arXiv subjects

Zahra Ebadi

Publications and source records attributed to Zahra Ebadi.

14 recordsLinked to original sources

arXiv2026

Thermodynamic Geometry of an Ideal Quon Gas

We investigate the equilibrium thermodynamics and thermodynamic Riemannian geometry of an ideal quon gas within the grand canonical ensemble. By incorporating the algebraic deformation parameter $q$, the system generalizes standard bosonic behavior while recovering the conventional ideal Bose gas in the undeformed limit. A rigorous examination of the ground-state occupation reveals two disconnected mathematical domains of the fugacity. By enforcing thermodynamic continuity, single-valuedness, and consistency with the high-temperature classical limit, we exclude the second mathematical branch and establish the lower interval as the unique physically admissible state space. This identifies the deformation parameter as an intrinsic, generalized Bose--Einstein condensation threshold. Employing the Fisher-Rao metric on the equilibrium parameter manifold, we probe the thermodynamic scalar curvature across all temperature regimes. The scalar curvature remains strictly positive throughout the physical domain, confirming that the deformation preserves an effectively attractive statistical interaction without inducing fermionic tendencies. Near the critical condensation threshold, the curvature increases sharply and exhibits a definitive divergence, providing an unambiguous geometric signature of macroscopic coherence and critical fluctuations. Below the transition temperature, the pinning of fugacity eliminates a fluctuating degree of freedom, collapsing the scalar curvature to zero.

cond-mat.stat-mech↗

arXiv2026

Thermodynamic geometry of inclusion statistics

We investigate the thermodynamic geometry of an ideal quantum gas obeying inclusion statistics, characterized by a negative statistical parameter $g < 0$. In this framework the grand-canonical partition function admits a finite maximum fugacity, and the thermodynamic scalar curvature $R$ is strictly positive for all $g < 0$, reflecting effective attractive statistical interactions analogous to those of a bosonic system. As the fugacity approaches its maximum value, $R$ diverges, signaling a phase transition of the Bose-Einstein condensation type. A key distinction from the ordinary ideal Bose gas is that the condensation temperature is elevated relative to the bosonic case, and finite-temperature condensation occurs even in the dimensional regime $1/2 < D/σ\leq 1$ where standard bosons do not condense, while for $D/σ\leq 1/2$ the transition temperature vanishes. Three independent criteria; divergence of $R$, the maximum fugacity singularity, and the non-analytic cusp in the specific heat, coincide at the same condensation point, confirming the thermodynamic consistency of the transition.

cond-mat.stat-mech↗

arXiv2026

Pseudo-Distributions: Thermodynamic Geometry and an Empirical Application

We develop a consistent pseudo-analytic framework based on $g$-calculus for constructing deformed statistical distributions. By mapping standard algebraic operations through a monotone generator function, we systematically derive the associated pseudo-logarithmic and pseudo-exponential structures. Applying this formalism, we introduce a new family of pseudo-distributions that generalizes nonextensive statistical mechanics at both the probability density and cumulative distribution levels, recovering classical and standard nonextensive statistics as limiting cases. We investigate the thermodynamic geometry of the proposed models using the Ruppeiner metric on the equilibrium manifold. A perturbative analysis around the classical limit reveals that, to leading order, the thermodynamic scalar curvature is governed solely by the generator deformation parameter, while the nonextensivity parameter remains decoupled. To evaluate the empirical robustness of the framework, we apply the model to analyze the absolute deviations of daily West Texas Intermediate crude oil prices from their hundred-day moving average. Model comparison based on information criteria demonstrates that the proposed pseudo-distributions provide a superior description of these high-frequency financial fluctuations and their heavy-tailed characteristics compared to standard benchmarks. These results suggest that $g$-calculus offers a flexible and physically grounded mathematical tool for generating deformed statistics and analyzing their geometric properties.

cond-mat.stat-mech↗

arXiv2026

Quantum Otto and Carnot Cycles via Skew Ising Model

We investigate the thermodynamic performance of quantum heat engines and refrigerators based on a two-spin system subject to a skew magnetic field. The working substance is described by an interacting spin model that incorporates both spin--spin coupling and anisotropy induced by a tilted magnetic field. We analyze and compare quantum Carnot and Otto cycles, showing that the Carnot cycle exhibits a universal, entropy-driven behavior with smooth phase boundaries, while the Otto cycle displays a much richer structure governed by the interplay between the energy spectrum and nonequilibrium population differences. In particular, we identify a crossover in both efficiency and coefficient of performance as a function of the interaction strength, which arises from the competition between the interaction energy scale and the magnetic field. We further demonstrate that the skew angle induces state hybridization, modifying both the energy levels and occupation probabilities. Our results highlight that interactions and anisotropy, when properly tuned, can enhance thermodynamic performance, and emphasize the importance of multi-level effects in the design of quantum thermal machines.

cond-mat.stat-mech↗

arXiv2026

Thermodynamic Geometry of Classical and Quantum Statistics in the Relativistic Regime

We investigate the thermodynamic geometry of classical and quantum ideal gases in the relativistic regime, with particular emphasis on the effects of particle mass and spatial dimensionality. Relativistic kinematics is incorporated through the full energy-momentum dispersion relation and the corresponding relativistic density of states. Using the Fisher-Rao information metric derived from the partition function, we analyze the thermodynamic curvature for Maxwell-Boltzmann, Bose-Einstein, and Fermi-Dirac statistics. Exact analytical expressions are obtained in two spatial dimensions, while the three-dimensional case is studied numerically. We show that the thermodynamic curvature preserves its characteristic sign-positive for bosons and negative for fermions; even in the relativistic regime, reflecting effective attractive and repulsive statistical interactions, respectively. A distinctive relativistic effect is the shift of curvature singularities from the non-relativistic critical point to a mass-dependent threshold at $μ=mc^{2}$. In addition, the relativistic Bose-Einstein condensation temperature is evaluated, revealing explicit mass-dependent corrections to the non-relativistic result. These findings provide a unified geometric perspective on relativistic statistical systems and clarify the interplay between quantum statistics, relativistic kinematics, and critical behavior.

cond-mat.stat-mech↗

arXiv2025

Mittag-Leffler Quantum Statistics and Thermodynamic Anomalies

Building upon the framework established in our recent work [M. Seifi et al., Phys. Rev. E 111, 054114 (2025)], wherein a generalized Maxwell Boltzmann distribution was formulated using the Mittag Leffler function within the superstatistical formalism, we extend this approach to the quantum domain. Specifically, we introduce two statistical distributions,termed the Mittag Leffler Bose Einstein (MLBE) and Mittag Leffler Fermi Dirac (MLFD) distributions, constructed by generalizing the conventional Bose-Einstein and Fermi-Dirac distributions through the Mittag-Leffler function. This generalization incorporates a deformation parameter (α), which facilitates a continuous interpolation between bosonic and fermionic statistics, while inherently capturing nonequilibrium effects and generalized thermodynamic behavior. We analyze the thermodynamic geometry associated with these distributions and identify significant departures from standard statistical models. Notably, the MLBE distribution manifests a Bose-Einstein-like condensation even in the absence of interactions, whereas the MLFD distribution exhibits unconventional features, such as negative heat capacity in the low-temperature regime. These findings highlight the pivotal role of statistical deformation in determining emergent macroscopic thermodynamic phenomena.

cond-mat.stat-mech↗

arXiv2025

Intrinsic Attractive and Repulsive Interactions: From Classical to Quantum Gases in the Generalized Maxwell-Boltzmann Distribution

The thermodynamic parameter space is flat for an ideal classical gas with non-interacting particles. In contrast, for an ideal quantum Bose (Fermi) gas, the thermodynamic curvature is positive (negative), indicating intrinsic attractive (repulsive) interactions. We generalize the classical Maxwell-Boltzmann distribution by employing a generalized form of the exponential function, proposing the Mittag-Leffler Maxwell-Boltzmann distribution within the framework of superstatistics. We demonstrate that the generalization parameter, $α$, quantifies the statistical interaction. When $α= 1$, the distribution coincides with the standard classical Maxwell-Boltzmann distribution, where no statistical interaction is present. For $0 < α< 1$ ($α> 1$), the statistical interaction is repulsive (attractive), corresponding to a negative (positive) thermodynamic curvature of the system.

cond-mat.stat-mech↗

arXiv2024

Eigenvalue Preferential Attachment Networks A Dandelion Structure

In this paper we introduce a new type of preferential attachment network, the growth of which is based on the eigenvalue centrality. In this network, the agents attach most probably to the nodes with larger eigenvalue centrality which represents that the agent has stronger connections. A new network is presented, namely a dandelion network, which shares some properties of star-like structure and also a hierarchical network. We show that this network, having hub-and-spoke topology is not generally scale free, and shows essential differences with respect to the Barab{á}si-Albert preferential attachment model. Most importantly, there is a super hub agent in the system (identified by a pronounced peak in the spectrum), and the other agents are classified in terms of the distance to this super-hub. We explore a plenty of statistical centralities like the nodes degree, the betweenness and the eigenvalue centrality, along with various measures of structure like the community and hierarchical structures, and the clustering coefficient. Global measures like the shortest path statistics and the self-similarity are also examined.

cond-mat.stat-mech↗

arXiv2022

Entangled vacuum state for accelerated observers

Entanglement of Dirac fields has been studied and it is known to decrease with increasing acceleration when a quantum state is shared between users in non-inertial frames. A new form of an entangled vacuum state observed by the accelerated observer is postulated in which it is assumed that entanglement is present between the modes of the quantum field with sharp and opposite momenta defined in two causally disconnected regions of space-time. We find that this assumption does not affect the entanglement of the system.

quant-ph↗

arXiv2020

Deformed Boson Condensate as a Model of Dark Matter

We consider the condensate of $q$-deformed bosons as a model of dark matter. Our observations demonstrate that for all $q$ values, the system condenses below a $q$-dependent critical temperature $T^{q}_c$. The critical temperature interestingly tends to infinity when $q\rightarrow 0$, so that the $q$- deformed boson gas is always in the condensed phase in this limit irrespective to the temperature. We argue that this has remarkable outcomes, e.g. on the entropy of the system, and also the fraction of the particles in the ground state. Especially, by direct evaluation of the entropy of the system we reveal that it tends to zero at this limit for all temperatures, and also the fraction of particles in the ground state becomes unity. These observations prove the consistency of the model, put it in the list of appropriate candidates for the dark matter. Also, the lower and upper bounds of mass are evaluated using the phase space density and observational data for $q$ deformed Bose-Einstein condensate ($q$-BEC) model.

gr-qc↗

arXiv2015

Quantum teleportation with nonclassical correlated states in noninertial frames

Quantum teleportation is studied in noninertial frame, for fermionic case, when Alice and Bob share a general nonclassical correlated state. In noninertial frames two fidelities of teleportation are given. It is found that the average fidelity of teleportation from a separable and nonclassical correlated state is increasing with the amount of nonclassical correlation of the state. However, for any particular nonclassical correlated state, the fidelity of teleportation decreases by increasing the acceleration.

quant-ph↗

arXiv2014

Entanglement Generation by Electric Field Background

The quantum vacuum is unstable under the influence of an external electric field and decays into pairs of charged particles, a process which is known as the Schwinger pair production. We propose and demonstrate that this electric field can generate entanglement. Using the Schwinger pair production for constant and pulsed electric fields, we study entanglement for scalar particles with zero spins and Dirac fermions. One can observe the variation of the entanglement produced for bosonic and fermionic modes with respect to different parameters.

quant-ph↗

arXiv2014

Entanglement of arbitrary spin modes in an expanding universe

Pair particle creation is a well-known effect on the domain of field theory in curved space-time. It is shown that the entanglement generations for spin-0 and spin-1/2 modes are different in Friedmann-Robertson-Walker (FRW) space-time. We consider the spin-1 particles in FRW space-time using Duffin-Kemmer-Petiao (DKP) equation and obtain a measure of the generated entanglement. Also, we consider the spin-3/2 particles. We argue that the absolute value of the spin does not play any role in entanglement generation and the differences are due to the bosonic or fermionic properties.

quant-ph↗

arXiv2013

Infinite Statistics Condensate as a Model of Dark Matter

In some models, dark matter is considered as a condensate bosonic system. In this paper, we prove that condensation is also possible for particles that obey infinite statistics and derive the critical condensation temperature. We argue that a condensed state of a gas of very weakly interacting particles obeying infinite statistics could be considered as a consistent model of dark matter.

hep-th↗