Statistical Complexity and Two Van Der Waals’ Phase Transitions

We show that the van der Waals gas does not exhibit just the celebrated liquid-gas 1 transition but also a quantum-classical one. We study the issue with reference to the LMC statistical 2 complexity and in relation to the order-disorder contrast.

Complexity-like properties and parameter asymptotics of Lq-norms of Laguerre and Gegenbauer polynomials.

The main monotonic statistical complexity-like measures of the Rakhmanov’s probability density associated to the hypergeometric orthogonal polynomials (HOPs) in a real continuous variable, each of them quantifying two configurational facets of spreading, are examined in this work beyond the Cramér-Rao one. The Fisher-Shannon and LMC (López-Ruiz-Mancini-Calvet) complexity measures, which have two entropic components, are analytically expressed in terms of the degree and the orthogonality weight’s parameter(s) of the polynomials. The degree and parameter asymptotics of these two-fold spreading measures are shown for the parameter-dependent families of HOPs of Laguerre and Gegenbauer types. This is done by using the asymptotics of the Rényi and Shannon entropies, which are closely connected to the Lq-norms of these polynomials, when the weight function’s parameter tends towards infinity. The degree and parameter asymptotics of these Laguerre and Gegenbauer algebraic norms control the radial and angular charge and momentum distributions of numerous relevant multidimensional physical systems with a spherically-symmetric quantum-mechanical potential in the high-energy (Rydberg) and high-dimensional (quasi-classical) states, respectively. This is because the corresponding states’ wavefunctions are expressed by means of the Laguerre and Gegenbauer polynomials in both position and momentum spaces.

Entropy and complexity unveil the landscape of memes evolution

On the Internet, information circulates fast and widely, and the form of content adapts to comply with users’ cognitive abilities. Memes are an emerging aspect of the internet system of signification, and their visual schemes evolve by adapting to a heterogeneous context. A fundamental question is whether they present culturally and temporally transcendent characteristics in their organizing principles. In this work, we study the evolution of 2 million visual memes published on Reddit over ten years, from 2011 to 2020, in terms of their statistical complexity and entropy. A combination of a deep neural network and a clustering algorithm is used to group memes according to the underlying templates. The grouping of memes is the cornerstone to trace the growth curve of these objects. We observe an exponential growth of the number of new created templates with a doubling time of approximately 6 months, and find that long-lasting templates are associated with strong early adoption. Notably, the creation of new memes is accompanied with an increased visual complexity of memes content, in a continuous effort to represent social trends and attitudes, that parallels a trend observed also in painting art.

Statistical odd-even staggering in few fermions systems

The odd-even staggering (OES) in nuclear binding energies is a well-known fact. A rather similar effect can be found in other finite fermion systems. For instance, ultra small metallic grains and metal clusters. The staggering in nuclei and grains is attributed primarily to pairing correlations. In clusters, it is originated by the Jahn–Teller effect [Phys. Rev. Lett. 81, 3599 (1998)]. Here, we work with a simple, Lipkin-like, exactly solvable two-level fermion model. A statistical mechanics’ treatment of it shows that OES effects also emerge here, as revealed by theoretical tools connected with the so-called statistical complexity.

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.