Fun and exciting textbook on the mathematics underpinning the most dynamic areas of modern science and engineering.

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Information Theory, Inference and Learning Algorithms

An expression is derived for the equilibrium free energy difference between two configurations of a system, in terms of an ensemble of finite-time measurements of the work performed in parametrically switching from one configuration to the other. Two well-known identities emerge as limiting cases of this result.

/pdf/nonequilibrium-equality-for-free-energy-differences-3wppbarpvj.pdf

Nonequilibrium Equality for Free Energy Differences

Preface. Part I: Gathering the Tools. 1. Introduction to Quantum Physics. 2. Quantum Tests. 3. Complex Vector Space. 4. Continuous Variables. Part II: Cryptodeterminism and Quantum Inseparability. 5. Composite Systems. 6. Bell's Theorem. 7. Contextuality. Part III: Quantum Dynamics and Information. 8. Spacetime Symmetries. 9. Information and Thermodynamics. 10. Semiclassical Methods. 11. Chaos and Irreversibility. 12. The Measuring Process. Author Index. Subject Index.

Quantum Theory: Concepts and Methods

We demonstrate that a monolayer graphene membrane is impermeable to standard gases including helium. By applying a pressure difference across the membrane, we measure both the elastic constants and the mass of a single layer of graphene. This pressurized graphene membrane is the world's thinnest balloon and provides a unique separation barrier between 2 distinct regions that is only one atom thick.

/pdf/impermeable-atomic-membranes-from-graphene-sheets-xtis5huy2d.pdf

Impermeable atomic membranes from graphene sheets.

Each complex network (or class of networks) presents specific topological features which characterize its connectivity and highly influence the dynamics of processes executed on the network. The analysis, discrimination, and synthesis of complex networks therefore rely on the use of measurements capable of expressing the most relevant topological features. This article presents a survey of such measurements. It includes general considerations about complex network characterization, a brief review of the principal models, and the presentation of the main existing measurements. Important related issues covered in this work comprise the representation of the evolution of complex networks in terms of trajectories in several measurement spaces, the analysis of the correlations between some of the most traditional measurements, perturbation analysis, as well as the use of multivariate statistics for feature selection and network classification. Depending on the network and the analysis task one has in mind, a s...

https://arxiv.org/pdf/cond-mat/0505185.pdf

Characterization of complex networks: A survey of measurements

This book is designed for the junior-senior thermodynamics course given in all departments as a standard part of the curriculum. The book is devoted to a discussion of some of the basic physical concepts and methods useful in the description of situations involving systems which consist of very many particulars. It attempts, in particular, to introduce the reader to the disciplines of thermodynamics, statistical mechanics, and kinetic theory from a unified and modern point of view. The presentation emphasizes the essential unity of the subject matter and develops physical insight by stressing the microscopic content of the theory.

Frederick Reif

Papers

Fundamentals of Statistical and Thermal Physics

Fundamentals of Statistical and Thermal Physics