Information Theory: Basic notation and conventions

TL;DR: It is shown that the free energy of thermodynamics emerges naturally from the resource theory of energy-preserving transformations, provided that a sublinear amount of coherent superposition over energy levels is available, a situation analogous to the sub linear amount of classical communication required for entanglement dilution.

TL;DR: Fixed-to-fixed length, invertible, and low complexity encoders and decoders based on constant composition and arithmetic coding are presented and the encoder achieves the maximum rate of the desired distribution, asymptotically in the blocklength.

TL;DR: In this paper, the authors highlight the mathematical and computational structure relating to the formulation of, and development of algorithms for, the Bayesian approach to inverse problems in differential equations, and describe measure-preserving dynamics on the underlying infinite dimensional space.

TL;DR: Systematic approaches to obtain f -divergence inequalities, dealing with pairs of probability measures defined on arbitrary alphabets, are developed, including “reverse Pinsker inequalities,” as well as on the Eγ divergence, which generalizes the total variation distance.