相关论文: A note on Onicescu's informational energy and corr…

Informational entropy is often identified as physical entropy. This is surprising because the two quantities are differently defined and furthermore the former is a subjective quantity while the latter is an objective one. We describe the…

It is shown that the standard expression for the information entropy, originally due to Shannon, is only valid for a particular set of states. For the general case of statistical mechanics, one needs to include an additional term in the…

A curious behavior of electron correlation energy is explored. Namely, the correlation energy is the energy that tends to drive the system toward that of the uniform electron gas. As such, the energy assumes its maximum value when a…

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…

Thermodynamic entropy, as defined by Clausius, characterizes macroscopic observations of a system based on phenomenological quantities such as temperature and heat. In contrast, information-theoretic entropy, introduced by Shannon, is a…

Information based uncertainty measures like R{\'e}nyi entropy (R), Shannon entropy (S) and Onicescu energy (E) (in both position and momentum space) are employed to understand the influence of radial confinement in isotropic harmonic…

The information causality principle is a generalisation of the no-signalling principle which implies some of the known restrictions on quantum correlations. But despite its clear physical motivation, information causality is formulated in…

We study a dynamical system with time dependent Hamiltonian by numerical experiments so as to find a relation between thermodynamics and chaotic nature of the system. Excess information loss, defined newly based on Lyapunov analysis, is…

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…

Counting ad infinitum is the holographic observable to a statistical dynamics with finite states under independent repeated sampling. Entropy provides the infinitesimal probability for an observed frequency $\hat{\boldsymbol{\nu}}$ w.r.t. a…

The information entropies in coordinate and momentum spaces and their sum ($S_r$, $S_k$, $S$) are evaluated for many nuclei using "experimental" densities or/and momentum distributions. The results are compared with the harmonic oscillator…

Entropic uncertainty relations are interesting in their own rights as well as for a lot of applications. Keeping this in mind, we try to make the corresponding inequalities as tight as possible. The use of parametrized entropies also allows…

A message of any sort can be regarded as a source of information. Claude. E. Shannon showed in the last century that information ("what we don't already know") is equivalent to the entropy as defined in statistical mechanics. A string of…

We consider the entropy of sums of independent discrete random variables, in analogy with Shannon's Entropy Power Inequality, where equality holds for normals. In our case, infinite divisibility suggests that equality should hold for…

We identify new universal properties of the energy eigenstates of chaotic systems with local interactions, which distinguish them both from integrable systems and from non-local chaotic systems. We study the relation between the energy…

Uncertainty relations are central to quantum physics. While they were originally formulated in terms of variances, they have later been successfully expressed with entropies following the advent of Shannon information theory. Here, we…

The nature of neural codes is central to neuroscience. Do neurons encode information through relatively slow changes in the emission rates of individual spikes (rate code), or by the precise timing of every spike (temporal codes)? Here we…

We present a quantum information theory that allows for a consistent description of entanglement. It parallels classical (Shannon) information theory but is based entirely on density matrices (rather than probability distributions) for the…

Maximum entropy estimation is of broad interest for inferring properties of systems across many different disciplines. In this work, we significantly extend a technique we previously introduced for estimating the maximum entropy of a set of…

The exponential family of models is defined in a general setting, not relying on probability theory. Some results of information geometry are shown to remain valid. Exponential families both of classical and of quantum mechanical…