Статті в журналах: "Wald Entropy"

1

Parikh, Maulik, and Sudipta Sarkar. "Generalized Einstein’s Equations from Wald Entropy." Entropy 18, no. 4 (March 31, 2016): 119. http://dx.doi.org/10.3390/e18040119.

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2

Astaneh, Amin Faraji, and Sergey N. Solodukhin. "The Wald entropy and 6d conformal anomaly." Physics Letters B 749 (October 2015): 272–77. http://dx.doi.org/10.1016/j.physletb.2015.07.077.

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3

Krishnan, Chethan, and Stanislav Kuperstein. "A comment on Kerr–CFT and Wald entropy." Physics Letters B 677, no. 5 (June 2009): 326–31. http://dx.doi.org/10.1016/j.physletb.2009.05.056.

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4

SEN, ASHOKE. "QUANTUM ENTROPY FUNCTION FROM AdS2/CFT1 CORRESPONDENCE." International Journal of Modern Physics A 24, no. 23 (September 20, 2009): 4225–44. http://dx.doi.org/10.1142/s0217751x09045893.

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We review and extend recent attempts to find a precise relation between extremal black hole entropy and degeneracy of microstates using AdS 2/ CFT 1 correspondence. Our analysis leads to a specific relation between degeneracy of black hole microstates and an appropriately defined partition function of string theory on the near horizon geometry — named the quantum entropy function. In the classical limit this reduces to the usual relation between statistical entropy and Wald entropy.

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5

MYUNG, YUN SOO. "ENTROPY OF EXTREMAL WARPED BLACK HOLES." Modern Physics Letters A 24, no. 19 (June 21, 2009): 1485–93. http://dx.doi.org/10.1142/s021773230903093x.

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We study the entropy of extremal warped black hole obtained from the topologically massive gravity with a negative cosmological constant of Λ = -1/l2. We compare the entropy Se = πα/3G from the Wald formalism with Sw = πl u /3G from the entropy function approach. These are the same if α = l u. Also we obtain the same Cardy formula when Je = l3 q with Je the angular momentum and q the conserved quantity.

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6

PADMANABHAN, T. "EQUIPARTITION OF MICROSCOPIC DEGREES OF FREEDOM, SPACE–TIME ENTROPY AND HOLOGRAPHY." International Journal of Modern Physics D 19, no. 14 (December 2010): 2275–80. http://dx.doi.org/10.1142/s0218271810018323.

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One can identify the number density of the microscopic space–time degrees of freedom in any diffeomorphism-invariant theory of gravity by using the principle of equipartition, applied to the area elements of a surface [Formula: see text] which are at the local Unruh temperature. The entropy associated with these degrees of freedom, which matches with the Wald entropy for the theory, can be used to obtain the field equations of the theory through an extremization priciple. When the microscopic degrees of freedom are in local thermal equilibrium, the entropy of a bulk region of space–time resides on its boundary. These facts support an emergent perspective of gravity.

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7

GERŠL, JAN. "THE BOUSSO ENTROPY BOUND FOR AN IDEAL GAS OF MASSIVE PARTICLES." International Journal of Modern Physics D 18, no. 05 (May 2009): 763–79. http://dx.doi.org/10.1142/s0218271809014741.

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The Bousso entropy bound is investigated for static, spherically symmetric configurations of an ideal gas with a Bose–Einstein or Fermi–Dirac distribution function. Gas of massive particles is considered. This paper is continuation of the previous work concerning the massless case. Special attention is devoted to light sheets generated by spheres. Conditions under which the Bousso bound can be violated are discussed and it is shown that a possible violating region cannot be arbitrarily large and that it is contained inside a sphere of unit Planck radius if the number of independent spin states gs is small enough. It is also shown that the central temperature must exceed the Planck temperature in order to get a violation of the Bousso bound for gs which is not too large. The situation for higher-dimensional space–times is also discussed and the conditions of Flanagan, Marolf and Wald are investigated.

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8

GHANAATIAN, MOHAMMAD, and AFSANEH BAZRAFSHAN. "NONLINEAR CHARGED BLACK HOLES IN AdS QUASI-TOPOLOGICAL GRAVITY." International Journal of Modern Physics D 22, no. 13 (October 20, 2013): 1350076. http://dx.doi.org/10.1142/s0218271813500764.

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In this paper, we present the static charged solutions of quartic quasi-topological gravity in the presence of a nonlinear electromagnetic field. Two branches of these solutions present black holes with one or two horizons or a naked singularity depending on the charge and mass of the black hole. The entropy of the charged black holes of fourth-order quasi-topological gravity through the use of Wald formula is computed and the mass, temperature and the charge of these black holes are found as well. We show that black holes with spherical, flat and hyperbolical horizon in quasi-topological gravity are stable for any allowed quasi-topological parameters. We also investigate the stability of nonlinear charged black holes.

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9

Celso-Arellano, Pedro, Victor Gualajara, Semei Coronado, Jose N. Martinez, and Francisco Venegas-Martínez. "Impact of the Global Fear Index (COVID-19 Panic) on the S&P Global Indices Associated with Natural Resources, Agribusiness, Energy, Metals, and Mining: Granger Causality and Shannon and Rényi Transfer Entropy." Entropy 25, no. 2 (February 8, 2023): 313. http://dx.doi.org/10.3390/e25020313.

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The Global Fear Index (GFI) is a measure of fear/panic based on the number of people infected and deaths due to COVID-19. This paper aims to examine the interconnection or interdependencies between the GFI and a set of global indexes related to the financial and economic activities associated with natural resources, raw materials, agribusiness, energy, metals, and mining, such as: the S&P Global Resource Index, the S&P Global Agribusiness Equity Index, the S&P Global Metals and Mining Index, and the S&P Global 1200 Energy Index. To this end, we first apply several common tests: Wald exponential, Wald mean, Nyblom, and Quandt Likelihood Ratio. Subsequently, we apply Granger causality using a DCC-GARCH model. Data for the global indices are daily from 3 February 2020 to 29 October 2021. The empirical results obtained show that the volatility of the GFI Granger causes the volatility of the other global indices, except for the Global Resource Index. Moreover, by considering heteroskedasticity and idiosyncratic shocks, we show that the GFI can be used to predict the co-movement of the time series of all the global indices. Additionally, we quantify the causal interdependencies between the GFI and each of the S&P global indices using Shannon and Rényi transfer entropy flow, which is comparable to Granger causality, to confirm directionality more robustly The main conclusion of this research is that financial and economic activity related to natural resources, raw materials, agribusiness, energy, metals, and mining were affected by the fear/panic caused by COVID-19 cases and deaths.

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10

Daye, Dania, Sophia C. Kamran, Azadeh Tabari, Mark Michalski, Jeffrey W. Clark, David P. Ryan, Jill N. Allen, Janet E. Murphy, Theodore S. Hong, and Michael S. Gee. "Quantitative MR imaging biomarkers of tumor heterogeneity predict prognosis in metastatic colorectal lesions." Journal of Clinical Oncology 35, no. 15_suppl (May 20, 2017): e15121-e15121. http://dx.doi.org/10.1200/jco.2017.35.15_suppl.e15121.

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e15121 Background: Intra-tumor heterogeneity is an independent determinant of patient survival outcomes in several tumor subtypes. Spatial variations in tumor enhancement on MRI is a macroscopic imaging marker of tumor heterogeneity. The goal of this study is to evaluate the potential role of MRI-based enhancement heterogeneity measures as predictors of survival in patients with metastatic colorectal cancer. Methods: We retrospectively analyzed T1-weighted contrast-enhanced MRI images of metastatic hepatic lesions in 41 patients (mean age 57.2 ±14.2 years) who were diagnosed with stage IV colorectal cancer between 2007 and 2013. Tumor Kras mutation status and patient survival data for up to 95 months was available for all patients. The largest metastatic hepatic lesion was identified by a radiologist and manually segmented. 14 Haralick texture features were extracted from each lesion. Cox proportional hazards regression analysis was used to assess the association between the enhancement heterogeneity measures and patient survival, with adjustment for Kras mutation status as a potential confounder. Backward stepwise feature selection was performed using p > 0.1 (Wald test) to select for statistically significant features. Results:Mean survival time was 39±3.9 months for the study population (51±4.1 months for Kras-wildtype and 37±5.1 for Kras-mutants). 68% of the patients had left-sided colon cancer; 21% had concurrent pulmonary metastases and 0.5% had concurrent brain metastasis. 61%, 27% and 12% of patients were on Flofox, Folfiri or other chemotherapeutic regimen, respectively. Texture matrix homogeneity (HR > 10; p = 0.016), inverse difference moment (HR < 0.1; p = 0.020), entropy (HR < 0.1; p = 0.033) and standard deviation (HR > 10; p = 0.006) exhibited significant independent association with patient survival. With the exception of entropy, these features maintained significant contribution to survival prediction independent of Kras mutation status. Conclusions: MRI-based quantitativeintra-metastasis heterogeneity measures are associated with patient survival and may add information beyond genetic mutation status to optimize prognosis prediction in metastatic colon cancer.

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11

García-Islas, J. Manuel. "Entropic motion in loop quantum gravity." Canadian Journal of Physics 94, no. 6 (June 2016): 569–73. http://dx.doi.org/10.1139/cjp-2015-0730.

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Entropic forces result from an increase of the entropy of a thermodynamical physical system. It has been proposed that gravity is such a phenomenon and many articles have appeared in the literature concerning this problem. We propose a method that may reproduce an entropic force and may be related to loop quantum gravity. By considering the interaction between a fixed gravity state space and a particle state in loop quantum gravity, we show that it leads to a mathematical description of a random walk of such a particle. The random walk, in special situations, can be seen as an entropic motion in such a way that the particle will move towards a location where entropy increases. This may prove that such a theory can reproduce gravity as it is expected.

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12

Li, Shu-Nan, and Bing-Yang Cao. "Fractional-order heat conduction models from generalized Boltzmann transport equation." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 378, no. 2172 (May 11, 2020): 20190280. http://dx.doi.org/10.1098/rsta.2019.0280.

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The relationship between fractional-order heat conduction models and Boltzmann transport equations (BTEs) lacks a detailed investigation. In this paper, the continuity, constitutive and governing equations of heat conduction are derived based on fractional-order phonon BTEs. The underlying microscopic regimes of the generalized Cattaneo equation are thereafter presented. The effective thermal conductivity κ eff converges in the subdiffusive regime and diverges in the superdiffusive regime. A connection between the divergence and mean-square displacement 〈|Δ x | 2 〉 ∼ t γ is established, namely, κ eff ∼ t γ −1 , which coincides with the linear response theory. Entropic concepts, including the entropy density, entropy flux and entropy production rate, are studied likewise. Two non-trivial behaviours are observed, including the fractional-order expression of entropy flux and initial effects on the entropy production rate. In contrast with the continuous time random walk model, the results involve the non-classical continuity equations and entropic concepts. This article is part of the theme issue ‘Advanced materials modelling via fractional calculus: challenges and perspectives’.

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13

Gavriil, Vassilios, Margarita Chatzichristidi, Dimitrios Christofilos, Gerasimos A. Kourouklis, Zoe Kollia, Evangelos Bakalis, Alkiviadis-Constantinos Cefalas, and Evangelia Sarantopoulou. "Entropy and Random Walk Trails Water Confinement and Non-Thermal Equilibrium in Photon-Induced Nanocavities." Nanomaterials 10, no. 6 (June 2, 2020): 1101. http://dx.doi.org/10.3390/nano10061101.

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Molecules near surfaces are regularly trapped in small cavitations. Molecular confinement, especially water confinement, shows intriguing and unexpected behavior including surface entropy adjustment; nevertheless, observations of entropic variation during molecular confinement are scarce. An experimental assessment of the correlation between surface strain and entropy during molecular confinement in tiny crevices is difficult because strain variances fall in the nanometer scale. In this work, entropic variations during water confinement in 2D nano/micro cavitations were observed. Experimental results and random walk simulations of water molecules inside different size nanocavitations show that the mean escaping time of molecular water from nanocavities largely deviates from the mean collision time of water molecules near surfaces, crafted by 157 nm vacuum ultraviolet laser light on polyacrylamide matrixes. The mean escape time distribution of a few molecules indicates a non-thermal equilibrium state inside the cavity. The time differentiation inside and outside nanocavities reveals an additional state of ordered arrangements between nanocavities and molecular water ensembles of fixed molecular length near the surface. The configured number of microstates correctly counts for the experimental surface entropy deviation during molecular water confinement. The methodology has the potential to identify confined water molecules in nanocavities with life science importance.

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14

Kloster, Kyle, Daniel Král', and Blair D. Sullivan. "Walk entropy and walk-regularity." Linear Algebra and its Applications 546 (June 2018): 115–21. http://dx.doi.org/10.1016/j.laa.2018.02.009.

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15

Estrada, Ernesto, and José A. de la Peña. "Maximum walk entropy implies walk regularity." Linear Algebra and its Applications 458 (October 2014): 542–47. http://dx.doi.org/10.1016/j.laa.2014.06.030.

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16

Ghai, Sanjeev Kr, Umair Ahmed, Nilanjan Chakraborty, and Markus Klein. "Entropy Generation during Head-On Interaction of Premixed Flames with Inert Walls within Turbulent Boundary Layers." Entropy 24, no. 4 (March 27, 2022): 463. http://dx.doi.org/10.3390/e24040463.

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The statistical behaviours of different entropy generation mechanisms in the head-on interaction of turbulent premixed flames with a chemically inert wall within turbulent boundary layers have been analysed using Direct Numerical Simulation data. The entropy generation characteristics in the case of head-on premixed flame interaction with an isothermal wall is compared to that for an adiabatic wall. It has been found that entropy generation due to chemical reaction, thermal diffusion and molecular mixing remain comparable when the flame is away from the wall for both wall boundary conditions. However, the wall boundary condition affects the entropy generation during flame-wall interaction. In the case of isothermal wall, the entropy generation due to chemical reaction vanishes because of flame quenching and the entropy generation due to thermal diffusion becomes the leading entropy generator at the wall. By contrast, the entropy generation due to thermal diffusion and molecular mixing decrease at the adiabatic wall because of the vanishing wall-normal components of the gradients of temperature and species mass/mole fractions. These differences have significant effects on the overall entropy generation rate during flame-wall interaction, which suggest that combustor wall cooling needs to be optimized from the point of view of structural integrity and thermodynamic irreversibility.

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17

LIU, WENBIAO, YIWEN HAN, and ZHOU'AN ZHOU. "BLACK HOLE ENTROPY INSIDE AND OUTSIDE THE BRICK WALL." International Journal of Modern Physics A 18, no. 15 (June 20, 2003): 2681–87. http://dx.doi.org/10.1142/s0217751x03013673.

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Applying the generalized uncertainty relation to the calculation of the free energy and entropy of a black hole inside the brick wall, the entropy proportional to the horizon area is derived from the contribution of the vicinity of the horizon. This is compared with the entropy calculated via the original brick wall model. The entropy given by the original brick wall model comes from the outside of the brick wall seemingly. The inside result using generalized uncertainty relation is similar to the outside result using original uncertainty relation, and the divergence inside the brick wall disappears. It is apparent that the cutoff is something related to the quantum theory of gravity.

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18

Benjamini, Itai, Gady Kozma, Ariel Yadin, and Amir Yehudayoff. "Entropy of random walk range." Annales de l'Institut Henri Poincaré, Probabilités et Statistiques 46, no. 4 (November 2010): 1080–92. http://dx.doi.org/10.1214/09-aihp345.

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19

Hou, Hucan, Yongxue Zhang, and Zhenlin Li. "A numerically research on energy loss evaluation in a centrifugal pump system based on local entropy production method." Thermal Science 21, no. 3 (2017): 1287–99. http://dx.doi.org/10.2298/tsci150702143h.

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Inspired by wide application of the second law of thermodynamics to flow and heat transfer devices, local entropy production analysis method was creatively introduced into energy assessment system of centrifugal water pump. Based on Reynolds stress turbulent model and energy equation model, the steady numerical simulation of the whole flow passage of one IS centrifugal pump was carried out. The local entropy production terms were calculated by user defined functions, mainly including wall entropy production, turbulent entropy production, and viscous entropy production. The numerical results indicated that the irreversible energy loss calculated by the local entropy production method agreed well with that calculated by the traditional method but with some deviations which were probably caused by high rotatability and high curvature of impeller and volute. The wall entropy production and turbulent entropy production took up large part of the whole entropy production about 48.61% and 47.91%, respectively, which indicated that wall friction and turbulent fluctuation were the major factors in affecting irreversible energy loss. Meanwhile, the entropy production rate distribution was discussed and compared with turbulent kinetic energy dissipation rate distribution, it showed that turbulent entropy production rate increased sharply at the near wall regions and both distributed more uniformly. The blade region in leading edge near suction side, trailing edge and volute tongue were the main regions to generate irreversible exergy loss. This research broadens a completely new view in evaluating energy loss and further optimizes pump using entropy production minimization.

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20

AMPADU, CLEMENT. "ASYMPTOTIC ENTANGLEMENT IN THE PARAMETRIZED HADAMARD WALK." International Journal of Quantum Information 10, no. 06 (September 2012): 1250066. http://dx.doi.org/10.1142/s0219749912500669.

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We study asymptotic entanglement properties of the Hadamard walk with phase parameters on the line using the Fourier representation. We use the von Neumann entropy of the reduced density operator to quantify entanglement between the coin and position degrees of freedom. We investigate obtaining exact expressions for the asymptotic entropy of entanglement, for different classes of initial conditions. We also determine under which conditions the asymptotic entropy of entanglement can be characterized as full, intermediate, or minimum.

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21

ZHAO, REN, JUNFANG ZHANG, and LICHUN ZHANG. "ENTROPY OF SCHWARZSCHILD–de SITTER BLACK HOLE IN NON-THERMAL-EQUILIBRIUM." Modern Physics Letters A 16, no. 11 (April 10, 2001): 719–23. http://dx.doi.org/10.1142/s0217732301003917.

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Starting from the Klein–Gordon equation, we calculate the entropy of Schwarzschild–de Sitter black hole in non-thermal-equilibrium by using the improved brick-wall method-membrane model. When taking the proper cutoff in the obtained result, we obtain that both black hole's entropy and cosmic entropy are proportional to the areas of event horizon. We avoid the logarithmic term and stripped term in the original brick-wall method. It offers a new way of studying the entropy of the black hole in non-thermal-equilibrium.

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22

Arzano, M., L. Brocki, J. Kowalski-Glikman, M. Letizia, and J. Unger. "Quantum ergosphere and brick wall entropy." Physics Letters B 797 (October 2019): 134887. http://dx.doi.org/10.1016/j.physletb.2019.134887.

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23

Berroug, Jack, Claudia E. Korcarz, Carol KC Mitchell, JoAnne M. Weber, Lu Tian, Mary M. McDermott, and James H. Stein. "Brachial artery intima–media thickness and grayscale texture changes in patients with peripheral artery disease receiving supervised exercise training in the PROPEL randomized clinical trial." Vascular Medicine 24, no. 1 (November 12, 2018): 12–22. http://dx.doi.org/10.1177/1358863x18804050.

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We performed an exploratory analysis to evaluate the effects of a treadmill exercise program on brachial artery (BA) intima–media thickness (IMT) and three BA grayscale ultrasound measures that may indicate subclinical arterial injury. Data were from a clinical trial in individuals with peripheral artery disease who were randomly assigned to treadmill exercise training or attention control. B-mode ultrasonography was performed at baseline and after 26 weeks. BA IMT, grayscale median (GSM), entropy, and gray-level difference statistic-contrast (GLDS-CON) were measured by a single reader. The 184 participants were (mean (SD)) 66.7 (8.2) years old and had an ankle–brachial index of 0.70 (0.18). Exercise training was associated with a 0.01 (0.06) mm ( p = 0.025) reduction in BA IMT compared to 0.00 (0.05) mm ( p = 0.807) in the control group (between-group p = 0.061). BA GSM, entropy, and GLDS-CON did not change significantly with exercise. Improvements in the 6-minute walk distance correlated with increases in resting BA blood flow ( r = 0.23, p = 0.032), flow-mediated dilation ( r = 0.24, p = 0.022), diameter ( r = 0.29, p = 0.005), entropy ( r = 0.21, p = 0.047), and GLDS-CON ( r = 0.22, p = 0.041). In a post hoc analysis, BA IMT improved significantly with treadmill exercise training but did not change with attention control; however, the between-group difference did not reach statistical significance. With exercise, improvements in the 6-minute walk distance were associated with improved endothelial function, increased resting blood flow, and BA dilation, as well as higher grayscale entropy and GLDS-CON, indicating that lower extremity exercise is associated with salutary changes in upper-extremity arterial wall structure and function. ClinicalTrials.gov Identifier: NCT01408901

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24

Davies, M. R. D., and F. K. O’Donnell. "Local Measurement of Loss Using Heated Thin-Film Sensors." Journal of Turbomachinery 121, no. 4 (October 1, 1999): 814–18. http://dx.doi.org/10.1115/1.2836735.

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A calibration equation is derived linking the nondimensional entropy generation rate per unit area with the nondimensional aerodynamic wall shear stress and free-stream pressure gradient. It is proposed that the latter quantities, which can be measured from surface sensors, be used to measure the profile entropy generation rate. It is shown that the equation is accurate for a wide range of well-defined laminar profiles. To measure the dimensional entropy generation rate per unit area requires measurement of the thickness of the boundary layer. A general profile equation is given and used to show the range of accuracy of a further simplification to the calibration. For flows with low free-stream pressure gradients, the entropy generation rate is very simply related to the wall shear stress, if both are expressed without units. An array of heated thin film sensors is calibrated for the measurement of wall shear stress, thus demonstrating the feasibility of using them to measure profile entropy generation rate.

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25

HARTMAN, YAIR, YURI LIMA, and OMER TAMUZ. "An Abramov formula for stationary spaces of discrete groups." Ergodic Theory and Dynamical Systems 34, no. 3 (January 15, 2013): 837–53. http://dx.doi.org/10.1017/etds.2012.167.

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AbstractLet $(G, \mu )$ be a discrete group equipped with a generating probability measure, and let $\Gamma $ be a finite index subgroup of $G$. A $\mu $-random walk on $G$, starting from the identity, returns to $\Gamma $ with probability one. Let $\theta $ be the hitting measure, or the distribution of the position in which the random walk first hits $\Gamma $. We prove that the Furstenberg entropy of a $(G, \mu )$-stationary space, with respect to the action of $(\Gamma , \theta )$, is equal to the Furstenberg entropy with respect to the action of $(G, \mu )$, times the index of $\Gamma $ in $G$. The index is shown to be equal to the expected return time to $\Gamma $. As a corollary, when applied to the Furstenberg–Poisson boundary of $(G, \mu )$, we prove that the random walk entropy of $(\Gamma , \theta )$ is equal to the random walk entropy of $(G, \mu )$, times the index of $\Gamma $ in $G$.

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26

Chang, Tong-Bou. "Theoretical Analysis of Effects of Wall Suction on Entropy Generation Rate in Laminar Condensate Layer on Horizontal Tube." Mathematical Problems in Engineering 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/172605.

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The effects of wall suction on the entropy generation rate in a two-dimensional steady film condensation flow on a horizontal tube are investigated theoretically. In analyzing the liquid flow, the effects of both the gravitational force and the viscous force are taken into account. In addition, a film thickness reduction ratio,Sf, is introduced to evaluate the effect of wall suction on the thickness of the condensate layer. The analytical results show that, the entropy generation rate depends on the Jakob number Ja, the Rayleigh number Ra, the Brinkman number Br, the dimensionless temperature differenceψ, and the wall suction parameterSw. In addition, it is shown that in the absence of wall suction, a closed-form correlation for the Nusselt number can be derived. Finally, it is shown that the dimensionless entropy generation due to heat transfer,NT, increases with an increasing suction parameterSw, whereas the dimensionless entropy generation due to liquid film flow friction,NF, decreases.

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27

Aghajani, Delavar, Mousa Farhadi, and Kurosh Sedighi. "Effect of discrete heater at the vertical wall of the cavity over the heat transfer and entropy generation using LBM." Thermal Science 15, no. 2 (2011): 423–35. http://dx.doi.org/10.2298/tsci1102423a.

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In this paper Lattice Boltzmann Method (LBM) was employed for investigation the effect of the heater location on flow pattern, heat transfer and entropy generation in a cavity. A 2D thermal lattice Boltzmann model with 9 velocities, D2Q9, is used to solve the thermal flow problem. The simulations were performed for Rayleigh numbers from 103 to 106 at Pr = 0.71. The study was carried out for heater length of 0.4 side wall length which is located at the right side wall. Results are presented in the form of streamlines, temperature contours, Nusselt number and entropy generation curves. Results show that the location of heater has a great effect on the flow pattern and temperature fields in the enclosure and subsequently on entropy generation. The dimensionless entropy generation decreases at high Rayleigh number for all heater positions. The ratio of averaged Nusselt number and dimensionless entropy generation for heater located on vertical and horizontal walls was calculated. Results show that higher heat transfer was observed from the cold walls when the heater located on vertical wall. On the other hand, heat transfer increases from the heater surface when it located on the horizontal wall.

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28

LIU, WENBIAO, and ZHENG ZHAO. "THE ENTROPY CALCULATED VIA BRICK-WALL METHOD COMES FROM A THIN FILM NEAR THE EVENT HORIZON." International Journal of Modern Physics A 16, no. 23 (September 20, 2001): 3793–803. http://dx.doi.org/10.1142/s0217751x01003524.

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The brick-wall method put forward by 't Hooft has contributed a great deal to the understanding and calculating of the entropy of a black hole. However, there are some drawbacks in it such as little mass approximation, neglecting logarithm terms, and taking the term including L3 as a contribution of the vacuum surrounding the black hole. Moreover, the fundamental problem is why the entropy of scalar field or Dirac field surrounding a black hole is the entropy of the black hole itself. It is well known that the event horizon is the characteristic of a black hole. The entropy calculation of a black hole should be only related to its horizon. Due to this analysis, we improve the brick-wall model by taking that the entropy of a black hole is only contributed by a thin film near the event horizon. This improvement not only gives us a satisfied result, but also avoids the drawbacks in the original brick-wall method. It is found that there is an intrinsic relation between the event horizon and the entropy. We also calculate the entropy of Schwarzschild–de Sitter space–time via the improved method, which can hardly be resolved via the original model.

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29

Mehrez, Zouhaier, Afif El Cafsi, Ali Belghith, and Patrick Le Quéré. "Effect of heated wall position on heat transfer and entropy generation of Cu–water nanofluid flow in an open cavity." Canadian Journal of Physics 93, no. 12 (December 2015): 1615–29. http://dx.doi.org/10.1139/cjp-2014-0388.

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This paper reports the numerical results of the mixed convection and entropy generation of Cu–water nanofluid flow in an open cavity heated from different sides with non-uniform temperature distribution. The finite volume method is used to solve the governing equations. The analysis is carried out by a range of Richardson numbers, 0.01 ≤ Ri ≤ 10, at a nanoparticle volume fraction of 0 ≤ [Formula: see text] ≤ 0.1, and Reynolds number Re = 200, with a cavity aspect ratio of L/H = 2. Three heating modes are considered: (A) the left wall is heated (inflow side, assisting flow); (B) the horizontal bottom wall is heated; and (C) the right wall is heated (outflow side, opposing flow). The results show that the heat transfer and the entropy generation increase with increasing Richardson number and nanoparticle volume fraction. The highest heat transfer and entropy generation are obtained with heating mode C (opposing flow). The contribution of heat transfer and fluid friction irreversibilities in the entropy generation depends on Richardson number and the heater position. The present investigation shows that the configuration with non-isothermal heater located at the bottom wall (B) has the highest performance in terms of heat transfer enhancement with minimum entropy generation.

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30

SHEN, YOU-GEN. "THE FERMIONIC ENTROPY OF SPHERICALLY SYMMETRIC BLACK HOLES." Modern Physics Letters A 15, no. 31 (October 10, 2000): 1901–14. http://dx.doi.org/10.1142/s0217732300002401.

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The free energy and entropy for Dirac field is derived in the general spherically symmetric black hole background, by using 't Hooft's brick wall model. It is found that, in such a black hole background, fermionic entropy is 7/2 times the value of bosonic entropy.

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31

Berrehal, Hamza, Abdelaziz Maougal, and Tasawar Hayat. "Radiation Effect on the Entropy Generation of Carbon Nanotubes Water-Based Nanofluid Flow by a Moving Wedge." Defect and Diffusion Forum 389 (November 2018): 138–52. http://dx.doi.org/10.4028/www.scientific.net/ddf.389.138.

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This paper deals with the effect of thermal radiation on the entropy generation of carbon nanotubes water-based nanofluid flow past a moving wedge. Two different types of nanoparticles, namely single wall carbon nanotube (SWCNT) and multi wall carbon nanotube (MWCNT) are considered. Governing equations of the problem are transformed by similarity method into a set of nonlinear ordinary differential equations (ODEs) and solved analytically using optimal homotopy asymptotic method (OHAM). Expression of entropy generation number is obtained in dimensionless form. Further the analytical results of temperature, Nusselt number, skin friction, entropy generation number and Bejan number are discussed and analyzed through graphs. These results show that the entropy generation number has a minimal value for larger radiation parameter and the negative values of velocity ratio parameter λ, while nanoparticles have influence to increase the entropy production.

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32

Pourmahmoud, Nader, Hosseinali Soltanipour, and Iraj Mirzaee. "The effects of longitudinal ribs on entropy generation for laminar forced convection in a microchannel." Thermal Science 20, no. 6 (2016): 1963–72. http://dx.doi.org/10.2298/tsci130920110s.

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This paper deals with fluid flow, heat transfer and entropy generation in an internally ribbed microchannel. Mass, momentum and energy equations for constant heat flux boundary condition are solved using the finite volume method. Average Nusselt number and Fanning friction factor are reported as a function of rib height at different Reynolds numbers. The effects of non-dimensional rib height, wall heat flux and the Reynolds number on the entropy generation attributed to friction, heat transfer and total entropy generation are explored. The first law indicates that rib height has the great effect on the flow filed and heat transfer. The second law analysis reveals that for any values of Reynolds number and wall heat flux, as rib height grows; the frictional irreversibility increases while, there is a rib height which provides the minimum heat transfer irreversibility. It is found that the optimum rib height with the minimum total entropy generation rate depends on Reynolds number and wall heat flux.

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33

SHEN, YOU-GEN, and DA-MING CHEN. "THE FERMIONIC ENTROPY IN DILATONIC BLACK HOLE BACKGROUND SPACETIME." International Journal of Modern Physics D 10, no. 04 (August 2001): 539–46. http://dx.doi.org/10.1142/s0218271801000871.

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The fermionic free energy and entropy are calculated in Garfinkle–Horowitz–Strominger dilatonic black hole background spacetime, by using 't Hfoot's brick wall model. It turns out that the fermionic entropy in Garfinkle–Horowitz–Strominger dilatonic black hole back ground spacetime is 7/2 times the Bosonic entropy.

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34

A. Carlen, Eric, Maria C. Carvalho, and Amit Einav. "Entropy production inequalities for the Kac Walk." Kinetic & Related Models 11, no. 2 (2018): 219–38. http://dx.doi.org/10.3934/krm.2018012.

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35

Ochab, J. K., and Z. Burda. "Maximal entropy random walk in community detection." European Physical Journal Special Topics 216, no. 1 (January 2013): 73–81. http://dx.doi.org/10.1140/epjst/e2013-01730-6.

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36

Gilbert, T., and J. R. Dorfman. "Entropy production in a persistent random walk." Physica A: Statistical Mechanics and its Applications 282, no. 3-4 (July 2000): 427–49. http://dx.doi.org/10.1016/s0378-4371(00)00082-0.

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37

Di Ilio, G., B. Dorschner, G. Bella, S. Succi, and I. V. Karlin. "Simulation of turbulent flows with the entropic multirelaxation time lattice Boltzmann method on body-fitted meshes." Journal of Fluid Mechanics 849 (June 15, 2018): 35–56. http://dx.doi.org/10.1017/jfm.2018.413.

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We propose a body-fitted mesh approach based on a semi-Lagrangian streaming step combined with an entropy-based collision model. After determining the order of convergence of the method, we analyse the flow past a circular cylinder in the lower subcritical regime, at a Reynolds number$Re=3900$, in order to assess the numerical performances for wall-bounded turbulence. The results are compared to experimental and numerical data available in the literature. Overall, the agreement is satisfactory. By adopting an efficient local refinement strategy together with the enhanced stability features of the entropic model, this method extends the range of applicability of the lattice Boltzmann approach to the solution of realistic fluid dynamics problems, at high Reynolds numbers, involving complex geometries.

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38

Semenov, Semen N., and Martin E. Schimpf. "Comparative Examination of Nonequilibrium Thermodynamic Models of Thermodiffusion in Liquids." Proceedings 46, no. 1 (November 17, 2019): 14. http://dx.doi.org/10.3390/ecea-5-06680.

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We analyze existing models for material transport in non-isothermal non-electrolyte liquid mixtures that utilize non-equilibrium thermodynamics. Many different sets of equations for material have been derived that, while based on the same fundamental expression of entropy production, utilize different terms of the temperature- and concentration-induced gradients in the chemical potential to express the material flux. We reason that only by establishing a system of transport equations that satisfies the following three requirements can we obtain a valid thermodynamic model of thermodiffusion based on entropy production, and understand the underlying physical mechanism: (1) Maintenance of mechanical equilibrium in a closed steady-state system, expressed by a form of the Gibbs–Duhem equation that accounts for all the relevant gradients in concentration, temperature, and pressure and respective thermodynamic forces; (2) thermodiffusion (thermophoresis) is zero in pure unbounded liquids (i.e., in the absence of wall effects); (3) invariance in the derived concentrations of components in a mixture, regardless of which concentration or material flux is considered to be the dependent versus independent variable in an overdetermined system of material transport equations. The analysis shows that thermodiffusion in liquids is based on the entropic mechanism.

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39

Fattahi, Abolfazl, Ebrahim Rahmani, Nader Karimi, and S. Mostafa Hosseinalipour. "On the decay of entropic-compositional sources of indirect noise in combustors." INTER-NOISE and NOISE-CON Congress and Conference Proceedings 265, no. 2 (February 1, 2023): 5167–78. http://dx.doi.org/10.3397/in_2022_0750.

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For nearly half a century, indirect combustion noise in gas turbine combustors was entirely attributed to entropy waves, as the convecting hot spots. However, recent studies identified another source of indirect noise called compositional waves, which consists of convecting chemical blobs. Understanding the evolution of this new source during its journey throughout the combustor requires attention due to the unknown physics of the turbulent, heat transferring flow in which it moves. In the current study, a hot chemical blob including a mixture of combustion products is introduced at the channel inlet. During its convection along the channel, degeneration of various thermal and chemical components of the entropic-compositional wave is investigated in the frequency domain using large-eddy simulations. It is shown that the wave annihilation due to wall cooling, as found in real combustors, can exceed those imposed by the flow hydrodynamics. Through a coherence analysis, it is found that mixture fraction is mainly responsible for deteriorating the chemical sources and that the contribution of potential function is comparatively smaller. Overall, it is concluded that compared to entropy waves, compositional waves are up to 20% more prone to decay.

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40

Dajani, Karma, and Ronald Meester. "Random entropy and recurrence." International Journal of Mathematics and Mathematical Sciences 2003, no. 47 (2003): 2977–88. http://dx.doi.org/10.1155/s0161171203212217.

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We show that a cocycle, which is nothing but a generalized random walk with index setℤd, with bounded step sizes is recurrent whenever its associated random entropy is zero, and transient whenever its associated random entropy is positive. This generalizes a well-known one-dimensional result and implies a Polya type dichotomy for this situation.

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41

Solimene, Raffaele, and Antonietta D'Alterio. "Entropy-Based Clutter Rejection for Intrawall Diagnostics." International Journal of Geophysics 2012 (2012): 1–7. http://dx.doi.org/10.1155/2012/418084.

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The intrawall diagnostic problem of detecting localized inhomogeneities possibly present within the wall is addressed. As well known, clutter arising from masonry structure can impair detection of embedded scatterers due to high amplitude reflections that wall front face introduces. Moreover, internal multiple reflections also can make it difficult ground penetrating radar images (radargramms) interpretation. To counteract these drawbacks, a clutter rejection method, properly tailored on the wall features, is mandatory. To this end, here we employ a windowing strategy based on entropy measures of temporal traces “similarity.” Accordingly, instants of time for which radargramms exhibit entropy values greater than a prescribed threshold are “silenced.” Numerical results are presented in order to show the effectiveness of the entropy-based clutter rejection algorithm. Moreover, a comparison with the standard average trace subtraction is also included.

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42

Vyas, Paresh, and Ashutosh Ranjan. "Entropy Analysis for MHD Generalised Couette Flow in a Composite Duct." Journal of Industrial Mathematics 2015 (March 4, 2015): 1–10. http://dx.doi.org/10.1155/2015/895046.

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This paper presents entropy analysis of electrically conducting Newtonian fluid flow inside a horizontal composite duct. The upper impermeable wall of the duct moves with a uniform velocity while the lower wall is porous strata of finite thickness with impermeable bottom. The upper wall and the impermeable bottom are at constant temperature but at different temperatures. The duct is divided into two regions: Region I of clear fluid and Region II of fluid saturated porous layer. Momentum and thermal regimes for clear and porous regions are matched at clear fluid-porous interface by employing suitable matching conditions. The governing equations are solved analytically. Analytical solutions obtained for velocity and temperature are utilized to compute entropy generation. The effects of pertinent parameter on temperature distribution, entropy generation, and Bejan number are portrayed graphically and discussed.

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43

Ortín, Tomás, and David Pereñíguez. "Magnetic charges and Wald entropy." Journal of High Energy Physics 2022, no. 11 (November 15, 2022). http://dx.doi.org/10.1007/jhep11(2022)081.

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Abstract Using Wald’s formalism, we study the thermodynamics (first laws and Smarr formulae) of asymptotically-flat black holes, rings etc. in a higher-dimensional higher-rank generalization of the Einstein-Maxwell theory. We show how to deal with the electric and magnetic charges of the objects and how the electric-magnetic duality properties of the theory are realized in their thermodynamics.

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44

Bodendorfer, N., and Y. Neiman. "Wald entropy formula and loop quantum gravity." Physical Review D 90, no. 8 (October 31, 2014). http://dx.doi.org/10.1103/physrevd.90.084054.

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45

Gómez-Fayrén, Carmen, Patrick Meessen, Tomás Ortín, and Matteo Zatti. "Wald entropy in Kaluza-Klein black holes." Journal of High Energy Physics 2023, no. 8 (August 9, 2023). http://dx.doi.org/10.1007/jhep08(2023)039.

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Abstract We study the thermodynamics of the 4-dimensional electrically charged black-hole solutions of the simplest 5-dimensional Kaluza-Klein theory using Wald’s formalism. We show how the electric work term present in the 4-dimensional first law of black-hole thermodynamics arises in the purely gravitational 5-dimensional framework. In particular, we find an interesting geometric interpretation of the 4-dimensional electrostatic potential similar to the angular velocity in rotating black holes. Furthermore, we show how the momentum map equation arises from demanding compatibility between the timelike Killing vector of the black-hole solution and the spatial Killing vector of the 5-dimensional background.

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46

Saha, Arunabha. "General theory of large D membranes consistent with second law of thermodynamics." Journal of High Energy Physics 2021, no. 4 (April 2021). http://dx.doi.org/10.1007/jhep04(2021)152.

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Abstract We write down the most general membrane equations dual to black holes for a general class of gravity theories, up to sub-leading order in 1/D in large D limit. We derive a “minimal” entropy current which satisfies a local form of second law from these membrane equations. We find that consistency with second law requires the membrane equations to satisfy certain constraints. We find additional constraints on the membrane equations from the existence of membrane solutions dual to stationary black holes. Finally we observe a tension between second law and matching with Wald entropy for dual stationary black hole configurations, for the minimal entropy current. We propose a simple modification of the membrane entropy current so that it satisfies second law and also the stationary membrane entropy matches the Wald entropy.

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47

Hollands, Stefan, Áron D. Kovács, and Harvey S. Reall. "The second law of black hole mechanics in effective field theory." Journal of High Energy Physics 2022, no. 8 (August 25, 2022). http://dx.doi.org/10.1007/jhep08(2022)258.

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Abstract We investigate the second law of black hole mechanics in gravitational theories with higher derivative terms in the action. Wall has described a method for defining an entropy that satisfies the second law to linear order in perturbations around a stationary black hole. We show that this can be extended to define an entropy that satisfies the second law to quadratic order in perturbations, provided that one treats the higher derivative terms in the sense of effective field theory. We also address some outstanding issues with Wall’s method, in particular its gauge invariance and its relation to the Iyer-Wald entropy.

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48

Tetradis, Nikolaos. "De Sitter entropy as holographic entanglement entropy." SciPost Physics Proceedings, no. 4 (August 13, 2021). http://dx.doi.org/10.21468/scipostphysproc.4.002.

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We review the results of refs. [1,2], in which the entanglement entropy in spaces with horizons, such as Rindler or de Sitter space, is computed using holography. This is achieved through an appropriate slicing of anti-de Sitter space and the implementation of a UV cutoff. When the entangling surface coincides with the horizon of the boundary metric, the entanglement entropy can be identified with the standard gravitational entropy of the space. For this to hold, the effective Newton's constant must be defined appropriately by absorbing the UV cutoff. Conversely, the UV cutoff can be expressed in terms of the effective Planck mass and the number of degrees of freedom of the dual theory. For de Sitter space, the entropy is equal to the Wald entropy for an effective action that includes the higher-curvature terms associated with the conformal anomaly. The entanglement entropy takes the expected form of the de Sitter entropy, including logarithmic corrections.

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49

Campos Delgado, Ruben. "Quantum gravitational corrections to the entropy of a Reissner–Nordström black hole." European Physical Journal C 82, no. 3 (March 2022). http://dx.doi.org/10.1140/epjc/s10052-022-10232-0.

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AbstractStarting from an effective action for quantum gravity, we calculate the quantum gravitational corrections to the Wald entropy of a four dimensional non-extremal Reissner–Nordström (RN) black hole in the limit of small electric charge, generalising a previous calculation carried out by Calmet and Kuipers (Phys Rev D 104(6):066012, 2021) for a Schwarzschild black hole. We show that, at second order in the Ricci curvature, the RN metric receives quantum corrections which shift the classical position of the event horizon. We apply the Wald entropy formula by integrating over the perimeter of the quantum corrected event horizon. We then compute the quantum gravitational corrections to the temperature and the pressure of the black hole.

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50

Liu, Hai-Shan, and H. Lü. "A note on Kerr/CFT and Wald entropy discrepancy in high derivative gravities." Journal of High Energy Physics 2021, no. 7 (July 2021). http://dx.doi.org/10.1007/jhep07(2021)213.

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Abstract We examine the Kerr/CFT correspondence in Einstein gravity extended with quadratic curvature invariants. We consider two explicit examples in four and five dimensions and compute the central charges of the asymptotic symmetry algebras of the near horizon geometries, using the improved version of the BBC formalism that encompasses the information of the Lagrangian. We find that the resulting Cardy entropy differs from the Wald entropy, caused by the Riemann-squared RμνρσRμνρσ term.

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