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.

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.