Related papers: Lectures on Entropy. Part I
Instructors of statistics who teach non-statistics majors possess varied academic backgrounds, and hence it is reasonable to expect variability in their content knowledge, and pedagogical approach. The aim of this study was to determine the…
Shannon's metric of "Entropy" of information is a foundational concept of information theory. This article is a primer for novices that presents an intuitive way of understanding, remembering, and/or reconstructing Shannon's Entropy metric…
These notes, connected to a "potpourri" topics class currently underway, discuss some basic topics in analysis and connections with other areas of mathematics.
These are notes from an informal mini-course on factorization homology, infinity-categories, and topological field theories. The target audience was imagined to be graduate students who are not homotopy theorists.
Information theory plays a central role in establishing fundamental limits on what any learning or estimation algorithm can -- and cannot -- achieve, regardless of computational power. In this chapter, we provide an introduction to these…
This series of introductory lectures consists of two parts. In the first part, I rapidly review the basic notions of quantum physics and many primitives of quantum information (i.e. notions that one must be somehow familiar with in the…
We present a conceptually clear introduction to quantum theory, deriving the theory from scratch from the point of view of quantum information. Different subsets of these lectures were taught to a wide variety of audiences, including…
The aim of these notes is to provide a succinct, accessible introduction to some of the basic ideas of category theory and categorical logic. The notes are based on a lecture course given at Oxford over the past few years. They contain…
These are general notes on tensor calculus which can be used as a reference for an introductory course on tensor algebra and calculus. A basic knowledge of calculus and linear algebra with some commonly used mathematical terminology is…
In these decades, it has been revealed that there is rich information-theoretic structure in thermodynamics of out-of-equilibrium systems in both the classical and quantum regimes. This has led to the fruitful interplay among statistical…
We study the entropy of Chinese and English texts, based on characters in case of Chinese texts and based on words for both languages. Significant differences are found between the languages and between different personal styles of debating…
A mathematical interpretation of the usual definition of entropy (for a discrete probability distribution or a trace 1 positive operator) is given. This formulation makes some properties of entropy immediate.
The purpose of these lecture notes is to give a quick and introductory overview of holographic superconductors. Besides the actual description of the standard holographic superconductor, attention is paid to the motivations and the relation…
Lecture-notes: introducing and discussing basic kp concepts related to bands interaction at an elementary level to beginners
I recall my 'matter-gravity entanglement hypothesis' and briefly review the evidence for it, based partly on its seeming ability to resolve a number of puzzles related to quantum black holes including the black hole information loss puzzle.…
The second half of this essay tells the story of the genesis and early development of the notion of black hole entropy, in the style of an after dinner talk (apart from a long technical footnote). The first half sketches the development of…
Exponential families form the backbone of modern statistics and machine learning, but textbooks seldom derive them from first principles in an accessible way. Although minimal sufficiency and the principle of maximum entropy, originating in…
This is a non-standard paper, containing some problems in set theory I have in various degrees been interested in. Sometimes with a discussion on what I have to say; sometimes, of what makes them interesting to me, sometimes the problems…
This article summarises a Web-book on "Complexity" that was developed to introduce undergraduate students to interesting complex systems in the biological, physical and social sciences, and the common tools, principles and concepts used for…
Entropy generation in a chemical reaction is analyzed without using the general formalism of non-equilibrium thermodynamics at a level adequate for advanced undergraduates. In a first approach to the problem, the phenomenological kinetic…