A simple link of information entropy of quantum and classical systems with Newtonian r−2r^{-2} dependence of Verlinde's entropic force

It is shown that the entropic force formula $F_e=-\lambda\partial S/\partial A$ leads to a Newtonian $r^{-2}$ dependence. Here we employ the universal property of the information entropy $S=a+b\ln N$ ($N$ is the number of particles of a quantum system and $A$ is the area containing the system). This property was previously obtained for fermionic systems (atoms, atomic clusters, nuclei and infinite Fermi systems i.e. electron gas, liquid $^3$He and nuclear matter) and bosonic ones (correlated boson-atoms in a trap). A similar dependence of the entropic force has been derived very recently by Plastino et al with a Bose or Fermi gas entropy, inspired by Verlinde's conjecture~\cite{Verlide-11} that gravity is an emergent entropic force. Finally, we point out that our simple argument holds for classical systems as well.Comment: 8pages, Closely matches the published version in Physica A ( 5 pages, 24 references). Our argument for quantum systems is extended for classical systems as well. Also a slight change has been made accordingly to the titl

Constraints on the equation of state from the stability condition of neutron stars

The stellar equilibrium and collapse, including mainly white dwarfs, neutron stars and supper massive stars, is an interplay between general relativistic effects and the equation of state of nuclear matter. In the present work, we use the Chandrasekhar criterion of stellar instability by employing a large number of realistic equations of state (EoS) of neutron star matter. We mainly focus on the critical point of transition from stable to unstable configuration. This point corresponds to the maximum neutron star mass configuration. We calculate, in each case, the resulting compactness parameter, $\beta=GM/c^2R$, and the corresponding effective adiabatic index, $\gamma_{\rm cr}$. The role of the trial function $\xi(r)$ is presented and discussed in details. We found that it holds a model-independent relation between $\gamma_{\rm cr}$ and $\beta$. This statement is strongly supported by the large number of EoS and it is also corroborated by using analytical solutions of the Einstein's field equations. In addition, we present and discuss the relation between the maximum rotation rate and the adiabatic index close to the instability limit. Accurate observational measurements of the upper bound of the neutron star mass and the corresponding radius, in connection with the present predictions, may help to impose constraints on the high density part of the neutron star equation of state.Comment: 15 pages, 1 table, 12 figure

Information and complexity measures in the interface of a metal and a superconductor

Fisher information, Shannon information entropy and Statistical Complexity are calculated for the interface of a normal metal and a superconductor, as a function of the temperature for several materials. The order parameter $\Psi({\bf r})$ derived from the Ginzburg-Landau theory is used as an input together with experimental values of critical transition temperature $T_c$ and the superconducting coherence length $\xi_0$. Analytical expressions are obtained for information and complexity measures. Thus $T_c$ is directly related in a simple way with disorder and complexity. An analytical relation is found of the Fisher Information with the energy profile of superconductivity i.e. the ratio of surface free energy and the bulk free energy. We verify that a simple relation holds between Shannon and Fisher information i.e. a decomposition of a global information quantity (Shannon) in terms of two local ones (Fisher information), previously derived and verified for atoms and molecules by Liu et al. Finally, we find analytical expressions for generalized information measures like the Tsallis entropy and Fisher information. We conclude that the proper value of the non-extensivity parameter $q\simeq 1$, in agreement with previous work using a different model, where $q\simeq 1.005$.Comment: 15 pages, 12 figures, 3 table

Natural orbitals representation and Fermi sea depletion in finite nuclei and nuclear matter

The natural orbitals and natural occupation numbers of various N = Z, sp and sd shell nuclei are calculated by applying a correlated one-body density matrix. The correlated density matrix has been evaluated by considering central correlations of Jastrow type and an approximation named factor cluster expansion. The correlation effects on the natural orbitals, natural occupation numbers and the Fermi sea depletion are discussed and analysed. In addition, an approximate expression for the correlated one-body density matrix of the nuclear matter has been used for the evaluation of the relative momentum distribution and the Fermi sea depletion. We found that the value of the Fermi sea depletion is higher in closed shell nuclei compared to open shell ones and it is lower compared to the case of nuclear matter. This statement could be confirmed by relevant experimental studies.Comment: 20 pages, 3 figures, 2 table

Effects of the equation of state on the bulk properties of maximally-rotating neutron stars

Neutron stars are among the densest known objects in the universe and an ideal laboratory for the strange physics of super-condensed matter. While the simultaneously measurements of mass and radius of non-rotating neutron stars may impose constraints on the properties of the dense nuclear matter, the observation and study of maximally-rotating ones, close to the mass-shedding limit, may lead to significantly further constraints. Theoretical predictions allow neutron stars to rotate extremely fast (even more than $2000 \ {\rm Hz}$). However, until this moment, the fastest observed rotating pulsar has a frequency of $716 \ {\rm Hz}$, much lower compared to the theoretical predictions. There are many suggestions for the mechanism which lead to this situation. In any case, the theoretical study of uniformly rotating neutron stars, along with the accurate measurements, may offer rich information concerning the high density part of the equation of state. In addition, neutron stars through their evolution, may provide us with a criteria to determine the final fate of a rotating compact star. Sensitivity of bulk neutron stars properties on the equation of state at the mass-shedding limit are the main subject of the present study.Comment: v1: 16 pages, 24 figures. v2: 18 pages, 14 labeled figures, 5 tables, sections and references had been updated, accepted for publication in Phys. Rev.

Fisher Information and Atomic Structure

We present a comparative study of several information and statistical complexity measures in order to examine a possible correlation with certain experimental properties of atomic structure. Comparisons are also carried out quantitatively using Pearson correlation coefficient. In particular, we show that Fisher information in momentum space is very sensitive to shell effects, and is directly associated with some of the most characteristic atomic properties, such as atomic radius, ionization energy, electronegativity, and atomic dipole polarizability. Finally we present a relation that emerges between Fisher information and the second moment of the probability distribution in momentum space i.e. an energy functional of interest in (e,2e) experiments.Comment: 8 pages, 5 figures; Corrected typo

Thermodynamical description of hot rapidly rotating neutron stars and neutron stars merger remnant

The prediction of the equation of state of hot dense nuclear matter is one of the most complicated and interesting problems in Nuclear Astrophysics. At the same time, its knowledge is the basic ingredient for some of the most interesting studies. In the present work we concentrate our study on the construction of the equation of state of hot dense nuclear matter, related mainly to the interior of the neutron star core. We employ a theoretical nuclear model, which includes momentum dependent interaction among the nucleons, along with the \textit{state-of-the-art} microscopic calculations. Thermal effects are introduced in a self-consistent way and a set of isothermal equations of state are predicted. The predicted equations of state are used in order to acquire and to extend the knowledge of thermal effect both on non-rotating and rapidly rotating with the Kepler frequency neutron stars. The simultaneously study of thermal and rotation effect provide useful information for some of the most important quantities, including the mass (gravitational and baryon) and radius, the Kepler frequency and kerr parameter, the moment of inertia etc. These quantities are directly related to studies of proto-neutron stars and mainly the hot and rapidly rotating remnant of a binary neutron stars merger. Data from the late observations of binary neutron stars mergers and the present study may offer useful tools for their investigation and help in providing possible constraints on the equation of state of nuclear matter.Comment: 24 pages, 17 figures, 5 table

Quantum Tunneling and Information Entropy in a Double Square Well Potential: Ammonia Molecule

Quantum tunneling is the quantum-mechanical effect where a particle tunnels through a classically forbidden region. Double Square Well Potential (DSWP) is a system where this phenomenon is feasible. Numerous phenomena can be illustrated by considering motion in a pair of wells that are separated by a barrier of finite height and width. The energy level splitting, resulting from barrier penetration, is the reason of the so-called inversion spectrum, which is an example of quantum tunneling. Out of several molecules ($NH_3$, $PH_3$, $AsH_3$, $NH_2CN$) where this inversion phenomenon occurs, ammonia molecule $NH_3$ provides a nice physical realization of a vibrational system with a DSWP. The main goal of the present work is to examine the implications of quantum tunneling on information entropy measures (Shannon's and Fisher's) and statistical complexity.Comment: 16 pages, 15 figures, 2 table

Statistical measure of complexity of hard-sphere gas: applications to nuclear matter

We apply the statistical measure of complexity, introduced by L\'{o}pez-Ruiz, Mancini and Calbet to a hard-sphere dilute Fermi gas whose particles interact via a repulsive hard-core potential. We employ the momentum distribution of this system to calculate the information entropy, the disequilibrium and the statistical complexity. We examine possible connections between the particle correlations and energy of the system with those information and complexity measures. The hard-sphere model serves as a test bed for concepts about complexity.Comment: 10 pages, 9 figure

Applications of density matrices in a trapped Bose gas

An overview of the Bose-Einstein condensation of correlated atoms in a trap is presented by examining the effect of interparticle correlations to one- and two-body properties of the above systems at zero temperature in the framework of the lowest order cluster expansion. Analytical expressions for the one- and two-body properties of the Bose gas are derived using Jastrow-type correlation function. In addition numerical calculations of the natural orbitals and natural occupation numbers are also carried out. Special effort is devoted for the calculation of various quantum information properties including Shannon entropy, Onicescu informational energy, Kullback-Leibler relative entropy and the recently proposed Jensen-Shannon divergence entropy. The above quantities are calculated for the trapped Bose gases by comparing the correlated and uncorrelated cases as a function of the strength of the short-range correlations. The Gross-Piatevskii equation is solved giving the density distributions in position and momentum space, which are employed to calculate quantum information properties of the Bose gas.Comment: 40 pages, 14 figures, 2 Table