The fermionic Rényi entanglement entropy is studied for causal diamonds in two-dimensional Minkowski space. Choosing the quasi-free state describing the Minkowski vacuum with an ultraviolet regularization, a logarithmically enhanced area law is derived.

This paper is devoted to characterize a generalized [Formula: see text]-tensor. In the second part of this paper, we describe the behavior of the associated vector field of a generalized [Formula: see text]-flat spacetime in some special cases. It has been investigated that such a spacetime turns into special spacetimes when the associated scalars have different structures. In the third part, generalized [Formula: see text]-flat spacetime in [Formula: see text]-gravity is examined.

The aim of this paper is to study geometrical aspects of the almost conformal Ricci solitons on weakly Ricci symmetric perfect fluid spacetime obeying Einstein field equations. Among others, we first find the soliton constant and cosmological constant in weakly Ricci symmetric spacetime. Further, we find in weakly Ricci symmetric spacetime, the symmetry inheritance property of energy–momentum tensor and establish a relation between conformal and isotropic pressure for an almost conformal Ricci soliton. Next, we explain the equation of state for weakly Ricci symmetric spacetime, and we find the phase of universe for such spacetime under matter collineation condition and when there is dust matter, radiation era and dark matter of fluid is obtained with potential vector field as torse forming vector field. Also, we calculate the weakly Ricci symmetric spacetime admitting an almost conformal Ricci soliton is acceleration-free, vorticity free, shear-free when the potential vector field is torse forming vector field and we obtain some results for conformally flat weakly Ricci symmetric spacetime admitting an almost conformal Ricci soliton. Finally, the study of space-matter tensor and Einstein tensor on weakly Ricci symmetric spacetime admitting an almost conformal Ricci soliton with potential vector field as torse forming vector field is made.

In this study, we examine the quantization of Hall conductance in an infinite plane geometry. We consider a microscopic charge-conserving system with a pure, gapped infinite-volume ground state. While Hall conductance is well-defined in this scenario, existing proofs of its quantization have relied on assumptions of either weak interactions, or properties of finite volume ground state spaces, or invertibility. Here, we assume that the conditions necessary to construct the braided [Formula: see text]-tensor category which describes anyonic excitations are satisfied, and we demonstrate that the Hall conductance is rational if the tensor category is finite.

In this paper, we give a complete classification of Hopf ∗-[Formula: see text]-Ricci–Yamabe soliton on real hypersurfaces in the complex projective space [Formula: see text]. As an application, first we give a complete classification of gradient ∗-[Formula: see text]-Ricci–Yamabe solitons on real hypersurfaces with isometric Reeb flow in the complex projective space [Formula: see text]. Next, we prove that a contact real hypersurface in [Formula: see text] which admits a gradient ∗-[Formula: see text]-Ricci–Yamabe soliton is pseudo-Einstein.

The reconstruction of stochastic evolution equations from time-series data in terms of the Langevin equation and the corresponding Fokker–Planck equation is often challenged by the inevitably finite temporal sampling of time-series data. With the aim of improving the reconstruction of stochastic evolution equations from empirical time-series data, one can use a finite sampling [Formula: see text] expansion of the Kramers–Moyal (KM) conditional moments. Depending on the number of terms used from such expansion one obtains different orders of approximation of the KM coefficients. In this paper, we derive and employ the second-order approximation [Formula: see text] of the KM conditional moments for the Langevin dynamics and demonstrate that its use leads to the modification of the diffusion coefficient. To demonstrate the substantial potential for practical applications, we utilize data-driven techniques to estimate fluctuations in synthetic time series generated from both linear and nonlinear diffusive processes. Furthermore, we show that when Langevin dynamics is specifically used to model asset prices (here gold price), the use of the second-order approximation of the KM coefficients leads to more accurate prices simulation and prediction that have not been observed in similar work by others.

Let [Formula: see text] be states of a general probability theory, and [Formula: see text] be the set of all subsets of indices [Formula: see text] such that the states [Formula: see text] are jointly (perfectly) distinguishable. All subsets with a single element are of course in [Formula: see text], and since smaller collections are easier to distinguish, if [Formula: see text] and [Formula: see text] then [Formula: see text]; in other words, [Formula: see text] is a so-called independence system on the set of indices [Formula: see text]. In this paper, it is shown that every independence system on [Formula: see text] can be realized in the above manner.

In this work, perfect fluid spacetimes obeying Gray’s decompositions have been studied. In the first part, after a brief summary about Gray’s decompositions used in this study, we work on properties of perfect fluid spacetimes obeying these decompositions. The results are obtained for different subspaces of a perfect fluid spacetime. Thereafter, we present the characterizations of these spacetimes by proving some theorems.

Feynman proposed a postulate or a method of quantization in his celebrated paper in 1948. Applying Feynman’s postulate to temporally continuous quantum measurements of the positions of particles, Mensky proposed the restricted Feynman path integrals (RFPIs) for continuous quantum measurements after phenomenological considerations. Our aim in this paper is to give a rigorous proof that Mensky’s RFPIs emerge out of Feynman’s postulate under a simple approximation. In addition, it is proved that the RFPIs emerge out of von Neumann’s postulate on instantaneous measurements as well as Feynman’s postulate. The quantum systems that we study include spin systems. These results are applied to formulations of the multi-split experiments, the quantum Zeno and the Aharonov–Bohm effects.

It is well known that [Formula: see text]-contact geometry is a suitable framework to deal with non-conservative field theories. In this paper, we study some relations between solutions of the [Formula: see text]-contact Euler–Lagrange equations, symmetries, dissipation laws and Newtonoid vector fields. We review the [Formula: see text]-contact Euler–Lagrange equations written in terms of [Formula: see text]-vector fields and sections and provide new results relating the solutions in both approaches. We also study different kinds of symmetries depending on the structures they preserve: natural (preserving the Lagrangian function), dynamical (preserving the solutions), and [Formula: see text]-contact (preserving the underlying geometric structures) symmetries. For some of these symmetries, we provide Noether-like theorems relating symmetries and dissipation laws. We also analyze the relation between [Formula: see text]-contact symmetries and Newtonoid vector fields. Throughout the paper, we will use the damped vibrating string as our main illustrative example.