Entropy Correction Research Articles

The fate for the interior content of a Black Hole from one-quarter entropy area-law

In this paper we continue investigations concerning the physical nature of the black hole entropy. In particular, in order to depict massless excitations (gravitons) leading to the one-quarter entropy area law, we use a mechanical statistical approach. As a first result, we obtain that, starting with a radiation field, we cannot exactly obtain the one-quarter factor in entropy area law. In the aforementioned framework, the correct black hole entropy is obtained only in the case where the internal temperature Ti, proportional to the Bekenstein-Hawking one, is such that Ti→0. As a consequence, according to other similar proposals in the literature, only a kind of Bose Einstein condensate (BEC) can exactly support the black hole entropy.

Quantum-gravitational effects on Joule-Thomson expansion and black hole shadows in F(R) gravity with barrow entropy corrections

We present a novel investigation into the thermodynamic properties and shadow images of a topological phantom AdS black hole within the framework of F(R) gravity, utilizing the Barrow entropy formulation. We introduce a detailed study of the Joule-Thomson expansion, calculating the Joule-Thomson coefficient and mapping isenthalpic and inversion curves to characterize heating/cooling phases. Our findings reveal that the Barrow parameter plays a crucial role in altering the shape and position of these thermodynamic curves, thereby significantly impacting the black hole's thermal behavior. Moreover, we demonstrate that variations in F(R) gravity parameters such as the scalar curvature R0, the type of field interaction η, and fR0—lead to substantial modifications in the shadow of the black hole. These changes in shadow size and shape underscore the direct influence of the underlying gravitational theory on the interaction between black holes and light, offering new perspectives on how black holes are perceived by distant observers. Additionally, we calculate the total observed intensities from the emission function of the accretion disk, with graphical analysis showing that the F(R) gravity parameters markedly affect the intensity distribution around the black hole. This has significant implications for the accretion disk's emission properties and the resulting shadow image, highlighting the critical impact of modified gravity theories on observable black hole phenomena. This work offers fresh insights and underscores the importance of considering modified gravity frameworks when studying black hole thermodynamics and optical properties.

Non-covalent interactions and charge transfer in the CO activation by low-valent group 14 complexes.

The CO activation by low-valent group 14 catalysts encompasses the rupture of varied covalent bonds in a single transition state through a concerted pathway. The bond between the central main group atom and the hydride in the complex is elongated to trigger the formation of the C-H bond with CO accompanied by the concomitant formation of the E-O bond between the complex and CO to lead the corresponding formate product. Prior studies have established that besides the apolar nature of CO , its initial interaction with the complex is primarily governed by electrostatic interactions. Notably, other stabilizing interactions and the transfer of charge between catalysts and CO during the initial phases of the reaction have been ignored. In this study, we have quantified the non-covalent interactions and charge transfer that facilitate the activation of CO by group 14 main group complex. Our findings indicate that electrostatic interactions predominantly stabilize the complex and CO in the reactant region. However, induction energy becomes the main stabilizing force as the reaction progresses towards the transition state, surpassing electrostatics. Induction contributes about 50% to the stabilization at the transition state, followed by electrostatics (40%) and dispersion interactions (10%). Atomic charges calculated with the minimal basis iterative stockholder (MBIS) method reveal larger charge transfer for the back-side reaction path in which CO approaches the catalysts in contrast to the front-side approach. Notably, it was discovered that a minor initial bending of CO to approximately initiates the charge transfer process for all systems. Furthermore, our investigation of group 14 elements demonstrates a systematic reduction in both activation energies and charge transfer to CO while descending in group 14. All studied reactions were characterized along the reaction coordinate obtained with the intrinsic reaction coordinate (IRC) methodology at the M06-2X/6-31g(d,p) level of theory. Gibbs free energy in toluene was computed using electronic energies at the DLPNO-CCSD(T)/cc-pVTZ-SSD(E) level of theory. Vibrational and translational entropy corrections were applied to provide a more accurate description of the obtained Gibbs free energies. To better characterize the changes in the reaction coordinate for all reactions, the reaction force analysis (RFA) has been employed. It enables the partition of the reaction coordinate into the reactant, transition state, and product regions where different stages of the mechanism occur. A detailed characterization of the main non-covalent driving forces in the initial stages of the activation of CO by low-valent group 14 complexes was performed using symmetry-adapted perturbation theory (SAPT). The SAPT0-CT/def2-SVP method was employed for these computations. Charge transfer descriptors based on atomic population using the MBIS scheme were also obtained to complement the SAPT analyses.

Analyzing inflationary parameters and swampland conjectures of modified cosmology according to various entropies

This paper investigates the inflationary phase of the FRW universe within the context of generalized Chaplygin gas. We explore modified cosmological scenarios incorporating two entropy corrections, namely Tsallis and Barrow. These proposed entropies lead to modifications in the Friedmann equations. By incorporating the generalized Chaplygin gas into these equations, we determine various parameters including the slow roll parameters, number of e-folds, curvature perturbation, tensor-to-scalar ratio, and spectral index. We observe variations in the values of the tensor-to-scalar ratio r and the scalar spectral index ns with respect to the Tsallis and Barrow parameters. Additionally, we plot the r−ns plane. For the Tsallis entropy, we obtain r≤0.012, r≤0.027, and r≤0.008, with ns lying between (0.961,0.964), (0.957,0.966), and (0.956,0.964), respectively. In Barrow cosmology, we find r≤0.0037, r≤0.12, and r≤0.010, while ns falls within (0.92,0.97), (0.855,0.995), and (0.960,0.966) for the chaotic, SFI, and exponential potentials, respectively. These graphical analyses demonstrate the compatibility of our models with the latest Planck data. Moreover, by considering these entropy corrections, we determine the bounds of the Swampland de Sitter conjecture for generalized Chaplygin gas. In all cases, this bound remains less than unity, satisfying the required condition for the Swampland de Sitter conjecture.

Entropy correction of Kerr–Newman-AdS black hole in Rastall gravity under Lorentz symmetry violation

The tunneling of scalar particles and fermions across the event horizon of KN-AdS black hole surrounded by perfect fluid in Rastall theory are investigated in the frame dragging coordinate systems by applying modified Klein–Gordon equation and modified Dirac equation under the influence of Lorentz symmetry violation in curved spacetime. The Hawking temperature and the heat capacity of the black hole are modified due to the influence of Lorentz symmetry violation. The Hawking temperature and the Bekenstein–Hawking entropy of the black hole beyond the semiclassical approximation are also derived by taking the effects of Planck constant [Formula: see text]. The modified Hawking temperature and entropy correction of the black hole are dependent on the Lorentz violation parameter [Formula: see text], the ether-like vectors [Formula: see text] and Planck constant [Formula: see text].

Thermal fluctuations, deflection angle, and greybody factor of a high-dimensional Schwarzschild black hole in scalar–tensor–vector gravity

In this study, we examined the thermal fluctuations, deflection angle, and greybody factor of a high-dimensional Schwarzschild black hole in scalar–tensor–vector gravity (STVG). We calculated some thermodynamic quantities related to the correction of the black hole entropy caused by thermal fluctuations and discussed the effect of the correction parameters on these quantities. By analyzing the changes in the corrected specific heat, we found that thermal fluctuations made the small black hole more stable. It is worth noting that the STVG parameter did not affect the thermodynamic stability of this black hole. Additionally, by utilizing the Gauss–Bonnet theorem, the deflection angle was obtained in the weak field limit, and the effects of the two parameters on the results were visualized. Finally, we calculated the bounds on the greybody factor of a massless scalar field. We observed that as the STVG parameter around the black hole increased, the weak deflection angle became larger, and more scalar particles can reach infinity. However, the spacetime dimension has the opposite effect on the STVG parameter on the weak deflection angle and greybody factor.

Holographic vacuum energy regularization and corrected entropy of de Sitter space

Abstract We propose that the spectrum of the surface area of the apparent horizon (AH) of de Sitter (dS) spacetime leads to corrected temperature and entropy of the dS spacetime, offering new insights into its thermodynamic properties. This is done by employing the spectrum of the AH radius, acquired from the Wheeler--DeWitt (WDW) equation, together with the Stefan--Boltzmann law, the time-energy uncertainty relation, and the unified first law of thermodynamics.

Exponential correction to Friedmann equations

In this paper, employing the exponential corrected entropy (Chatterjee and Ghosh in Phys Rev Lett 125:041302, 2020), we derive the modified Friedmann equations from the first law of thermodynamics at apparent horizon and Verlinde’s entropic gravity scenario. First, we derive the modified Friedmann equations from the first law of thermodynamics. We investigate the validity of generalised second law (GSL) of thermodynamics and find that it is always satisfied for the all eras of universe. Moreover, we investigate the deceleration parameter for the case k=0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$k=0$$\\end{document} in two frameworks. Finally, we numerically study the bouncing behaviour for the modified Friedmann equations obtained from entropic gravity. The results indicate that the bouncing behaviour is possible for the cases k=1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$k=1$$\\end{document} and k=-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$k=-1$$\\end{document}.

Higher-derivative corrections to flavoured BPS black hole thermodynamics and holography

A Cardy-like regime of the four-dimensional superconformal index has been shown to be governed by ’t Hooft anomalies and to single out a large-N saddle carrying the Bekenstein-Hawking entropy of dual supersymmetric black holes in AdS5. For the universal index where no flavour fugacities are turned on, this correspondence has been improved by matching the first subleading corrections to the saddle-point action with the four-derivative corrections to the black hole action in minimal gauged supergravity, as well as the respective corrected entropies. Here, we extend this match by including flavour symmetries. We consider five-dimensional gauged supergravity with vector multiplet and four-derivative couplings, and provide an effective theory reproducing the ’t Hooft anomalies of the R- and flavour symmetries of generic holographic superconformal field theories at next-to-leading order in the large-N expansion. Then we focus on a specific model dual to ℂ3/ℤν quiver gauge theories, where the ’t Hooft anomaly coefficients receive simple but sufficiently generic corrections. In this model, we evaluate the four-derivative corrections to the on-shell action of the supersymmetric multi-charge black hole, showing agreement with the flavoured Cardy-like formula from the index. We give a prediction for the corrected entropy of the supersymmetric black hole and discuss the general validity of our results. Taking the limit of infinite AdS5 radius, we also obtain four-derivative corrections to the action and entropy of supersymmetric asymptotically flat black holes.

Joule–Thomson expansion of Bardeen black hole with a cloud of strings

This study focuses on the newly suggested Bardeen BH concept with a cloud of strings around it. Isenthalpic curves in the [Formula: see text] plane are explored concurrently with the investigation of the Joule–Thomson coefficient and inversion temperature. A comparison between the behavior of the BH and the Van der Waals fluid is made in order to shed light on the system and clarify its similarities and differences. A crucial component of our research entails determining corrected entropy in order to comprehend thermal fluctuations. Based on corrected entropy, the thermal stability debate shows that there is no fluctuation when it comes to small BHs. Additionally, we investigate the energy emission process from the Bardeen BH solution with a cloud of strings in order to clarify this important thermodynamic feature.

DynamicKD: An effective knowledge distillation via dynamic entropy correction-based distillation for gap optimizing

The knowledge distillation uses a high-performance teacher network to guide the student network. However, the performance gap between the teacher and student networks can affect the student’s training. This paper proposes a novel knowledge distillation algorithm based on dynamic entropy correction, which adjusts the student instead of the teacher to reduce the gap. Firstly, the effect of changing the output entropy (short for output information entropy) on the distillation loss in the student is analyzed in theory. This paper shows that correcting the output entropy can reduce the gap. Then, a knowledge distillation algorithm based on dynamic entropy correction is created, which can correct the output entropy in real-time with an entropy controller updated dynamically by the distillation loss. The proposed algorithm is validated on the CIFAR100, ImageNet, and PASCAL VOC 2007. The comparison with various state-of-the-art distillation algorithms shows impressive results, especially in the experiment on the CIFAR100 regarding teacher–student pair resnet32x4–resnet8x4. The proposed algorithm raises 2.64 points over the traditional distillation algorithm and 0.87 points over the state-of-the-art algorithm CRD in classification accuracy, demonstrating its effectiveness and efficiency.

Disentanglement of Evolutionary Constraints in Statistical Models of Proteins

The exponential growth of protein sequences in the post-genomic era has revolutionized the application of generative sequence models for pivotal tasks such as contact prediction, protein design, alignment, and homology search. Despite remarkable progress in these areas, the interpretability of the modeled pairwise parameters remains limited due to complexities arising from coevolution, phylogeny, and entropy. While post-correction methods for contact prediction have been developed to eliminate entropy-related contributions from predicted contact maps, there is currently no direct approach to correct entropy in other applications reliant on raw parameters. In this paper, we investigate the sources of entropy signal and propose a novel spectral regularizer, LH (an abbreviation of Henri Lebesgue), to mitigate its impact during model fitting. By incorporating this regularizer into the GREMLIN framework (utilizing a Markov random field or Potts model), we enable the accurate inference of sparse contact maps while simultaneously improving interpretability and addressing overfitting concerns critical for sequence evaluation and design. To validate the efficacy of our approach, we design multiple protein sequences based on GREMLIN with both L2 and LH regularizers, and subsequently experimentally measure their using cDNA display proteolysis. Our findings demonstrate that proteins designed using the LH regularizer exhibit increased diversity and enhanced folding stability. Published by the American Physical Society 2024

Upper Bound of Barrow Entropy Index from Black Hole Fragmentation

Both classical and quantum arguments suggest that if Barrow entropy is correct, its index δ must be energy-dependent, which would affect the very early universe. Based on thermodynamic stability that sufficiently large black holes should not fragment, we argue that Barrow entropy correction must be small, except possibly at the Planckian regime. Furthermore, the fact that a solar mass black hole does not fragment implies an upper bound δ≲O(10−3), which surprisingly lies in the same range as the bound obtained from some cosmological considerations assuming fixed δ. This indicates that allowing δ to run does not raise its allowed value. We briefly comment on the case of Kaniadakis entropy.

Non-perturbative correction on the black hole geometry

In this paper, we use the holographic principle to obtain a modified metric of black holes that reproduces the exponentially corrected entropy. The exponential correction of the black hole entropy comes from non-perturbative corrections. It interprets as a quantum effect which affects black hole thermodynamics especially in the infinitesimal scales. Hence, it may affect black hole stability at the final stage. Then, we study modified thermodynamics due to the non-perturbative corrections and calculate thermodynamics quantities of several non-rotating black holes.

Nonextensive statistics and the entropy on the horizon

We explore the application of nonextensive Bose statistics to describe the behavior of an ideal gas near the horizon of black holes, presenting a compelling case for its efficacy as an effective theory for interacting bosons. The central focus is on the careful selection of a nonextensive parameter, a critical aspect that enables the derivation of the correct entropy on the black hole horizon. Remarkably, this approach aligns with the well-established Bekenstein–Hawking entropy, showcasing the utility of nonextensive Bose statistics in capturing the thermodynamic properties of particles near black hole horizons. The study contributes to our understanding of fundamental interactions in extreme gravitational environments and provides a novel perspective on the statistical mechanics of black hole thermodynamics.

Correction of Kerr-Sen Black Hole Temperature and Entropy by Lorentz Invariance Violation* *Supported by National Natural Science Foundation of China (Grant No.12373109) and the Natural Science Foundation of Shandong Province of China(Grant No.ZR202102220686).

In this paper, we modify the action of spin field in Kerr-Sen curved space-time through Lorentz invariance violation (LIV). The tunneling radiation rate of Fermion in the Kerr-Sen black hole and the correction of the black hole entropy are studied. In the curved space-time of the Kerr-Sen black hole, by considering the inclusion of LIV correction terms in the action of a spinor field, the modified form of the fermion dynamics equation, the tunneling radiation rate and Bekenstein-Hawking entropy of the black hole are obtained. In this paper, we further consider the modification of the results obtained under quantum perturbation theory and discuss the significance of the results obtained. We have used quantum perturbation theory to perform a more accurate correction of the above results.

Sequential formulation of all‐way coupled finite strain thermoporomechanics for largely deformable gas hydrate deposits

AbstractWe develop a numerically stable sequential formulation of thermoporomechanics for largely deformable gas hydrate deposits, extended from the fixed stress split of infinitesimal transformation. Constitutive equations are based on the total Lagrangian approach for both flow and geomechanics, including dynamic full tensor permeability and thermal conductivity updated from the deformation gradient. For space discretization, we take the cell‐centered finite volume and node‐based finite element method for flow and geomechanics, respectively. Then, we propose a sequential implicit method for all‐way coupled thermoporomechanics, where the nonisothermal multiphase flow problem of gas hydrates is solved implicitly first and then the geomechanics problem is solved implicitly at the next step. During solution of the flow problem, we fix the rate of first Pioal total stress for numerical stability as well as apply porosity correction and entropy correction to account for geomechanical effects. We test numerical examples where flow and geomechanics parameters are based on deep oceanic gas hydrate deposits. When applying depressurization, even though the results between the infinitesimal transformation and finite strain geomechanics are similar in the early stages due to small deformation, we find differences between them in the late times as deformation becomes large. Accordingly, permeability and thermal conductivity tensors become nonisotropic full tensors although they are initially isotropic. We identify numerical stability of the developed sequential method from the test cases that exhibit the highly complex coupled gas hydrate systems with large deformation. Thus, the proposed sequential formulation can be applied in largely deformable gas hydrate systems.

KMT-PLL: K-Means Cross-Attention Transformer for Partial Label Learning.

Partial label learning (PLL) studies the problem of learning instance classification with a set of candidate labels and only one is correct. While recent works have demonstrated that the Vision Transformer (ViT) has achieved good results when training from clean data, its applications to PLL remain limited and challenging. To address this issue, we rethink the relationship between instances and object queries to propose K-means cross-attention transformer for PLL (KMT-PLL), which can continuously learn cluster centers and be used for downstream disambiguation tasks. More specifically, K-means cross-attention as a clustering process can effectively learn the cluster centers to represent label classes. The purpose of this operation is to make the similarity between instances and labels measurable, which can effectively detect noise labels. Furthermore, we propose a new corrected cross entropy formulation, which can assign weights to candidate labels according to the instance-to-label relevance to guide the training of the instance classifier. As the training goes on, the ground-truth label is progressively identified, and the refined labels and cluster centers in turn help to improve the classifier. Simulation results demonstrate the advantage of the KMT-PLL and its suitability for PLL.

Dissipation in nonequilibrium thermodynamics and its connection to the Rayleighian functional

We examine quantitatively the role of dissipation in nonequilibrium thermodynamics and its connection to variational principles and the Rayleighian functional. The extremum of the Rayleighian is sometimes used to describe the inertialess (dissipation-dominated) dynamics of continuum systems, and it has been applied recently for the modeling of soft matter dynamics. We discuss how dissipation is considered within one of the modern complete descriptions of nonequilibrium thermodynamics, namely the single generator bracket formalism. Within this formalism, dissipation is introduced through the use of the dissipation bracket, describing irreversible dynamics, which is added to a Poisson bracket that describes the reversible dynamics of the system. A possible connection with the Rayleighian functional is then demonstrated that in all cases considered herein, the Rayleighian is equal to minus one half of the effective dissipation rate of the Lagrangian functional. The effective dissipation rate is obtained starting with an inertial (i.e., flux-based or velocity-based) system description, involving the Poisson bracket and the primitive part (i.e., without the entropy correction term) of the dissipative bracket. Several examples are discussed in detail, ranging from an algebraic model (damped oscillator) to continuum ones: modeling of fluid flow in porous particle media, viscous Newtonian compressible and incompressible fluid flows, and more interestingly, flow of a nematic liquid-crystalline material.

Derivative corrections to extremal black holes with moduli

We derive formulas for the leading mass, entropy, and long-range self-force corrections to extremal black holes due to higher-derivative operators. These formulas hold for black holes with arbitrary couplings to gauge fields and moduli, provided that the leading-order solutions are static, spherically-symmetric, extremal, and have nonzero horizon area. To use these formulas, both the leading-order black hole solution and the higher-derivative effective action must be known, but there is no need to solve the derivative-corrected equations of motion. We demonstrate that the mass, entropy and self-force corrections involve linearly-independent combinations of the higher-derivative couplings at any given point in the moduli space, and comment on their relations to various swampland conjectures.