Information Theoretical Analysis of Quantum Mixedness in a Finite Model of Interacting Fermions.

In this study, we utilize information theory tools to investigate notable features of the quantum degree of mixedness (Cf) in a finite model of interacting fermions. This model serves as a simplified proxy for an atomic nucleus, capturing its essential features in a more manageable form compared to a realistic nuclear model, which would require the diagonalization of matrices with millions of elements, making the extraction of qualitative features a significant challenge. Specifically, we aim to correlate Cf with particle number fluctuations and temperature, using the paradigmatic Lipkin model.

Brief Review on the Connection between the Micro-Canonical Ensemble and the -Canonical Probability Distribution.

Non-standard thermostatistical formalisms derived from generalizations of the Boltzmann-Gibbs entropy have attracted considerable attention recently. Among the various proposals, the one that has been most intensively studied, and most successfully applied to concrete problems in physics and other areas, is the one associated with the Sq non-additive entropies. The Sq-based thermostatistics exhibits a number of peculiar features that distinguish it from other generalizations of the Boltzmann-Gibbs theory.

Entropy Optimization, Generalized Logarithms, and Duality Relations.

Several generalizations or extensions of the Boltzmann-Gibbs thermostatistics, based on non-standard entropies, have been the focus of considerable research activity in recent years. Among these, the power-law, non-additive entropies Sq≡k1-∑ipiqq-1(q∈R;S1=SBG≡-k∑ipilnpi) have harvested the largest number of successful applications. The specific structural features of the Sq thermostatistics, therefore, are worthy of close scrutiny.

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.

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.

Information-Theoretic Features of Many Fermion Systems: An Exploration Based on Exactly Solvable Models.

Finite quantum many fermion systems are essential for our current understanding of Nature. They are at the core of molecular, atomic, and nuclear physics. In recent years, the application of information and complexity measures to the study of diverse types of many-fermion systems has opened a line of research that elucidates new aspects of the structure and behavior of this class of physical systems.

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.

Nonlinear Fokker-Planck Equation Approach to Systems of Interacting Particles: Thermostatistical Features Related to the Range of the Interactions.

Nonlinear Fokker-Planck equations (NLFPEs) constitute useful effective descriptions of some interacting many-body systems. Important instances of these nonlinear evolution equations are closely related to the thermostatistics based on the S q power-law entropic functionals. Most applications of the connection between the NLFPE and the S q entropies have focused on systems interacting through short-range forces.

Entropic Characterization of Quantum States with Maximal Evolution under Given Energy Constraints.

A measure D [ t 1 , t 2 ] for the amount of dynamical evolution exhibited by a quantum system during a time interval [ t 1 , t 2 ] is defined in terms of how distinguishable from each other are, on average, the states of the system at different times. We investigate some properties of the measure D showing that, for increasing values of the interval's duration, the measure quickly reaches an asymptotic value given by the linear entropy of the energy distribution associated with the system's (pure) quantum state. This leads to the formulation of an entropic variational problem characterizing the quantum states that exhibit the largest amount of dynamical evolution under energy constraints given by the expectation value of the energy.

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.

Logical Structures Underlying Quantum Computing.

In this work we advance a generalization of quantum computational logics capable of dealing with some important examples of quantum algorithms. We outline an algebraic axiomatization of these structures.

Associating an Entropy with Power-Law Frequency of Events.

Events occurring with a frequency described by power laws, within a certain range of validity, are very common in natural systems. In many of them, it is possible to associate an energy spectrum and one can show that these types of phenomena are intimately related to Tsallis entropy S q . The relevant parameters become: (i) The entropic index , which is directly related to the power of the corresponding distribution; (ii) The ground-state energy ε 0 , in terms of which all energies are rescaled.

Revisiting Entanglement within the Bohmian Approach to Quantum Mechanics.

We revisit the concept of entanglement within the Bohmian approach to quantum mechanics. Inspired by Bohmian dynamics, we introduce two partial measures for the amount of entanglement corresponding to a pure state of a pair of quantum particles. One of these measures is associated with the statistical correlations exhibited by the joint probability density of the two Bohmian particles in configuration space.

Positive operator valued measures and the quantum Monty Hall problem.

A quantum version of the Monty Hall problem, based upon the Positive Operator Valued Measures (POVM) formalism, is proposed. It is shown that basic normalization and symmetry arguments lead univocally to the associated POVM elements, and that the classical probabilities associated with the Monty Hall scenario are recovered for a natural choice of the measurement operators.