Abstract We present a unified entropy-based method for localizing inequality in probability distributions using recursive Hahn decomposition of an entropy-derived signed measure. Unlike traditional metrics that collapse entire distributions into single numbers, this method partitions the domain into regions of provably higher or lower uniformity, preserving monotonicity across recursive splits. Applied to two canonical distributions—power law and exponential—we obtain closed-form formulas for cutoff points and uniformity ratios. For power laws, these formulas reveal how inequality concentrates along heavy tails, replacing heuristic thresholds with analytic ones. For exponential distributions, including the Boltzmann form, we show that the entropy-based cutoff equals the conditional mean, giving it a new interpretation as an \emph{entropic equilibrium point} where energy minimization and entropy maximization balance. This hierarchical decomposition moves beyond scalar summaries such as Gini or Theil, constructing a multiscale map of disparity that is both interpretable and computationally tractable. The approach generalizes to any continuous or discrete distribution, providing a unified, information-theoretic lens for analyzing inequality in economics, reliability theory, and statistical physics.

Abstract We present a new quantum speed limit (QSL) for open quantum systems governed by Markovian dynamics. Our approach is based on analyzing the time derivative of the Bures angle between the initial pure state and its time-evolved state, leading to an analytically computable upper bound on the evolution speed. This bound naturally decomposes into three distinct physical contributions: a unitary term, a dissipative deformation term, and a fluctuation term. Building on this structure, we establish a general inequality that connects the QSL to the quantum Fisher information (QFI) in the short-time regime. This reveals a fundamental trade-off between evolution speed and estimation precision, and clarifies how decoherence can both accelerate and constrain information acquisition in open quantum systems.

Abstract As a continuation of our earlier investigations into electron wave–spin, we analyze the electron spin and its qubit in a cavity by treating the electron as a physical wave obeying the Dirac equation. In this view, a qubit is a current–density configuration whose orientation is fixed by the relative phase, rather than a particle carrying simultaneous ‘up’ and ‘down’ spin states with assigned probabilities. The resulting magnetic–moment density, derived from the current, displays a richer vector distribution and topology than the fixed axial dipole weighted by probability density in the conventional wave–particle model. Both frameworks yield the same total moment of one Bohr magneton and are indistinguishable in uniform external fields, yet their ontological differences predict distinct couplings to structured fields and spin–spin interactions. These contrasts motivate further exploration of dynamical consequences within the wave–entity framework, including Aharonov–Bohm–like responses that provide testable alternatives to conventional wave–particle duality.

Abstract We consider the linear vector Schrödinger equation subjected to quadratic constraints. We demonstrate that the resulting nonlinear system is closely related to the Ablowitz-Ladik hierarchy and use this fact to derive the N-soliton solutions for the discussed model. As an example of application of these results we present solitons of some vector nonlinear Schrödinger equation with gradient nonlinearity.

Abstract In this article, we explore a noteworthy aspect of Negative Capacitance FETs (NCFETs): the influence of transistor feature size on hysteresis behavior. The ferroelectric capacitance is directly proportional to the channel length, so as the transistor is scaled down, both the ferroelectric and MOS capacitances decrease. Our analysis shows that at a channel length of 16 nm, the ferroelectric capacitance falls below the MOS capacitance, resulting in the emergence of hysteresis in the device characteristics. Additionally, we investigate how scaling the transistor feature size impacts key phenomena such as negative Drain-Induced Barrier Lowering (DIBL), negative differential resistance (NDR), and the negative body effect coefficient. We also evaluate the performance of an NCFET-based inverter across different channel lengths and find that the device with a 22 nm channel length exhibits the lowest static and dynamic power dissipation among the cases studied.