Related papers: Formal Groups and $Z$-Entropies

I show that non-decreasing entropy provides a necessary and sufficient condition to convert the state of a physical system into a different state by a reversible transformation that acts on the system of interest and a further "catalyst"…

Here we deconstruct, and then in a reasoned way reconstruct, the concept of "entropy of a system," paying particular attention to where the randomness may be coming from. We start with the core concept of entropy as a COUNT associated with…

Using arguments built on ergodicity, we derive an analytical expression for the Renyi entanglement entropies corresponding to the finite-energy density eigenstates of chaotic many-body Hamiltonians. The expression is a universal function of…

The Boltzmann--Gibbs entropy is a functional on the space of probability measures. When a state space is countable, one characterization of the Boltzmann--Gibbs entropy is given by the Shannon--Khinchin axioms, which consist of continuity,…

A definition of the nonadditive (nonextensive) conditional entropy indexed by q is presented. Based on the composition law in terms of it, the Shannon-Khinchin axioms are generalized and the uniqueness theorem is established for the Tsallis…

The notion of entropy penetrates much of science. A key feature of the all-important notion of Boltzmann-Gibbs-Shannon entropy is its extensivity (additivity over independent subsystems). However, there is a need for other quantities. In…

The relative entropy of two n-party quantum states is an important quantity exhibiting, for example, the extent to which the two states are different. The relative entropy of the states formed by reducing two n-party to a smaller number $m$…

Zipf's law, and power laws in general, have attracted and continue to attract considerable attention in a wide variety of disciplines - from astronomy to demographics to software structure to economics to linguistics to zoology, and even…

Recently, Suyari has proposed a generalization of Shannon-Khinchin axioms, which determines a class of entropies containing the well-known Tsalis and Havrda-Charvat entropies [H. Suyari, IEEE Trans. Inf. Theory, vol. 50, pp. 1783-1787, Aug.…

The entropy of probability distribution defined by Shannon has several extensions. R\'enyi entropy is one of the general extensions of Shannon entropy and is widely used in engineering, physics, and so on. On the other hand, the quantum…

Relative entropy is a fundamental class of distances between probability distributions, with widespread applications in probability theory, statistics, and machine learning. In this work, we study relative entropy from a categorical…

We introduce a new class of locally compact groups, namely the strongly compactly covered groups, which are the Hausdorff topological groups $G$ such that every element of $G$ is contained in a compact open normal subgroup of $G$. For…

We introduce an axiomatic approach to entropies and relative entropies that relies only on minimal information-theoretic axioms, namely monotonicity under mixing and data-processing as well as additivity for product distributions. We find…

Observational entropy -- a quantity that unifies Boltzmann's entropy, Gibbs' entropy, von Neumann's macroscopic entropy, and the diagonal entropy -- has recently been argued to play a key role in a modern formulation of statistical…

Entropy is the distinguishing and most important concept of our efforts to understand and regularize our observations of a very large class of natural phenomena, and yet, it is one of the most contentious concepts of physics. In this…

Configurational entropy, or complexity, plays a critical role in characterizing disordered systems such as glasses, yet its measurement often requires significant computational resources. Recently, R\'enyi entropy, a one-parameter…

Regardless of studies and debates over a century, the statistical origin of the second law of thermodynamics still remains illusive. One essential obstacle is the lack of a proper theoretical formalism for non-equilibrium entropy. Here I…

Various lower bounds are established for the entropy of sums, products and their combinations. First, we derive a prime-field analogue of a version of the entropy power inequality established by Tao over torsion-free groups. Next, we prove…

We give systematic ways of defining monotone quantum relative entropies and (multi-variate) quantum R\'enyi divergences starting from a set of monotone quantum relative entropies. Despite its central importance in information theory, only…

The paper suggests the concepts of an upper entropy and a lower entropy. We propose a new axiomatic definition, namely, upper entropy axioms, inspired by axioms of metric spaces, and also formulate lower entropy axioms. We also develop weak…