The appearance of the spin-$\frac{1}{2}$ and spin-1 representations in the Frieden-Soffer extreme physical information (EPI) statistical approach to the Einstein-Podolsky-Rosen-Bohm (EPR-Bohm) experiment is shown. In order to obtain the EPR-Bohm result, in addition to the observed structural and variational information principles of the EPI method, the condition of the regularity of the probability distribution is used. The observed structural information principle is obtained from the analyticity of the logarithm of the likelihood function. It is suggested that, due to the self-consistent analysis of both information principles, quantum mechanics is covered by the statistical information theory. The estimation of the angle between the analyzers in the EPR-Bohm experiment is discussed. DOI: http://dx.doi.org/10.1103/PhysRevE.88.032130 ©2013 American Physical Society

The symmetry energy is an invaluable tool for studying dense nuclear matter. Unfortunately, its definition is somewhat implicit, and therefore, phenomenological methods are necessary to describe experimental facts. This paper discusses the differences arising from the use of Taylor series expansion and Padé approximation to determine theoretically the symmetry energy and the possible consequences for neutron stars. For this purpose, a form of the nuclear matter equation of state that explicitly depends on the symmetry energy is used. The obtained results point out that the applied approximations lead to modifications of the equilibrium proton fractions and equation of state, especially in their high-density limit. However, this effect is small near the saturation density $n_0$ .

The paper examines the geometrical properties of a six-dimensional Kaluza-Klein type model. They may have an impact on the model of the structure of a neutron and its excited states in the realm of particle physics. The statistical reason for the six-dimensionality and the stability of the solution is given. The derivation of the weak limit approximation of the general wave mechanical (quantum mechanical) approach, defined in the context of losing its self-consistency (here gravitational), is presented. The non self-consistent case for the Klein-Gordon equation is defined. The derivation of the energy of states and the analysis of the spin origin of the analyzed fields configuration is presented as the manifestation of both the geometry of the internal sample two-dimensional parametric space and kinematics of fields inside it. The problem of the departure from the (gravitational) self-consistent calculations of the metric tensor and of other fields of the configuration is discussed. The implementation of the model for the description of a neutron and its excited states, including their spins and energies, is given. The informational reason for the existence of the internal extra parametric space dimensions is proposed.

There are generally two factors on which the form of the symmetry energy depends. The first one is the model involved in determining the nuclear matter equation of state, and the second the accuracy of the approximation of the symmetry energy function given by a Taylor series. Including the fourth-order term in the Taylor series accounts for a more reasonable representation of the symmetry energy. This paper focuses on understanding the symmetry energy influence on the neutron star crust-core phase boundary characteristics in terms of the above factors. All calculations were based on selected models of the relativistic mean field theory. The analysis begins with determining the analytical form of the fourth-order symmetry energy. The applied method allows for deriving the potential part of the fourth-order symmetry energy when the model contains various nonlinear couplings between mesons. The presence of the fourth-order term in the symmetry energy description affects the neutron star crust-core phase boundary characteristics by changing the transition density $n_t$, the corresponding pressure $P_t$, and the equilibrium proton fraction $Y_p^{\mathrm{eq}}\left(n_t\right)$ value. The performed statistical analysis clarifies the role of the second- and fourth-order symmetry energy in determining the relationships between the transition density $n_t$ and the leading coefficients characterizing the density dependence of the symmetry energy $[E_{\mathrm{sym}}\left(n_0\right),$ $L_{\mathrm{sym}},$ $K_{\mathrm{sym}}]$, where $L_{\mathrm{sym}}$ is the slope and $K_{\mathrm{sym}}$ is the curvature. It is shown that the regression analysis makes it possible to identify $(P_t,L_{\mathrm{sym}},K_{\mathrm{sym}})$ as the group of factors that significantly influence the variability of the transition density $n_t$. The results also allow for estimating the effect of the fourth-order symmetry energy term inclusion. Additionally, the correlation analysis points to the individual role of $L_{\mathrm{sym}}$ and $K_{\mathrm{sym}}$. Only when the fourth-order term is included are both variables $K_{\mathrm{sym}}$ and $L_{\mathrm{sym}}$ equally anticorrelated with $n_t$, leading to the increasing role of $L_{\mathrm{sym}}$ in analyzing the variability of $n_t$.