arXiv subjects

Omid Yahyayi Monem

Publications and source records attributed to Omid Yahyayi Monem.

3 recordsLinked to original sources

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

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

Haldane-Inspired Generalized Statistics

We propose and study a generalized quantum statistical framework, referred to as \emph{alpha statistics}, that continuously interpolates between Bose--Einstein and Fermi--Dirac statistics and naturally extends into the hyperbosonic regime for $α< 0$. Inspired by Haldane's exclusion statistics, this formulation introduces a modified occupation weight function that encodes effective statistical interactions via the parameter $α$. Using thermodynamic geometry, we analyze the sign and singular behavior of the thermodynamic curvature as a diagnostic of underlying interactions and phase structures. A crossover temperature $T^{*}$, at which the curvature changes sign, marks the transition between effectively attractive (Bose-like) and repulsive (Fermi-like) statistical regimes. When expressed relative to the Bose--Einstein condensation temperature $T_{c}$, the ratio $T^{*}/T_{c}$ depends universally on $α$. For negative $α$, corresponding to hyperbosonic statistics, we find curvature singularities at specific fugacities, indicating modified condensation phenomena distinct from conventional Bose condensation. These results highlight the geometric and thermodynamic consequences of alpha statistics and establish a link between fractional exclusion principles and curvature-induced interaction signatures in statistical thermodynamics.

cond-mat.stat-mech↗