Related papers: Which entropy for general physical theories?

In this paper, I expand Shannon's definition of entropy into a new form of entropy that allows integration of information from different random events. Shannon's notion of entropy is a special case of my more general definition of entropy.…

All entropy is entanglement entropy. This appears as the result of the existence of black holes. The origin of entropy and the way in which it defines the perceived time direction in macroscopic systems has been discussed and can be debated…

The von Neumann entropy is a key quantity in quantum information theory and, roughly speaking, quantifies the amount of quantum information contained in a state when many identical and independent i.i.d. copies of the state are available,…

We describe the universe as a single entangled ensemble of quantum particles. The total entropy of this world ensemble, which can be expressed as a sum of information, thermodynamic and entanglement components, is assumed to be always zero.…

Uncertainty relations are central to quantum physics. While they were originally formulated in terms of variances, they have later been successfully expressed with entropies following the advent of Shannon information theory. Here, we…

There are (at least) three approaches to quantifying information. The first, algorithmic information or Kolmogorov complexity, takes events as strings and, given a universal Turing machine, quantifies the information content of a string as…

We prove that the average smooth Renyi entropy rate will approach the entropy rate of a stationary, ergodic information source, which is equal to the Shannon entropy rate for a classical information source and the von Neumann entropy rate…

Information theory provides tools to predict the performance of a learning algorithm on a given dataset. For instance, the accuracy of learning an unknown parameter can be upper bounded by reducing the learning task to hypothesis testing…

Statistical formulations of thermodynamic entropy, such as those by Boltzmann and Gibbs, were originally developed for classical systems and are well understood in that context. However, the foundational aspects of quantum statistical…

The study of mutual entropy (information) and capacity in classica l system was extensively done after Shannon by several authors like Kolmogor ov and Gelfand. In quantum systems, there have been several definitions of t he mutual entropy…

An essential quantity in quantum information theory is the von Neumann entropy which depends entirely on the quantum density operator. Once known, the density operator reveals the statistics of observables in a quantum process, and the…

The formalism of statistical mechanics can be generalized by starting from more general measures of information than the Shannon entropy and maximizing those subject to suitable constraints. We discuss some of the most important examples of…

Entropic quantifiers of states lie at the cornerstone of the quantum information theory. While a quantum state can be abstracted as a device that only has outputs, the most general quantum device is a quantum channel that also has inputs.…

We introduce a hierarchical classification of theories that describe systems with fundamentally limited information content. This property is introduced in an operational way and gives rise to the existence of mutually complementary…

After Shannon, entropy becomes a fundamental quantity to describe not only uncertainity or chaos of a system but also information carried by the system. Shannon's important discovery is to give a mathematical expression of the mutual…

We demonstrate that Shannon's information entropy and the thermodynamic entropy of Boltzmann and Gibbs are quantitatively equivalent for real condensed-matter systems. By interpreting atomic configurations as information sources, we compute…

In classical Hamiltonian theories, entropy may be understood either as a statistical property of canonical systems, or as a mechanical property, that is, as a monotonic function of the phase space along trajectories. In classical mechanics,…

We present a problem relating measurements and information theory in spin foam models. In the three dimensional case of quantum gravity we can compute probabilities of spin network graphs and study the behaviour of the Shannon entropy…

This thesis consolidates, improves and extends the smooth entropy framework for non-asymptotic information theory and cryptography. We investigate the conditional min- and max-entropy for quantum states, generalizations of classical R\'enyi…

Researchers have proposed formal definitions of quantitative information flow based on information theoretic notions such as the Shannon entropy, the min entropy, the guessing entropy, belief, and channel capacity. This paper investigates…