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 D in the text). We find it interesting to define an extension of this D-IM indicator in a classical context. This generalization turns out to have useful conceptual consequences when used in conjunction with the classical Shannon entropy S. Implications for the Nernst law are discussed.

Complexity and disequilibrium in the dipole-type Hamiltonian mean-field model.

This research studies information properties, such as complexity and disequilibrium, in the dipole-type Hamiltonian mean-field model. A fundamental analytical assessment is the partition function in the canonical ensemble to derive statistical, thermodynamical, and information measures. They are also analytical, dependent on the number of particles, consistent with the theory for high temperatures, and rising some limitations at shallow temperatures, giving us a notion of the classicality of the system defining an interval of temperatures where the model is well working.

Reply to "Comment on 'Troublesome aspects of the Renyi-MaxEnt treatment' ".

This Reply is intended as a refutation of the preceding Comment [Oikonomou and Bagci, Phys. Rev. E 96, 056101 (2017)10.1103/PhysRevE.96.056101] on our paper [Plastino et al., Phys. Rev. E 94, 012145 (2016).1539-375510.1103/PhysRevE.94.012145]. We show that the Tsallis probability distribution of our paper does not coincide with the Tsallis distribution studied by Oikonomou and Bagci. Consequently, their findings do not apply to our paper.

Troublesome aspects of the Renyi-MaxEnt treatment.

We study in great detail the possible existence of a Renyi-associated thermodynamics, with negative results. In particular, we uncover a hidden relation in Renyi's variational problem (MaxEnt). This relation connects the two associated Lagrange multipliers (canonical ensemble) with the mean energy 〈U〉 and the Renyi parameter α. As a consequence of such relation, we obtain anomalous Renyi-MaxEnt thermodynamic results.

Temperature-driven nonclassical light.

With reference to two well known scenarios, we discuss, for nonclassical light, the competition between quantum and thermal effects. It is seen that for nonclassical light to be produced some amount of temperature-induced disorder is needed plus quantum fluctuations of order h squared.

Thermodynamics in a complete description of Landau diamagnetism.

In the present study we analyze some consequences that come from revised measures as the Wehrl entropy and the Fisher information for the problem of a particle in a magnetic field starting from a complete description of the Husimi function. We discuss in the most complete form (three dimensions) some results related to measures in contrast with the incomplete form (two dimensions) shown in previous contributions. Some limiting cases as high and low temperatures are discussed. From the present reasoning, it is suggested that the formulation in two dimensions is sufficient unto itself to explain the problem whenever the length of the cylindrical geometry of the system is large enough. Otherwise, it is not possible to work in all finite temperatures, a natural lower temperature bound emerges from the analysis when three dimensions are considered.

Reciprocity relations between ordinary temperature and the Frieden-Soffer Fisher temperature.

Frieden and Soffer conjectured some years ago [Phys. Rev. E 52, 2274 (1995)] the existence of a "Fisher temperature" T(F) that would play, with regards to Fisher's information measure I , the same role that the ordinary temperature T plays in relation to Shannon's logarithmic measure. Here we exhibit the existence of reciprocity relations between T(F) and T and provide an interpretation with reference to the meaning of T(F) for the canonical ensemble.

Heisenberg-Fisher thermal uncertainty measure.

We establish a connection among (i) the so-called Wehrl entropy, (ii) Fisher's information measure I(beta), and (iii) the canonical ensemble entropy for the one-dimensional quantum harmonic oscillator (HO). We show that the contribution of the excited HO spectrum to the mean thermal energy is given by I(beta), while the pertinent canonical partition function is essentially given by another Fisher measure: the so-called shift invariant one. Our findings should be of interest in view of the fact that it has been shown that the Legendre transform structure of thermodynamics can be replicated without any change if one replaces the Boltzmann-Gibbs-Shannon entropy by Fisher's information measure [Phys. Rev. E 60, 48 (1999)]]. Fisher-related uncertainty relations are also advanced, together with a Fisher version of thermodynamics' third law.

Naudts-like duality and the extreme fisher information principle

We show that using Frieden and Soffer's extreme information principle [Phys. Rev. E 52, 2274 (1995)] with a Fisher measure constructed with escort probabilities [C. Beck and F. Schlogel, Thermodynamics of Chaotic Systems (Cambridge University Press, Cambridge, England, 1993)], the concomitant solutions obey a type of Naudts's duality (e-print cond-mat/990470) for nonextensive ensembles [C. Tsallis, in Nonextensive Statistical Mechanics and its Applications, Lecture Notes in Physics, edited by S. Abe and Y. Okamoto (Springer-Verlag, Berlin, in press)].