Restricted Phase Space Research Articles

Restricted Phase Space Thermodynamics of NED-AdS Black Holes

Abstract We study the Restricted Phase Space Thermodynamics (RPST) of magnetically charged Anti de Sitter (AdS) black holes sourced by nonlinear electrodynamics(NED). The first law and the corresponding Euler relation are examined using the scaling properties. While the mass is homogeneous in the first order, the intensive variables are observed to follow zeroth order homogeneity. We use numerical and graphical techniques to find the critical points of the various thermodynamic quantities. By utilizing the re-scaling properties of the equation of states, we study the thermodynamic processes using different pairs of variables. From our analysis, we infer that although the RPS thermodynamics of NED-AdS black hole resembles those of RN-AdS, Kerr-AdS, Kerr-Sen-Ads black holes in most of its aspects, hinting at a possible universality, there exists one particular μ − C process that differs in its behaviour from its counterparts in earlier reported works.

Topology of charged AdS black hole in restricted phase space* *Supported by the National Natural Science Foundation of China (12075143, 12375050), and the Natural Science Foundation of Shanxi Province, China (202203021221209, 202303021211180)

The local topological properties of black hole systems can be expressed through winding numbers as defects. To date, AdS black hole thermodynamics are often depicted by the dual parameters of in the extended phase space, while there have been several studies on the black hole thermodynamics in the restricted phase space. In this paper, we analyze the topological properties of charged AdS black holes in the restricted phase space under the higher-dimension and higher-order curvature gravity frame. The results show that the topological number of the charged black hole in the same canonical ensembles is a constant and is independent of the concrete dual thermodynamical parameters. However, the topological number in the grand canonical ensemble is different from that in the canonical ensemble for the same black hole system. Furthermore, these results are independent of dimension d and highest order k of the Lanczos-Lovelock densities.

Thermodynamics of charged AdS black hole surrounded by quintessence in restricted phase space

Thermodynamics of charged AdS black hole surrounded by quintessence in restricted phase space

Exploring critical behavior of thermodynamic variables of the Kerr-Newman-AdS black hole in the restricted phase space

The present work investigates the thermodynamic properties of the four-dimensional Kerr-Newmann-AdS black hole, utilizing the recently proposed framework of restricted phase space thermodynamics. This approach introduces a novel set of paired thermodynamic variables; the central charge (C) of the corresponding dual conformal field theory and the chemical potential (μ). Through rigorous analysis, we establish fundamental relationships, including the Euler relation, Gibbs-Duhem relation, and the zeroth-order homogeneity of intensive variables. Furthermore, numerical techniques are employed to explore thermodynamic processes between the conjugate variables in canonical and grand canonical ensembles. Our investigation reveals first-order and second-order phase transitions across various macroscopic processes. Despite the absence of complete analytical expressions, our findings unveil striking similarities in behavior between Reissner-Nordström-Anti-de Sitter and Kerr-anti–de Sitter, underscoring the presence of underlying universality within the restricted phase space thermodynamics formalism. Published by the American Physical Society 2024

Bulk-boundary and RPS thermodynamics from topology perspective

In this study, we investigate the bulk-boundary and restricted phase space (RPS) thermodynamics of Rissner-Nordström (R-N) AdS and 6-dimensional charged Gauss-Bonnet AdS black holes. Additionally, we examine the topological characteristics of the considered black holes and compare them with the results of extended thermodynamics. We determine that the topological behavior of the bulk-boundary thermodynamics is the same as that of the extended thermodynamics, whereas the RPS thermodynamics exhibits a distinct behavior. Furthermore, we demonstrate that within the RPS formalism, there is only one critical point with a topological charge of +1 . Moreover, in the RPS formalism, the inclusion of higher-derivative curvature terms in the form of Gauss-Bonnet gravity does not alter the topological classification of critical points in charged AdS black holes.

Barrow entropy and AdS black holes in RPS thermodynamics

In this paper, we examine the restricted phase space (RPS) thermodynamics for charged AdS black holes by considering the impact of quantum gravity on the event horizon area. The primary aim of this work is to elucidate the influence of quantum gravitational effects on thermodynamic behaviors, critical phenomena, phase transitions, and the stability of black holes. We observe that charged AdS black holes exhibit thermodynamic behavior similar to that of Van der Waals fluids when influenced by quantum gravity. Furthermore, we introduce a novel black hole thermodynamic phenomenon, which we term “resistance of phase transitions”. Our study uncovers a violation of the homogeneity property of the Smarr relation in RPS thermodynamics due to the effects of quantum gravity.

Thermodynamics for regular black holes as intermediate thermodynamic states and quasinormal frequencies

The thermodynamics for regular black holes (RBHs) is considered under the restricted phase space (RPS) formalism. It is shown that the RPS formalism seems to hold for RBHs, however, in order for the extensive thermodynamic parameters to be independent from each other, the RBHs need to be viewed as intermediate thermodynamic states in a larger class of black holes (BHs) which admit both regular and singular states. This idea is checked for several classes of BHs. In particular, for the electrically charged Hayward class BHs, it is shown that the regular states can either be thermodynamically stable or unstable, depending on the amount of charges carried by the BHs. The quasinormal frequencies for the Hayward class BHs are also analyzed, and it turns out that, even for the thermodynamically unstable regular states, the dynamic stability still holds, at least under massless scalar perturbations.

Thermodynamic topology of black holes from bulk-boundary, extended, and restricted phase space perspectives

In this article, we investigate the thermodynamic topology of some black holes, namely AdS Reissner Nordstrom (R–N), AdS Einstein–Gauss–Bonnet (EGB), and AdS Einstein-power-Yang–Mills (EPYM), from different frameworks: bulk-boundary (BB) and restricted phase space (RPS). Using the generalized off-shell Helmholtz free energy method, we calculate the thermodynamic topology of the selected black holes in each space separately and determine their topological classifications. We show that the addition of GB terms, dimensions, and other factors do not affect the topological classes of black holes in both spaces. The calculations and plots indicate that the AdS R–N and AdS EGB black holes show similar behavior and their topological numbers sets in both spaces, i.e., BB and RPS, are similar and equal to (W=+1). However, AdS EPYM black holes show an interesting behavior. In addition to BBT and RPS, we also consider the extended phase space thermodynamics (EPST) and evaluate the thermodynamic topology for AdS EPYM black hole. The changing (r−τ) in both spaces shows similar behavior. Also, the topological number and the total topological numbers for this black hole in the BB, RPS and EPS thermodynamics are completely same, i,e., (ωBBT=ωRPS=ωEPST=+1,−1) or WBBT=WRPS=WEPST=0. An important point is that the Einstein–Yang–Mills black hole has thermodynamic topology equivalence in three spaces. The present result may be due to the non-linear YM charge parameter and the difference between the gauge and gravity corrections in the above black holes.

Topological black holes in Einstein-Maxwell and 4D conformal gravities revisited

The thermodynamics of charged topological black holes (TBHs) with different horizon geometries in d-dimensional Einstein-Maxwell and 4-dimensional conformal gravities is revisited using the restricted phase space formalism. The concept of subsystems for black holes is introduced, which enables a precise description for the thermodynamic behaviors of (non-compact) black holes with infinitely large horizon area. The concrete behaviors can be different for TBHs in the same underlying theory but with different horizon geometries, or for those with the same horizon geometry but from different underlying theories. The high and low temperature limits of the TBHs are also considered, and the high temperature limits behave universally as low temperature phonon gases. Finally, using the concept of subsystems, some conceptual issues in the description for thermal fluctuations in black hole systems are clarified, and the relative thermal fluctuations for finite subsystems are also analyzed in some detail.

Thermodynamics of Kerr-Sen-AdS black holes in the restricted phase space

Thermodynamics of Kerr-Sen-AdS black holes in the restricted phase space

4D-EGB black holes in RPS thermodynamics

In this paper, we study thermodynamics of charged and uncharged 4-Dimension Einstein-Gauss–Bonnet (4D-EGB) black holes. The context of this study is the Visser’s holographic thermodynamics with a fixed anti-de Sitter radius and a variable Newton constant known as restricted phase space thermodynamics (RPST). Our setup is constructed by using the AdS/CFT correspondence and by introducing a conjugate quantity of the Gauss–Bonnet parameter. By this ansatz, we conclude that the Gauss–Bonnet action multiplied by a temperature, behaves as a free energy. We derive the conjugate quantities corresponding to the first law in the RPST formalism. The study of the T−S processes and the effect of the Gauss–Bonnet constant, α, show that thermodynamic properties of charged black holes depend on the Gauss–Bonnet term and the charge of black holes. For an uncharged black holes, the effect of Gauss–Bonnet becomes crucial, as it behaves as a charged black hole with an effective charge. Finally, we find that the Hawking-Page phase transition occurs between a large black hole and a thermal AdS space.

Restricted phase space thermodynamics of charged AdS black holes in conformal gravity* *Supported by the National Natural Science Foundation of China (12275138)

The thermodynamics of charged spherically symmetric AdS black holes in conformal gravity is revisited using the recently proposed restricted phase space (RPS) formalism. This formalism avoids all the bizarreness arising in the extended phase space formalism for this model. It is found that the charged AdS black holes in this model may belong to a new universality class that is different from all previously studied cases under the RPS formalism. Besides the distinguished isocharge and isothermal behaviors, the absence of the Hawking-Page transition is another notable feature. However, in the high temperature limit, the thermodynamic behavior of the present model becomes exactly the same as that of the Einstein gravity and black hole scan models, which adds further evidence for the universality of the recently reported correspondence between high temperature AdS black holes and low temperature quantum phonon gases in nonmetallic crystals.

High temperature AdS black holes are low temperature quantum phonon gases

We report a precise match between the high temperature (D+2)-dimensional Tangherlini-AdS black hole and the low temperature quantum phonon gas in D-dimensional nonmetallic crystals residing in (D+1)-dimensional flat spacetime. The match is realized by use of the recently proposed restricted phase space formalism for black hole thermodynamics, and the result can be viewed as a novel contribution to the AdS/CMT correspondence on a quantitative level.

RPS thermodynamics of Taub–NUT AdS black holes in the presence of central charge and the weak gravity conjecture

We study the thermodynamics of the Taub–NUT AdS black holes by Visser’s holographic method using AdS radius as a constant parameter under the restricted phase space approach. Instead of the variables P and V, we deal with the central charge and also chemical potential as a unique couple of conjugate thermodynamic variables. We study some interesting properties of the Taub–NUT black holes e.g. supercritical phase equilibrium in the $$T-S$$ processes, $$Q-\Phi $$ and the Hawking-Page phase transition in the $$\mu -C$$ processes. As a consequence, the consistency of the weak gravity conjecture of multi-charge for Taub–NUT-AdS black holes at critical points is proved. We conclude that in the presence of the central charge and assuming $$C=\frac{3}{8}\ell ^2$$ , weak gravity conjecture could be satisfied in the Taub–NUT-AdS black holes with $${\hat{n}}\ll 1$$ .

Restricted Phased Space Thermodynamics for Black Holes in Higher Dimensions and Higher Curvature Gravities.

The recently proposed restricted phase space thermodynamics is shown to be applicable to a large class of higher dimensional higher curvature gravity models coupled to Maxwell field, which are known as black hole scan models and are labeled by the spacetime dimension d and the highest order k of the Lanczos-Lovelock densities appearing in the action. Three typical example cases with and are chosen as example cases and studied in some detail. These cases are representatives of Einstein-Hilbert, Chern-Simons and Born-Infield like gravity models. Our study indicates that the Einstein-Hilbert and Born-Infield like gravity models have similar thermodynamic behaviors, e.g., the existence of isocharge phase transitions with the same critical exponents, the existence of isovoltage transitions and the Hawking-Page like transitions, and the similar high temperature asymptotic behaviors for the isocharge heat capacities, etc. However, the Chern-Simons like -model behaves quite differently. Neither isocharge nor isovoltage transitions could occur and no Hawking-Page like transition is allowed. This seems to indicate that the Einstein-Hilbert and Born-Infield like models belong to the same universality class while the Chern-Simons like models do not.

Restricted phase space thermodynamics for AdS black holes via holography

A new formalism for thermodynamics of AdS black holes called the restricted phase space thermodynamics (RPST) is proposed. The construction is based on top of Visser’s holographic thermodynamics, but with the AdS radius fixed as a constant. Thus the RPST is free of the (P, V) variables but inherits the central charge and chemical potential as a new pair of conjugate thermodynamic variables. In this formalism, the Euler relation and the Gibbs–Duhem equation hold simultaneously with the first law of black hole thermodynamics, which guarantee the appropriate homogeneous behaviors for the black hole mass and the intensive variables. The formalism is checked in detail in the example case of four-dimensional Reissner–Nordström anti-de Sitter black hole in Einstein–Maxwell theory, in which some interesting thermodynamic behaviors are revealed.

Thermodynamics of Kerr-AdS black holes in the restricted phase space

The thermodynamics for Kerr-AdS black hole in four dimensions is revisited using the recently proposed restricted phase space formalism, which includes the central charge C of the dual CFT and the chemical potential mu , but excludes the pressure and the conjugate volume, as thermodynamic variables. The Euler relation holds automatically, and the first order homogeneity of the mass and the zeroth order homogeneity of the intensive variables are made explicit. Thermodynamic processes involving each pair of conjugate variables are studied in some detail, with emphasis on the scaling properties of the equations of states. It turns out that the thermodynamic behavior of the Kerr-AdS black hole is very similar to that of the RN-AdS black hole studied earlier. In particular, it is found that, there is a first order supercritical phase equilibrium in the T-S processes at fixed nonvanishing angular momentum, while at vanishing angular momentum or at fixed angular velocities, there is always a non-equilibrium transition from a small unstable black hole state to a large stable black hole state. Moreover, there is a Hawking–Page phase transition in the mu -C processes. Due to the complicatedness of the Kerr metric, the exact critical point and the Hawking–Page temperature are worked out explicitly only in the slow rotating limit, however the characteristic thermodynamic properties do not rely on the slow rotating approximation.

Black hole thermodynamics is extensive with variable Newton constant

Inspired by the recent studies on the thermodynamics of AdS black holes in the restricted phase space formalism, we propose a similar formalism for the thermodynamics of non-AdS black holes with variable Newton constant. It is shown that, by introducing the new variables N,μ, where N is proportional to the inverse Newton constant and μ its conjugate variable, referred to as the chemical potential, the black hole thermodynamics can be formulated in a form which is consistent with the standard extensive thermodynamics for open macroscopic systems, with the first law and the Euler relation hold simultaneously. This formalism has profound implications, in particular, the mass is a homogeneous function of the first order in the extensive variables and the intensive variables are zeroth order homogeneous functions. The chemical potential is shown to be closely related to the Euclidean action evaluated at the black hole configuration.

Stronger three-phonon interactions revealed by molecular dynamics in materials with restricted phase space

Utilizing molecular dynamics (MD) simulations based on the highly precise force-fields, we find that phonon scattering strengths induced by the cubic anharmonicity can be significantly underestimated by the perturbation theory (PT) approach in materials with sizable frequency gaps or branch bunching. We trace this result to the additional three-phonon scatterings in MD enabled by the fluctuating phonon energy and the continuous energy exchange between modes. These channels are essential to accurately evaluate the zone-center phonon linewidth in boron arsenide as compared to the experiment and could noticeably lower the lattice thermal conductivity of beryllium telluride and tungsten carbide. Accordingly, due to the stronger three-phonon scatterings, four-phonon scatterings would become less important than previously believed in this type of material. Moreover, our work emphasizes the different phonon scattering processes in MD and PT simulations, offering new insights for an improved description of anharmonic properties.

Relativistic nuclear collisions: Establishing a non-critical baseline for fluctuation measurements

We study the influence of global baryon number conservation on the non-critical baseline of net baryon cumulants in heavy-ion collisions in a given acceptance, accounting for the asymmetry between the mean-numbers of baryons and antibaryons. We derive the probability distribution of net baryon number in a restricted phase space from the canonical partition function that incorporates exact conservation of baryon number in the full system. Furthermore, we provide tools to compute cumulants of any order from the generating function of uncorrelated baryons constrained by exact baryon number conservation. The results are applied to quantify the non-critical baseline for cumulants of net proton number fluctuations obtained in heavy-ion collisions by the STAR collaboration at different RHIC energies and by the ALICE collaboration at the LHC. Furthermore, volume fluctuations are added by a Monte Carlo procedure based on the centrality dependence of charged particle production as measured experimentally. Compared to the predictions based on the hadron resonance gas model or Skellam distribution a clear suppression of fluctuations is observed due to exact baryon-number conservation. The suppression increases with the order of the cumulant and towards lower collision energies. Predictions for net proton cumulants up to the eight order in heavy-ion collisions are given for experimentally accessible collision energies.