Related papers: General Information Theory: Time and Information
We propose a unified theoretical framework for quantifying spatio-temporal interactions in a stochastic dynamical system based on information geometry. In the proposed framework, the degree of interactions is quantified by the divergence…
Information is everywhere in nature which is very uncertain and unpredictable. But information, in itself, is a very ambiguous term. In this cursory write-up, we attempt to understand the formal meaning of information by quantifying…
We develop a general formalism for representing and understanding structure in complex systems. In our view, structure is the totality of relationships among a system's components, and these relationships can be quantified using information…
We propose a new framework for reasoning about information in complex systems. Our foundation is based on a variational extension of Shannon's information theory that takes into account the modeling power and computational constraints of…
In this article a notion of information is presented which stresses the contextuality of quantum objects and their measurement. Mathematically this is reached by a quantification of the quantum mechanical surplus knowledge which has been…
It is well known that a Shannon based definition of information entropy leads in the classical case to the Boltzmann entropy. It is tempting to regard the Von Neumann entropy as the corresponding quantum mechanical definition. But the…
Information theory is a practical and theoretical framework developed for the study of communication over noisy channels. Its probabilistic basis and capacity to relate statistical structure to function make it ideally suited for studying…
We address the problem of quantifying the information content of a source for an arbitrary information theory, where the information content is defined in terms of the asymptotic achievable compression rate. The functions that solve this…
We review with a tutorial scope the information theory foundations of quantum statistical physics. Only a small proportion of the variables that characterize a system at the microscopic scale can be controlled, for both practical and…
The notion of Shannon entropy is crucial for the theory of classical information. In quantum information theory, an analogous key role is played by the von Neumann entropy: quantum information processing is closely related to entropy…
Information Theory concepts and methodologies conform the background of how communication systems are studied and understood. They are mainly focused on the source-channel-receiver problem and on the asymptotic limits of accuracy and…
We obtain generalizations of the Kelvin-Planck, Clausius, and Carnot statements of the second law of thermodynamics, for situations involving information processing. To this end, we consider an information reservoir (representing, e.g. a…
Markov categories are a novel framework to describe and treat problems in probability and information theory. In this work we combine the categorical formalism with the traditional quantitative notions of entropy, mutual information, and…
Information is the basic concept of information theory. However, there is no definition of this concept that can encompass all uses of the term information in information theories and beyond. Many question a possibility of such a…
Even today, the concept of entropy is perceived by many as quite obscure. The main difficulty is analyzed as being fundamentally due to the subjectivity and anthropocentrism of the concept that prevent us to have a sufficient distance to…
The concept of time mostly plays a subordinate role in finance and economics. The assumption is that time flows continuously and that time series data should be analyzed at regular, equidistant intervals. Nonetheless, already nearly 60…
Prompted by the realisation that the statistical entropy of an ideal gas in the micro-canonical ensemble should not fluctuate or change over time, the meaning of the H-theorem is re-interpreted from the perspective of information theory in…
A measurement performed on a quantum system is an act of gaining information about its state, a view that is widespread in practical and foundational work in quantum theory. However, the concept of information in quantum theory…
While the quantum mutual information is a fundamental measure of quantum information, it is only defined for spacelike-separated quantum systems. Such a limitation is not present in the theory of classical information, where the mutual…
Energy has no definition, except that given by a conservation principle which essentially amounts to defining it as the elements of an open list of unknown cardinality. Entropy, identified by Shannon as information we lack, has too many…