We explore the thermodynamic properties of the regular Bardeen-AdS black hole obtained by imposing an additional constraint on a singular "mother" black hole. This constraint eliminates the physical singularity but leads to the breakdown of the standard first law of black hole thermodynamics. The singular black hole exhibits a reentrant phase transition similar to that of the higher-dimensional Kerr-AdS black hole. The Bardeen-AdS black hole exhibits $P-V$ criticalities similar to that of the RN-AdS black hole, however has striking differences in its Gibbs free energy behavior. In particular, the characteristic "swallow-tail" structure associated with first-order phase transitions disappears. Instead, an "8-shaped" or "c-shaped" structure occurs, signifying a first-order phase transition or a zeroth-order phase transition between the small black hole and the large black hole phases, respectively. Our analysis suggests that constraint-induced modifications in the thermodynamic phase space may have deep consequences for the critical behaviors of black holes.

This study aimed to develop a deep learning model for the classification of bearing faults in wind turbine generators from acoustic signals. A convolutional LSTM model was successfully constructed and trained by using audio data from five predefined fault types for both training and validation. To create the dataset, raw audio signal data was collected and processed in frames to capture time and frequency domain information. The model exhibited outstanding accuracy on training samples and demonstrated excellent generalization ability during validation, indicating its proficiency of generalization capability. On the test samples, the model achieved remarkable classification performance, with an overall accuracy exceeding 99.5%, and a false positive rate of less than 1% for normal status. The findings of this study provide essential support for the diagnosis and maintenance of bearing faults in wind turbine generators, with the potential to enhance the reliability and efficiency of wind power generation.

The Yongle Palace murals, as valuable cultural heritage, have suffered varying degrees of damage, making their restoration of significant importance. However, the giant size and unique data of Yongle Palace murals present challenges for existing deep-learning based restoration methods: 1) The distinctive style introduces domain bias in traditional transfer learning-based restoration methods, while the scarcity of mural data further limits the applicability of these methods. 2) Additionally, the giant size of these murals results in a wider range of defect types and sizes, necessitating models with greater adaptability. Consequently, there is a lack of focus on deep learning-based restoration methods for the unique giant murals of Yongle Palace. Here, a 3M-Hybrid model is proposed to address these challenges. Firstly, based on the characteristic that the mural data frequency is prominent in the distribution of low and high frequency features, high and low frequency features are separately abstracted for complementary learning. Furthermore, we integrate a pre-trained Vision Transformer model (VIT) into the CNN module, allowing us to leverage the benefits of a large model while mitigating domain bias. Secondly, we mitigate seam and structural distortion issues resulting from the restoration of large defects by employing a multi-scale and multi-perspective strategy, including data segmentation and fusion. Experimental results demonstrate the efficacy of our proposed model. In regular-sized mural restoration, it improves SSIM and PSNR by 14.61% and 4.73%, respectively, compared to the best model among four representative CNN models. Additionally, it achieves favorable results in the final restoration of giant murals.

The thermodynamic inconsistency observed in regular black holes is resolved through the framework of reduced thermodynamic phase spaces. We demonstrate that regular black holes are essentially induced from singular black holes by adding an extra requirement, which imposes a constraint among black hole parameters. This constraint reduces the thermodynamic phase space, rendering the standard form of the first law of black hole thermodynamics inapplicable. Accordingly, we propose a novel methodology to study the thermodynamic properties of regular black holes. Thermodynamic quantities must be defined in the full, unconstrained thermodynamic phase space of the underlying singular black holes, only afterward is the constraint imposed to derive the consistent and meaningful thermodynamic quantities of the regular black holes. Crucially, this framework extends beyond regular black holes and applies universally to any black hole with this kind of constraint.

Based on the idea of quantized space-time of Snyder, we derive new generalized uncertainty principle and new modified density of states. Accordingly we discuss the influences of the modified density of states on some physical quantities and laws. In addition we analyzed the exact solution of the harmonic oscillator in Snyder's quantized space-time.

In this study, the methodology proposed by Goon and Penco for investigating the universality on thermodynamic relations with corrections in de Sitter black holes is extended. A universal thermodynamic extremality relation, under consideration of the mass of the spacetime $M$ with various state parameters, proposed by Goon and Penco is investigated in higher dimensional spacetime, the established universal conclusions are not impacted by the convergence of energy from the coexistence region of two horizons to the point $N$ or $C$. Furthermore, by incorporating the shift of the angular momentum into our analysis, a more universal relation is derived, specifically applicable to rotating configurations. Notably, a novel conjecture is formulated that establishes a universal relationship framework connecting shifted thermodynamic quantities across arbitrary black hole backgrounds. These findings are expected to offer profound insights into the fundamental principles of quantum gravity.

The generalized thermodynamic extremum relation, as proposed by Goon and Penco, establishes a novel theoretical framework for the study of spacetime thermodynamics. However, extant investigations generally assume that the black hole state parameter is solely a first-order function of the perturbation parameter when exploring the Goon-Penco relation in diverse spacetime contexts. An analytic expression for the perturbation parameter as a function of the black hole entropy can be expressed by treating the black hole mass as constant. The present study addresses this limitation and provides insight into the universal Goon-Penco relation when multiple thermodynamic state parameters behave as higher order functions of the perturbation parameters. Notably, we have not only established a universal relational formula in the case of multiple state variables, but more importantly, we have put forward an innovative conjecture that reveals the existence of a universal relation between displaced thermodynamic quantities in spacetime in the context of an arbitrary black hole. These theoretical breakthroughs are expected to open up new exploration directions for quantum gravity research.

Quantum Fisher information (QFI) is an important feature for the precision of quantum parameter estimation based on the quantum Cram\'er-Rao inequality. When the quantum state satisfies the von Neumann-Landau equation, the local quantum uncertainty (LQU), as a kind of quantum correlation, present in a bipartite mixed state guarantees a lower bound on QFI in the optimal phase estimation protocol [Phys. Rev. Lett. 110 (2013) 240402]. However, in the open quantum systems, there is not an explicit relation between LQU and QFI generally. In this paper, we study the relation between LQU and QFI in open systems which is composed of two interacting two-level systems coupled to independent non-Markovian environments with the entangled initial state embedded by a phase parameter $\theta$. The analytical calculations show that the QFI does't depend on the phase parameter $\theta$, and its decay can be restrained through enhancing the coupling strength or non-Markovianity. Meanwhile, the LQU is related to the phase parameter $\theta$ and shows plentiful phenomena. In particular, we find that the LQU can well bound the QFI when the coupling between the two systems is switched off or the initial state is Bell state.

We perform a study of phase transitions of RN-AdS black hole at its Davies points according to a generalized Ehrenfest classification of phase transition established on the basis of fractional derivatives. Davies points label the positions where heat capacity diverges. According to the usual Ehrenfest classification, second-order phase transitions occur there. For RN-AdS black hole, the Davies points can be classified into two types. The first type corresponds to the extreme values of temperature and the second type corresponds to the infection point(namely the critical point) of temperature. Employing the generalized Ehrenfest classification, we find that the orders of phase transition at the two types of Davies points are different. It is $3/2$-order for the first type and $4/3$-order for the second type. Thus this finer-grained classification can discriminate phase transitions that are supposed to be in the same category, which may provide some new insights toward a better understanding of black hole thermodynamics.

Employing the fractional derivatives, we construct a more elaborate classification of phase transitions compared to the original Ehrenfest classification. In this way, a thermodynamic system can even undergo a fractional-order phase transition. We use this method to restudy the charged AdS black hole and Van der Waals fluids and find that at the critical point they both have a $4/3$-order phase transition, but not the previously recognized second-order one.

The Goon-Penco (GP) relation was investigated on rotating charged black strings with an arbitrary cosmological constant. It has been demonstrated that the GP relation retains its form in the context of spacetimes described by cylindrical coordinates. In addition, the GP relation is derived in scenarios where the energy state parameters (including angular momentum $J$ and charge $Q$, etc.) are expressed as functions of the perturbation parameter $\eta$. This finding indicates that the GP relation is not only valid for spacetimes described by spherically symmetric coordinates, but also prevalent for non-spherically symmetric spacetimes, such as cylindrical coordinates. Therefore, the present study demonstrated that the GP relation is universal for spacetimes with arbitrary cosmological constants, irrespective of the adopted coordinate system.

The principle of superposition is a key ingredient for quantum mechanics. A recent work [M. Oszmaniec et al., Phys. Rev. Lett. 116, 110403 (2016)] has shown that a quantum adder that deterministically generates a superposition of two unknown states is forbidden. Here we propose a probabilistic approach for creating a superposition state of two arbitrary states encoded in two three-dimensional cavities. Our implementation is based on a three-level superconducting transmon qubit dispersively coupled to two cavities. Numerical simulations show that high-fidelity generation of the superposition of two coherent states is feasible with current circuit QED technology. Our method also works for other physical systems such as other types of superconducting qubits, natural atoms, quantum dots, and nitrogen-vacancy (NV) centers.

It is well known that there are black hole and the cosmological horizons for the Reissner-Nordström-de Sitter spacetime. Although the thermodynamic quantities on the horizons are not irrelevant, they satisfy the laws of black hole thermodynamics respectively. In this paper by considering the relations between the two horizons we give the effective thermodynamic quantities in $(n+2)$-dimensional Reissner-Nordström-de Sitter spacetime. The thermodynamic properties of these effective quantities are analyzed, moreover, the critical temperature, critical pressure and critical volume are obtained. We carry out an analytical check of Ehrenfest equations and prove that both Ehrenfest equations are satisfied. So the spacetime undergoes a second order phase transition at the critical point. This result is consistent with the nature of liquid--gas phase transition at the critical point, hence deepening the understanding of the analogy of charged dS spacetime and liquid--gas systems.

We use the variational method for the Sturm-Liouville eigenvalue problem to analytically calculate some properties of holographic superconductors with Gauss-Bonnet gravity in probe limit. By studying the holographic p-wave and s-wave superconductors in (3+1)-dimensional boundary field theories, it is found that near the critical temperature, the critical exponent of the condensation is 1/2 which is the universal value in mean-field theory. We also find that when Gauss-Bonnet coefficients grow bigger the operators on the boundary field theory will be harder to condense. These are in good agreement with the numerical results.

It is well known that there are black hole and the cosmological horizons for the Reissner-Nordström-de Sitter spacetime. Although the thermodynamic quantities on the horizons are not irrelevant, they satisfy the laws of black hole thermodynamics respectively. In this paper by considering the relations between the two horizons we give the effective thermodynamic quantities in $(n+2)$-dimensional Reissner-Nordström-de Sitter spacetime. The thermodynamic properties of these effective quantities are analyzed, moreover, the critical temperature, critical pressure and critical volume are obtained. We carry out an analytical check of Ehrenfest equations and prove that both Ehrenfest equations are satisfied. So the spacetime undergoes a second order phase transition at the critical point. This result is consistent with the nature of liquid--gas phase transition at the critical point, hence deepening the understanding of the analogy of charged dS spacetime and liquid--gas systems.

As we know that the horizon area of a black hole will increase when it absorbs matters. While based on Barrow's idea of fractal black hole horizon, ones [Phys. Lett. B 831 (137181) 2022] had proposed that for a spherically fractal structure the minimal increase of the horizon area is the area of the smallest bubble sphere. And the corresponding black hole entropy is of a logarithmic form, which is similar to that of Boltzmann entropy under a certain condition. Based on these, we re-derive the entropy of the Barrow's Einstein-power-Yang-Mills (EPYM) AdS black hole, and calculate the temperature and heat capacity of the Barrow's EPYM AdS black hole. There exists an interesting phenomena that the ratio between the Barrow's temperature and the Hawking temperature of the EPYM AdS black hole is fully consistent with that of other Schwarzschild-like black holes. The Barrow's temperature and Hawking temperature with the certain range of $\Lambda$ are monotonically increasing and the corresponding heat capacities are all positive, which means these black holes are thermodynamically stable. Besides, for the Barrow's EPYM AdS black hole its heat capacity has a Schottky anomaly-like behavior, which may reflect the existence of the discrete energy level and the microscopical degree of freedom.

As we know that due to the quantum gravitational effects black hole horizons are ``fractalized'' into a sphereflake by Barrow. Based on this issue, in this work we investigate the phase structure and stability of the Einstein-Power-Yang-Mills AdS black holes with the fractal structure on the black hole horizon in the restricted phase space. Through the thermodynamics first law and the Smarr relation in the restricted phase space, we observe that the mass parameter is understood as the inter energy and the Smarr relation is not a homogeneous function of order one for all quantities due to the fractal structure. And the fractal structure can be regarded as a phase transition probe. When this system with the fixed central charge there exists a novel phenomena: the supercritical phase transition. Furthermore the effects of the fractal parameter and non-linear Yang-Mills parameter on the thermodynamics stability of this system are also investigated.

This paper investigates the thermodynamic properties of the coexistence region of two horizons in the charged 4-dimensional Einstein-Gauss-Bonnet (4D-EGB) spacetime. Initially, we apply the universal first law of thermodynamics to derive the corresponding thermodynamic quantities for the coexistence region between the black hole event horizon and the cosmological event horizon, subject to the relevant boundary conditions. Next we examine the thermal properties of the thermodynamic system described by these equivalent quantities. Our analysis reveals that the peak of the heat capacity as a function of temperature exhibits characteristics similar to those observed in a paramagnetic system under specific conditions. We further conclude that, under certain conditions, the heat capacity mirrors that of a two-level system formed by two horizons with distinct temperatures. By comparing the heat capacity of the 4D-EGB spacetime's equivalent thermodynamic system with that of a two-level system defined by the two horizons in the spacetime, we can estimate the number of microscopic degrees of freedom at the two horizons. This findings sheds light on the quantum properties of de Sitter (dS) spacetime with two horizon interfaces and offers a novel approach to exploring the quantum properties of black holes and dS spacetime.

We investigated the Goon-Penco(GP) relationship in (n+1)-dimensional black branes with an arbitrary cosmological constant. Our analysis revealed that the GP relation preserved its form in four-dimensional and (n+1)-dimensional spacetimes, demonstrating its universal behavior with respect to dimensionality. Furthermore, we established that the GP relation exhibits universality across all states of the black hole, including those associated with the event horizon and the cosmological horizon. These findings confirm that the GP relationship remains valid for (n+1)-dimensional black holes and black branes with an arbitrary cosmological constant, independent of the coordinate system employed.