Weak Fault Feature Extraction of the Rotating Machinery Using Flexible Analytic Wavelet Transform and Nonlinear Quantum Permutation Entropy

Addressing the challenges posed by the nonlinear and non-stationary vibrations in rotating machinery,where weak fault characteristic signals hinder accurate fault state representation,we propose a novel feature extraction method that combines the Flexible Analytic Wavelet Transform(FAWT)with Nonlinear Quantum Permutation Entropy.FAWT,leveraging fractional orders and arbitrary scaling and translation factors,exhibits superior translational invariance and adjustable fundamental oscillatory characteristics.This flexibility enables FAWT to provide well-suited wavelet shapes,effectively matching subtle fault components and avoiding performance degradation associated with fixed frequency partitioning and low-oscillation bases in detecting weak faults.In our approach,gearbox vibration signals undergo FAWT to obtain sub-bands.Quantum theory is then introduced into permutation entropy to propose Nonlinear Quantum Permutation Entropy,a feature that more accurately characterizes the operational state of vibration simulation signals.The nonlinear quantum permutation entropy extracted from sub-bands is utilized to characterize the operating state of rotating machinery.A comprehensive analysis of vibration signals from rolling bearings and gearboxes validates the feasibility of the proposed method.Comparative assessments with parameters derived from traditional permutation entropy,sample entropy,wavelet transform(WT),and empirical mode decomposition(EMD)underscore the superior effectiveness of this approach in fault detection and classification for rotating machinery.

A Study of Entropy Change in a Spin Quantum System

The entropy change in a spin system coupled to a magnetic field is investigated by solving an evolution equation for a quantum spin system. Entropy of the system is discussed and the exchange of entropy between the spins and field can be studied. The full quantum treatment of spins and field shows that the coherent nature of this field is very important for reaching the spin echo.

Single-atom entropy squeezing and quantum entanglement in Tavis-Cummings model with atomic motion

We examine the single-atom entropy squeezing and the atom-field entanglement in a system of two moving twolevel atoms interacting with a single-mode coherent field in a lossless resonant cavity. Our numerical calculations indicate that the squeezing period, the squeezing time and the maximM squeezing can be controlled by appropriately choosing the atomic motion and the field-mode structure. The atomic motion leads to a periodical time evolution of entanglement between the two-atom and the field. Moreover, there exists corresponding relation between the time evolution properties of the atomic entropy squeezing and that of the entanglement between the two atoms and the field.

Quantum Extensions to the Einstein Field Equations

This paper proposes an extension to the Einstein Field Equations by integrating quantum informational measures, specifically entanglement entropy and quantum complexity. These modified equations aim to bridge the gap between general relativity and quantum mechanics, offering a unified framework that incorporates the geometric properties of spacetime with fundamental aspects of quantum information theory. The theoretical implications of this approach include potential resolutions to longstanding issues like the black hole information paradox and new perspectives on dark energy. The paper presents modified versions of classical solutions such as the Schwarzschild metric and Friedmann equations, incorporating quantum corrections. It also outlines testable predictions in areas including gravitational wave propagation, black hole shadows, and cosmological observables. We propose several avenues for future research, including exploring connections with other quantum gravity approaches designing experiments to test the theory’s predictions. This work contributes to the ongoing exploration of quantum gravity, offering a framework that potentially unifies general relativity and quantum mechanics with testable predictions.

The Emergence of Time from Quantum Information Dynamics

This paper presents a novel framework for understanding time as an emergent phenomenon arising from quantum information dynamics. We propose that the flow of time and its directional arrow are intrinsically linked to the growth of quantum complexity and the evolution of entanglement entropy in physical systems. By integrating principles from quantum mechanics, information theory, and holography, we develop a comprehensive theory that explains how time can emerge from timeless quantum processes. Our approach unifies concepts from quantum mechanics, general relativity, and thermodynamics, providing new perspectives on longstanding puzzles such as the black hole information paradox and the arrow of time. We derive modified Friedmann equations that incorporate quantum information measures, offering novel insights into cosmic evolution and the nature of dark energy. The paper presents a series of experimental proposals to test key aspects of this theory, ranging from quantum simulations to cosmological observations. Our framework suggests a deeply information-theoretic view of the universe, challenging our understanding of the nature of reality and opening new avenues for technological applications in quantum computing and sensing. This work contributes to the ongoing quest for a unified theory of quantum gravity and information, potentially with far-reaching implications for our understanding of space, time, and the fundamental structure of the cosmos.

Quantum Entropy of Black Hole with Internal Global Monopole

Using the generalized uncertainty relation, the new equation of state density is obtained, and then the entropy of black hole with an internal global monopole is discussed. The divergence that appears in black hole entropy calculation through original brick-wall model is overcome. The result of the direct proportion between black hole entropy and its event horizon area is drawn and given. The result shows that the black hole entropy must be the entropy of quantum state near the event horizon.

Information Entropy and Squeezing of Quantum Fluctuations in a Two-Level Atom

We study the atomic squeezing in the language of the quantum information theory.A rigorous entropy uncertainty relation which suits for characterizing the squeezing of a two-level atoms is obtained,and a general definition of information entropy squeezing in the two-level atoms is given.The information entropy squeezing of two-level atoms interacting with a single-mode quantum field is examined.Our results show that the information entropy is a superior measure of the quantum uncertainty of atomic observable,also is a remarkable good precision measure of atomic squeezing.When the population difference of two-level atom is zero,the definition of atomic squeezing based on the Heisenberg uncertainty relation is trivial,while the definition of information entropy squeezing of the atom based on the entropy uncertainty relation is valid and can provide full information on the atomic squeezing in any cases.

Entropy as a measure of the noise extent in a two-level quantum feedback controlled system

By introducing the von Neumann entropy as a measure of the extent of noise, this paper discusses the entropy evolution in a two-level quantum feedback controlled system. The results show that the feedback control can induce the reduction of the degree of noise, and different control schemes exhibit different noise controlling ability, the extent of the reduction also related with the position of the target state on the Bloch sphere. It is shown that the evolution of entropy can provide a real time noise observation and a systematic guideline to make reasonable choice of control strategy.

Conditional Entropy of Partitions on Quantum Logic

A construction of conditional entropy of partitions on quantum logic is given,and the properties ofconditional entropy are investigated.

Quantum entanglement between the two-mode fields and atomic entropy squeezing in the system of a moving atom interacting with two-mode entangled coherent field

This paper investigates the entropy squeezing of a moving two-level atom interacting with the two-mode entangled coherent field via two-photon transition by using an entropic uncertainty relation and the degree of entanglement between the two-mode fields by using quantum relative entropy.The results obtained from numerical calculation indicate that the squeezed period,the duration of entropy squeezing and the maximal squeezing can be controlled by appropriately choosing the intensity of the light field,the atomic motion and the field-mode structure.The atomic motion leads to the periodic recovery of the initial maximal degree of entanglement between the two-mode fields.Moreover,there exists a corresponding relation between the time evolution properties of the atomic entropy squeezing and those of the entanglement between the two-mode fields.

Quantum Statistical Entropy of Five-Dimensional Black Hole

The generalized uncertainty relation is introduced to calculate quantum statistic entropy of a black hole. By using the new equation of state density motivated by the generalized uncertainty relation, we discuss entropies of Bose field and Fermi field on the background of the five-dimensional spacetime. In our calculation, we need not introduce cutoff. There is not the divergent logarithmic term as in the original brick-wall method. And it is obtained that the quantum statistic entropy corresponding to black hole horizon is proportional to the area of the horizon. Fhrther it is shown that the entropy of black hole is the entropy of quantum state on the surface of horizon. The black hole＇s entropy is the intrinsic property of the black hole. The entropy is a quantum effect. It makes people further understand the quantum statistic entropy.

Quantum information entropy for one-dimensional system undergoing quantum phase transition

Calculations of the quantum information entropy have been extended to a non-analytically solvable situation. Specifically, we have investigated the information entropy for a one-dimensional system with a schematic ＂Landau＂ potential in a numerical way. Particularly, it is found that the phase transitional behavior of the system can be well expressed by the evolution of quantum information entropy. The calculated results also indicate that the position entropy S_x and the momentum entropy S_p at the critical point of phase transition may vary with the mass parameter M but their sum remains as a constant independent of M for a given excited state. In addition, the entropy uncertainty relation is proven to be robust during the whole process of the phase transition.

Effects of Shannon entropy and electric field on polaron in RbCl triangular quantum dot

In this paper, the time evolution of the quantum mechanical state of a polaron is examined using the Pekar type variational method on the condition of the electric-LO-phonon strong-coupling and polar angle in RbC1 triangular quantum dot. We obtain the eigenenergies, and the eigenfunctions of the ground state, and the first excited state respectively. This system in a quantum dot can be treated as a two-level quantum system qubit and the numerical calculations are performed. The effects of Shannon entropy and electric field on the polaron in the RbC1 triangular quantum dot are also studied.

Quantum Entropy of a Cooper-Pair Box in a Single-Mode Cavity Field

A Cooper-pair box biased by a classical voltage and also irradiated by a squeezed state field is considered in order to find new ways to quantum communication and calculation. The quantum dynamics of the Cooper-pair box and the entanglement which is the core theoretics of quantum communication and calculation is investigated in this system, which is related to the squeezing parameter of the squeezed state, A model of Hamiltonian which represents the interaction between box and quantum field is introduced. Finally, the relationship between the entanglement and the squeezing parameter of the squeezed state is demonstrated.

Entropy of Quantum Dynamical Systems and Sufficient Families in Orthomodular Lattices with Bayessian State

The purpose of the present paper is to study the entropy hs（Ф） of a quantum dynamical systems Ф = （ L, s, Ф）, where s is a bayessian state on an orthomodular lattice L. Having introduced the notion of entropy hs（ Ф, A） of partition A of a Boolean algebra B with respect to a state s and a state preserving homomorphism Ф, we prove a few results on that, define the entropy of a dynamical system hs（Ф）, and show its invariance. The concept of sufficient families is also given and we establish that hs （Ф） comes out to be equal to the supremum of hs （Ф,A）, where A varies over any sufficient family. The present theory has then been extended to the quantum dynamical system （ L, s, Ф）, which as an effect of the theory of commutators and Bell inequalities can equivalently be replaced by the dynamical system （B, s0, Ф）, where B is a Boolean algebra and so is a state on B.

Entropy squeezing of a moving atom and control of noise of the quantum mechanical channel via the two-photon process

Based on the quantum information theory, we have investigated the entropy squeezing of a moving two-level atom interacting with the coherent field via the quantum mechanical channel of the two-photon process. The results are compared with those of atomic squeezing based on the Heisenberg uncertainty relation. The influences of the atomic motion and field-mode structure parameter on the atomic entropy squeezing and on the control of noise of the quantum mechanical channel via the two-photon process are examined. Our results show that the squeezed period, duration of optimal entropy squeezing of a two-level atom and the noise of the quantum mechanical channel can be controlled by appropriately choosing the atomic motion and the field-mode structure parameter, respectively. The quantum mechanical channel of two-photon process is an ideal channel for quantum information （atomic quantum state） transmission. Quantum information entropy is a remarkably accurate measure of the atomic squeezing.

Quantum Entropy of a Single Cooper-Pair Box Interacting with Two Electromagnetic Fields

A Hamiltonian which represents the interaction between a single Cooper-pair box and two quantized electromagnetic fields is considered in order to find new ways for quantum information. The wave function in Schrodinger picture is obtained. The evolution of the entropy of the box as a function of the scaled time is ploted to measure the entanglement between the box and the fields. It is found that the entanglement is sensitive to the detuning between the Josephson energy and the fields frequency, increasing the detuning can decrease the entanglement.

Properties of field quantum entropy evolution in the Jaynes-Cummings model with initial squeezed coherent states field

The properties of the field quantum entropy evolution in a system of a single-mode squeezed coherent state field interacting with a two-level atom is studied by utilizing the complete quantum theory, and we focus our attention on the discussion of the influences of field squeezing parameter γ, atomic distribution angle θ and coupling strength g between the field and the atom on the properties of the evolution of field quantum entropy. The results obtained from numerical calculation indicate that the amplitude of oscillation of field quantum entropy evolution decreases with the increasing of squeezing parameter γ, and that both atomic distribution angle θ and coupling strength g between the field and the atom can influence the periodicity of field quantum entropy evolution.

Quantum watermarking based on threshold segmentation using quantum informational entropy

We propose a new quantum watermarking scheme based on threshold selection using informational entropy of quantum image.The core idea of this scheme is to embed information into object and background of cover image in different ways.First,a threshold method adopting the quantum informational entropy is employed to determine a threshold value.The threshold value can then be further used for segmenting the cover image to a binary image,which is an authentication key for embedding and extraction information.By a careful analysis of the quantum circuits of the scheme,that is,translating into the basic gate sequences which show the low complexity of the scheme.One of the simulation-based experimental results is entropy difference which measures the similarity of two images by calculating the difference in quantum image informational entropy between watermarked image and cover image.Furthermore,the analyses of peak signal-to-noise ratio,histogram and capacity of the scheme are also provided.

Entropy of Partitions on Quantum Logic

Partition and entropy of partitions in quantum logic are introduced and their properties are investigated.The results are generalized to the general case of T-norm and T-conorm.