Narrow Results

This research paper aims to redefine the complexity factor in $f(R,G)$ gravity and the appearance of electric charge, where $R$ is the Ricci scalar and $G$ is the Gauss–Bonnet term. In this context, we intend to analyze the splitting of the Riemann tensor after considering the anisotropic distribution of the charged fluid related to the spherically symmetric spacetime. We interpret $Y_{\mathrm{\text{TF}}}$ as the complexity factor among all the determined structural scalars that encompasses the characteristics of anisotropic pressure and the effective representation of the energy density. The correction terms associated with modified theory are considered to calculate some significant results related to the Weyl scalar, Tolman mass, and the complexity factor (CF). Moreover, the expression for CF is established by using the structure scalars determined in our paper, and the diminishing complexity restraint is utilized to determine the solutions for the various models. The celestial object having non-uniform energy density and anisotropic pressure asserts the maximum intricacy. But, if the effects of non-uniform energy density and anisotropic distribution of pressure are eradicated due to the presence of dark source terms associated with modified gravity then these fluids may not exhibit any complexity. Consequently, it is revealed that the constituents of effective and electromagnetic parts directly influence the structure scalars and CF.

We investigate the effect of different metrizations of probability spaces on the information geometric complexity of entropic motion on curved statistical manifolds. Specifically, we provide a comparative analysis based upon Riemannian geometric properties and entropic dynamical features of a Gaussian probability space where the two distinct dissimilarity measures between probability distributions are the Fisher–Rao information metric and the $\alpha$-order entropy metric. In the former case, we observe an asymptotic linear temporal growth of the information geometric entropy (IGE) together with a fast convergence to the final state of the system. In the latter case, instead, we note an asymptotic logarithmic temporal growth of the IGE together with a slow convergence to the final state of the system. Finally, motivated by our findings, we provide some insights on a tradeoff between complexity and speed of convergence to the final state in our information geometric approach to problems of entropic inference.

In an attempt to find the dynamical foundations for $q$-entropies, we examine the special case of Lagrangian/Hamiltonian systems of many degrees of freedom whose statistical behavior is conjecturally described by the $q$-entropic functionals. We follow the spirit of the canonical ensemble approach. We consider the system under study as embedded in a far larger total system. We explore some of the consequences that such an embedding has, if it is modeled by a Riemannian submersion. We point out the significance in such a description of the finite-dimensional Bakry–Émery Ricci tensor, as a local mesoscopic invariant, for understanding the collective dynamical behavior of systems described by the $q$-entropies.