurements. Properties of corresponding probability distributions are characterized by means of both the R\'{e}nyi and Tsallis entropies. Related…
PAE cannot be made a basis for either a generalized statistical mechanics or a generalized information theory. Either statistical independence must be waived, or the expression of the averaged conditional probability as the difference…
Entropy is a very useful concept from physics that tries to explain how a system behaves from a point of view of the thermodynamics. However, there are two ways to explain entropy, and it depends on if we are studying a microsystem or a…
Within the task of collaborative filtering two challenges for computing conditional probabilities exist. First, the amount of training data available is typically sparse with respect to the size of the domain. Thus, support for higher-order…
It is shown that the structure of thermodynamics is "form invariant", when it is derived using maximum entropy principle for various choices of entropy and even beyond equilibrium. By the form invariance of thermodynamics, it is meant that…
Entropy is a concept that has traditionally been reliant on a definite notion of causality. However, without a definite notion of causality, the concept of entropy is not all lost. Indefinite causal structure results from combining…
We extend the notion of estimation entropy of autonomous dynamical systems proposed by Liberzon and Mitra [1] to nonlinear dynamical systems with uncertain inputs with bounded variation. We call this new notion the {$\epsilon$}-estimation…