Zhenzhou Lei | Searcharxiv

arXiv2026

Legendre Transformation under Micro Canonical Ensemble

The Legendre transformation is a crucial tool in theoretical physics, known for its symmetry, especially when applied to multivariate functions. In statistical mechanics, ensembles represent the central focus. Leveraging the dimensionless aspect of Legendre transformation, this paper explores the transformation process from the entropy characteristic function of microcanonical ensembles to the analogous definition of partition function transformation. Additionally, it derives characteristic functions, partition functions, and establishes their interrelations, along with deriving corresponding thermodynamic formulas for various ensembles. This streamlined approach sheds light on the fundamental principles of statistical mechanics and underscores the symmetry inherent in Legendre transformation.

cond-mat.stat-mech↗

arXiv2026

Model dependent analytic spin torsion corrections to Blandford Znajek energy extraction in Einstein Cartan gravity

We investigate the leading near-horizon response of Blandford-Znajek energy extraction to a compact, neutral spin-polarized source within minimally coupled Einstein-Cartan-Dirac-Maxwell theory. Eliminating the algebraic contortion yields an effective axial contact interaction, which we embed into a conserved, anisotropic phenomenological completion. Working at leading order in the torsion parameter $ε_T$, spatial anisotropy $ξ$, and slow rotation $χ=a/M$ on the fixed-ADM branch, we derive the modified energy extraction rate at optimal load. We find that the leading-order power ratio $P_{\rm BZ}^{\rm EC}/P_{\rm BZ}^{\rm K}$ receives distinct contributions from rotational dragging ($\ell=1$) and magnetostatic flux redistribution ($\ell=2$). In the isotropic limit ($ξ=0$), the power is enhanced for a co-rotating completion and suppressed for a counter-rotating one, whereas for $ξ\neq0$ the net shift depends on the polar quadrupole response. We also formulate the generalized Znajek identity and linearized Grad--Shafranov framework, demonstrating that undetermined load-factor shifts leave the leading power coefficient invariant due to stationarity at the matched load point.

physics.gen-ph↗