相关论文: The Boltzmann/Shannon entropy as a measure of corr…

The Boltzmann-Gibbs celebrated entropy $S_{BG}=-k\sum_ip_i \ln p_i$ is {\it concave} (with regard to all probability distributions $\{p_i\}$) and {\it stable} (under arbitrarily small deformations of any given probability distribution). It…

In statistical physics, if we successively divide an equilibrium system into two parts, we will face a situation that, within a certain length $\xi$, the physics of a subsystem is no longer the same as the original system. Then the…

The log-periodic equation for the entropy $S = - (k/a) \sum_{i=1}^{N} p_{i} \sin(a \ln p_{i})$, based on the forgotten Sharma-Taneja entropy measure, is studied for the first time with $N$ the total number of system states and $p_{i}$ the…

The Shannon entropy, one of the cornerstones of information theory, is widely used in physics, particularly in statistical mechanics. Yet its characterization and connection to physics remain vague, leaving ample room for misconceptions and…

We revisit textbook claims that entropy must increase and show that, under time-reversal invariant microscopic dynamics, no universal trajectory-wise or statistical assertion that the coarse-grained entropy $S(t)$ is non-decreasing can…

Entropy and information provide natural measures of correlation among elements in a network. We construct here the information theoretic analog of connected correlation functions: irreducible $N$--point correlation is measured by a decrease…

By using the Jacobi metric of the configuration space, and assuming ergodicity, we calculate the Boltzmann entropy $S$ of a finite-dimensional system around a non-degenerate critical point of its potential energy $V$. We compare $S$ with…

In ordinary statistical mechanics the Boltzmann-Shannon entropy is related to the Maxwell-Bolzmann distribution $p_i$ by means of a twofold link. The first link is differential and is offered by the Jaynes Maximum Entropy Principle. The…

The cornerstone of Boltzmann-Gibbs ($BG$) statistical mechanics is the Boltzmann-Gibbs-Jaynes-Shannon entropy $S_{BG} \equiv -k\int dx f(x)\ln f(x)$, where $k$ is a positive constant and $f(x)$ a probability density function. This theory…

Experimental and theoretical results about entropy limits for macroscopic and single-particle systems are reviewed. It is clarified when it is possible to speak about a quantum of entropy, given by the Boltzmann constant k, and about a…

In statistical mechanics entropy is a measure of disorder obeying Boltzmann's formula $S=\log{\cal N}$, where ${\cal N}$ is the accessible phase space volume. In black hole thermodynamics one associates to a black hole an entropy…

Entropy is a measure of self-information which is used to quantify losses. Entropy was developed in thermodynamics, but is also used to compare probabilities based on their deviating information content. Corresponding model uncertainty is…

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…

By explicit counterexample, we show that the "reflected entropy" defined by Dutta and Faulkner is not monotonically decreasing under partial trace, and so is not a measure of physical correlations. In fact, our counterexamples show that…

We examine the fundamental aspects of statistical mechanics, dividing the problem into a discussion purely about probability, which we analyse from a Bayesian standpoint. We argue that the existence of a unique maximising probability…

Statistical mechanics relies on the complete though probabilistic description of a system in terms of all the microscopic variables. Its object is to derive therefrom static and dynamic properties involving some reduced set of variables.…

We introduce a new measure of interdependence among the components of a random vector along the main diagonal of the vector copula, i.e. along the line $u_{1}=\ldots=u_{J}$, for $\left(u_{1},\ldots,u_{J}\right)\in\left[0,1\right]^{J}$. Our…

We define correlational (von Neumann) entropy for an individual quantum state of a system whose time-independent hamiltonian contains random parameters and is treated as a member of a statistical ensemble. This entropy is representation…

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…

We start with reviewing the origin of the idea that entropy and the Second Law are associated with the Arrow of Time. We then introduced a new definition of entropy based on Shannons Measure of Information, SMI. The SMI may be defined on…