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.

Magic Numbers and Mixing Degree in Many-Fermion Systems.

We consider an fermion system at low temperature in which we encounter special particle number values Nm exhibiting special traits. These values arise when focusing attention upon the degree of mixture (DM) of the pertinent quantum states. Given the coupling constant of the Hamiltonian, the DMs stay constant for all -values but experience sudden jumps at the Nm.

Quantum Purity as an Information Measure and Nernst Law.

We propose to re-express Nernst law in terms of a suitable information measure (IM) parameter. This is achieved by dwelling on the idea of adapting the notion of purity in the case of a thermal Gibbs environment, yielding what we might call the "purity" indicator (which we denote by the symbol in the text). We find it interesting to define an extension of this D-IM indicator in a classical context.

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.

Dynamical classic limit: Dissipative vs conservative systems.

We analyze the nonlinear dynamics of a quartic semiclassical system able to describe the interaction of matter with a field. We do it in both dissipative and conservative scenarios. In particular, we study the classical limit of both frameworks and compare the associated features.