Fisher and Shannon Functionals for Hyperbolic Diffusion.

The complexity measure for the distribution in space-time of a finite-velocity diffusion process is calculated. Numerical results are presented for the calculation of Fisher's information, Shannon's entropy, and the Cramér-Rao inequality, all of which are associated with a positively normalized solution to the telegrapher's equation. In the framework of hyperbolic diffusion, the non-local Fisher's information with the x-parameter is related to the local Fisher's information with the t-parameter. A perturbation theory is presented to calculate Shannon's entropy of the telegrapher's equation at long times, as well as a toy model to describe the system as an attenuated wave in the ballistic regime (short times).

Rényi's Entropy, Statistical Order and van der Waals Gas.

The notion of statistical order derives from the disequilibrium concept introduced by López-Ruiz, Mancini, and Calbet thirty years ago. In this effort, it is shown that the disequilibrium is intimately linked to the celebrated Rényi entropy. One also explores this link in connection with the van der Waals gas description.

Energetic Cost of Statistical Order-Degree Change in a Fermions' Set.

We discuss novel many-fermions thermodynamics' features. They refer to the energy cost associated to order-disorder changes. Our thermal quantum statistical scenario is controlled by suitable fermion-fermion interactions. We deal with two well-known quantum interactions that operate within an exactly solvable model. This model is able to adequately describe some aspects of fermion-dynamics, particularly level-crossings. We describe things via employment of Gibbs' canonical ensemble strictures. We show that judicious manipulation of the energy cost associated to statistical order (disorder) variations generates useful information-quantifiers. The underlying idea is that changes in the degree of order are intimately linked to level-crossings energetic costs.

The Classical-Quantum Passage: A van der Waals Description.

We undertake a van der Waals inquiry at very low temperatures so as to find signs of a classical-quantum frontier. We investigate the relation of such signs with the celebrated van der Waals gas-liquid transition. We specialize the discussion with respect to the noble gases. For such purpose, we use rather novel thermal statistical quantifiers such as the disequilibrium, the statistical complexity, and the thermal efficiency. Fruitful insights are thereby gained.

Thermal-Statistical Odd-Even Fermions' Staggering Effect and the Order-Disorder Disjunction.

We review thermal-statistical considerations on the odd-even staggering effect (OES) in fermions. There is a well known OES in nuclear binding energies at zero temperature. We discuss here a thermal OES (finite temperatures) that establishes links with the order-disorder disjunction. The present thermal considerations cannot be found in the nuclear literature.

Structural Statistical Quantifiers and Thermal Features of Quantum Systems.

This paper deals primarily with relatively novel thermal quantifiers called disequilibrium and statistical complexity, whose role is growing in different disciplines of physics and other sciences. These quantifiers are called L. Ruiz, Mancini, and Calvet (LMC) quantifiers, following the initials of the three authors who advanced them. We wish to establish information-theoretical bridges between LMC structural quantifiers and (1) Thermal Heisenberg uncertainties ΔxΔp (at temperature T); (2) A nuclear physics fermion model. Having achieved such purposes, we determine to what an extent our bridges can be extended to both the semi-classical and classical realms. In addition, we find a strict bound relating a special LMC structural quantifier to quantum uncertainties.

Useful Dual Functional of Entropic Information Measures.

There are entropic functionals galore, but not simple objective measures to distinguish between them. We remedy this situation here by appeal to Born's proposal, of almost a hundred years ago, that the square modulus of any wave function | ψ | 2 be regarded as a probability distribution P. the usefulness of using information measures like Shannon's in this pure-state context has been highlighted in [Phys. Lett. A1993, 181, 446]. Here we will apply the notion with the purpose of generating a dual functional [ F α R : { S Q } ⟶ R + ], which maps entropic functionals onto positive real numbers. In such an endeavor, we use as standard ingredients the coherent states of the harmonic oscillator (CHO), which are unique in the sense of possessing minimum uncertainty. This use is greatly facilitated by the fact that the CHO can be given analytic, compact closed form as shown in [Rev. Mex. Fis. E 2019, 65, 191]. Rewarding insights are to be obtained regarding the comparison between several standard entropic measures.

Statistical Complexity of the Coriolis Antipairing Effect.

Using the entropic quantifier called statistical complexity, we investigate the interplay between (1) pairing interactions between fermions, can be viewed as analogous with superconductivity based on Cooper pairs; (2) rotations of the system as a whole around an axis; and (3) thermal excitations. Two different ordering processes are at work: alignment and pairing of two fermions to total spin zero. They compete among themselves and with thermal disorder. A complex physics ensues as a consequence. The existence of novel phenomena is revealed by the behavior of the statistical complexity. In particular, it is seen how order can arise out of disorder in originating high-temperature superconductivity.

A Review of the Classical Canonical Ensemble Treatment of Newton's Gravitation.

It is common lore that the canonical gravitational partition function Z associated with the classical Boltzmann-Gibbs (BG) exponential distribution cannot be built up because of mathematical pitfalls. The integral needed for writing up Z diverges. We review here how to avoid this pitfall and obtain a (classical) statistical mechanics of Newton's gravitation. This is done using (1) the analytical extension treatment obtained of Gradshteyn and Rizhik and (2) the well known dimensional regularization technique.