Recently, it has been shown that for out-of-equilibrium systems, there are additional constraints on thermodynamical evolution besides the ordinary second law. These form a new family of second laws of thermodynamics, which are equivalent to the monotonicity of quantum Rényi divergences. In black hole thermodynamics, the usual second law is manifest as the area increase theorem. Hence one may ask if these additional laws imply new restrictions for gravitational dynamics, such as for out-of-equilibrium black holes? Inspired by this question, we study these constraints within the AdS/CFT correspondence. First, we show that the Rényi divergence can be computed via a Euclidean path integral for a certain class of excited CFT states. Applying this construction to the boundary CFT, the Rényi divergence is evaluated as the renormalized action for a particular bulk solution of a minimally coupled gravity-scalar system. Further, within this framework, we show that there exist transitions which are allowed by the traditional second law, but forbidden by the additional thermodynamical constraints. We speculate on the implications of our findings.
We show that field equations of some typical modified gravity theories can be recast as thermodynamic first law on dynamical holographic screens. The thermodynamic second law are also presented.
In this paper, we will analyze the connection between the fidelity susceptibility, the holographic complexity and the thermodynamic volume. We will regularize the fidelity susceptibility and the holographic complexity by subtracting the contribution of the background AdS spacetime from the deformation of the AdS spacetime. It will be demonstrated that this regularized fidelity susceptibility has the same behavior as the thermodynamic volume and that the regularized complexity has a very different behavior. As the information dual to different volumes in the bulk would be measured by the fideli…
Carrollian-holographic Derivation of Gravitational Flux-Balance Laws
Centre de Physique Théorique, École polytechnique, Centre National de la Recherche Scientifique – Unité Mixte de Recherche 7644, Institut Polytechnique de Paris（巴黎综合理工学院理论物理中心）；International School for Advanced Studies (SISSA)（国际高等研究院）；Istituto Nazionale di Fisica Nucleare, Sezione di Trieste（意大利国家核物理研究所的里雅斯特分部）；Université de Mons（蒙斯大学）
The near-horizon conformal symmetry of nonextremal black holes is shown to be a mandatory ingredient for the holographic scaling of the scalar-field contribution to the black hole entropy. This conformal tightness is revealed by semiclassical first-principle scaling arguments through an analysis of the multiplicative factors in the entropy due to the radial and angular degrees of freedom associated with a scalar field. Specifically, the conformal SO(2,1) invariance of the radial degree of freedom conspires with the area proportionality of the angular momentum sums to yield a robust holographic…
In this paper, we have investigated the entanglement thermodynamics for $d$-dimensional charged $AdS$ black hole by studying the holographic entanglement entropy in different cases. We have first computed the holographic entanglement entropy in extremal and non-extremal cases in two different regimes, namely, the low temperature and high temperature limits. We then obtain the first law of entanglement thermodynamics for boundary field theory in the low temperature regime in $d$-dimensions.
By following the spirit of Verlinde's entropic force proposal arXiv:1001.0785, we give the differential and integral form of the first law of thermodynamics on the holographic screen enclosing a spherical symmetric black hole. It is consistent with equipartition principle and the form of Komar mass. The entropy of the holographic screen determines its area, i. e. $S=\frac{A}{4}$. And then we express the metric by thermodynamic variables, to give an illustration of how the space is foliated by the thermodynamical potentials.
We derive the Einstein field equations and black hole entropy from the first law of thermodynamics on a holographic time-like screen. Because of the universality of gravity, the stress tensor on the screen must be independent of the details of matter fields, so it should be a pure geometric quantity. For simplicity, we assume that the stress tensor on the screen depends on surface Ricci curvature and extrinsic curvature linearly. Then we prove that the surface stress tensor is just the Brown-York stress tensor plus terms which do not affect the field equations of gravitation and the entropy of…
The thermodynamics of a scheme of dark matter-dark energy interaction is studied considering a holographic model for the dark energy in a flat Friedmann-Lemaitre-Robertson- Walker background. We obtain a total entropy rate for a general horizon and we study the Generalized Second Law of Thermodynamics for a cosmological interaction as a free function. Additionally, we discuss two horizons related to the Ricci and Ricci-like model and its effect on an interacting system.
Gravitational area laws are expected to arise as a result of ignorance of "UV gravitational data". In AdS/CFT, the UV/IR correspondence suggests that this data is dual to infrared physics in the CFT. Motivated by these heuristic expectations, we define a precise framework for explaining bulk area laws (in any dimension) by discarding IR CFT data. In (1+1) boundary dimensions, our prescribed mechanism shows explicitly that the boundary dual to these area laws is strong subadditivity of von Neumann entropy. Moreover, such area laws may be of arbitrary (and mixed) signature; thus our framework gi…
We construct a generalized Smarr formula which could provide a thermodynamic route to derive the covariant field equation of general theories of gravity in dynamic spacetimes. Combining some thermodynamic variables and a new chemical potential conjugated to the number of degree of freedom on the holographic screen, we find a universal Cardy-Verlinde formula and give its braneworld interpretation. We demonstrate that the associated AdS-Bekenstein bound is tighten than the previous expression for multi-charge black holes in the gauged supergravities. The Cardy-Verlinde formula and the AdS-Bekens…
Recently, Verlinde conjectured that gravity may be an entropic force, arising from thermodynamics on the holographic screen. We investigate the implications of the entropic force formalism for inflationary cosmology. We find the background dynamics of inflation can be dually described in the holographic language. At the perturbation level, two kinds of novel scale invariant scalar fluctuations arise from thermal fluctuations on the holographic screen. These fluctuations can be responsible for CMB anisotropy and structure formation.
We study the holographic complexity conjectures for rotating black holes, uncovering a relationship between the complexity of formation and the thermodynamic volume of the black hole. We suggest that it is the thermodynamic volume and not the entropy that controls the complexity of formation of large black holes in both the Complexity Equals Action and Complexity Equals Volume proposals in general. Our proposal reduces to known results involving the entropy in settings where the thermodynamic volume and entropy are not independent, but has broader scope. Assuming a conjectured inequality is ob…
We prove a new, large family of area laws in general relativity, which apply to certain classes of untrapped surfaces that we dub generalized holographic screens. Our family of area laws contains, as special cases, the area laws for marginally-trapped surfaces (holographic screens) and the event horizon (Hawking's area theorem). In addition to these results in general relativity, we show that in the context of holography the geometry of a generalized holographic screen is related to the outer entropy of the screen. Specifically, we show for spherically-symmetric spacetimes that the area of the…
The dynamics of general Lovelock gravity, viewed on an arbitrary spherically symmetric surface as a holographic screen, is recast as the form of some generalized first law of thermodynamics on the screen. From this observation together with other two distinct aspects, where exactly the same temperature and entropy on the screen arise, it is argued that the thermodynamic interpretation of gravity is physically meaningful not only on the horizon, but also on a general spherically symmetric screen.
We have analytically investigated the effects of non-linearity on the free energy and thermodynamic geometry of holographic superconductors in $2+1 -$dimensions. The non-linear effect is introduced by considering the coupling of the massive charged scalar field with Born-Infeld electrodynamics. We then calculate the relation between critical temperature and charge density from two different methods, namely, the matching method and the divergence of the scalar curvature which is obtained by investigating the thermodynamic geometry of the model. The two results are slightly different from numeri…
We introduce a new interpretation of chemical potential and show that holographic entropy is entropy bound, which is supported by two ideal cases discussed in detail. One is sparse but incompressible liquid like a star of uniform density and the other is a screen at infinity in spherically symmetric sapcetime. Our work is based on the new scenario of entropy force and holographic thermodynamics, and the Brown-York quasi-local energy.
We analytically obtain the free energy and thermodynamic geometry of holographic superconductors in $2+1$-dimensions. The gravitational theory in the bulk dual to this $2+1$-dimensional strongly coupled theory lives in the $3+1$-dimensions and is that of a charged $AdS$ black hole together with a massive charged scalar field. The matching method is applied to obtain the nature of the fields near the horizon using which the holographic free energy is computed through the gauge/gravity duality. The critical temperature is obtained for a set of values of the matching point of the near horizon and…
A necessary condition for the validity of the holographic principle is the holographic bound: the entropy of a system is bounded from above by a quarter of the area of a circumscribing surface measured in Planck areas. This bound cannot be derived at present from consensus fundamental theory. We show with suitable {\it gedanken} experiments that the holographic bound follows from the generalized second law of thermodynamics for both generic weakly gravitating isolated systems and for isolated, quiescent and nonrotating strongly gravitating configurations well above Planck mass. These results j…
We review 5D holographic approaches to finite temperature QCD. Thermodynamic properties of the "hard-wall" and the "soft-wall" models are derived. Various non-realistic features in these models are cured by the set-up of improved holographic QCD, that we review here.
We propose a new holographic program of gravity in which we introduce a surface stress tensor. Our proposal differs from Verlinde's in several aspects. First, we use an open or a closed screen, a temperature is not necessary but a surface energy density and pressure are introduced. The surface stress tensor is proportional to the extrinsic curvature. The energy we use is Brown-York energy and the equipartiton theorem is violated by a non-vanishing surface pressure. We discuss holographic thermodynamics of a gas of weak gravity and find a chemical potential, and show that Verlinde's program doe…
The holographic bound asserts that the entropy $S$ of a system is bounded from above by a quarter of the area ${\cal A}$ of a circumscribing surface measured in Planck areas: $S\leq {\cal A}/4{\ell^2_P}$. This bound is widely regarded a desideratum of any fundamental theory. Moreover, it was argued that the holographic bound is necessary for the validity of the generalized second law (GSL) of thermodynamics. However, in this work we explicitly show that hyperentropic systems (those violating the holographic entropy bound) do exist in higher-dimensional spacetimes. We resolve this apparent viol…
By respecting the conformal symmetry of the dual CFT, and treating the conformal factor of the AdS boundary as a thermodynamic parameter, we formulate the holographic first law that is exactly dual to the first law of extended black hole thermodynamics with variable cosmological constant but fixed Newton's constant.
We obtain the thermodynamic geometry of a (2+1) dimensional strongly coupled quantum field theory at a finite temperature in a holographic set up, through the gauge/gravity correspondence. The bulk dual gravitational theory is described by a (3+1) dimensional charged AdS black hole in the presence of a massive charged scalar field. The holographic free energy of the (2+1) dimensional strongly coupled boundary field theory is computed analytically through the bulk boundary correspondence. The thermodynamic metric and the corresponding scalar curvature is then obtained from the holographic free …
Standard thermodynamic treatments of quantum field theory in the presence of black-hole backgrounds reproduce the black hole entropy by usually specializing to the leading order of the heat-kernel or the high-temperature expansion. By contrast, this work develops a hybrid framework centered on geometric spectral asymptotics whereby these assumptions are shown to be unwarranted insofar as black hole thermodynamics is concerned. The approach--consisting of the concurrent use of near-horizon and heat-kernel asymptotic expansions--leads to a proof of the holographic scaling of the entropy as a uni…
We present a careful study of accelerating black holes in anti-de Sitter spacetime, formulating the thermodynamics and resolving discrepancies that have appeared in previous investigations of the topic. We compute the dual stress-energy tensor for the spacetime and identify the energy density associated with a static observer at infinity. The dual energy-momentum tensor can be written as a three-dimensional perfect fluid plus a non-hydrodynamic contribution with a universal coefficient which is given in gauge theory variables. We demonstrate that both the holographic computation and the method…
Using the holographic model for spontaneous symmetry breaking, we study some properties of the dual superfluid such as the thermodynamic exponents, Joule-Thomson coefficient, compressibility etc. Our focus is on how these properties vary with the scaling dimension and the charge of the operator that undergoes condensation.
We argue that the relativistic Unruh temperature cannot be associated with the bits on the screen, in the form considered by Verlinde. The acceleration $a$ is a scalar quantity (the modulus of the acceleration four vecor) and not a vector. When the mass $m$ approaches the holographic screen, viewed as a stretched horizon, the shift $Δx$ from Verlinde's Eq. (3.15) becomes $c^{2}/a$ and the entropy variation equals $(1/2) k_{B} ΔN$, in accordance with Gao's calculations. Using the Heisenberg Principle we show that the energy on the causal horizon (viewed as a holographic screen) of an inertial o…
By the assumption that the thermodynamics second law is valid, we study the possibility of $ω=-1$ crossing in interacting holographic dark energy model. Depending on the choice of the horizon and the interaction, the transition from quintessence to phantom regime and subsequently from phantom to quintessence phase may be possible. The second transition avoids the big rip singularity. We compute the dark energy density at transition time and show that by choosing appropriate parameters we can alleviate the coincidence problem.
In this work, we formulate a Non-Commutative (NC) extension of AdS-CFT correspondence that is manifested in the modification of behavior of a holographic superconductor. The noncommutativity is introduced in the model through the NC corrected AdS charged black hole metric developed by Nicolini, Smailagic and Spallucci. First of all we discuss thermodynamic properties of this black hole in Euclidean formalism. In particular, we compute trace of the boundary energy-momentum tensor which, as expected, is non-zero due to the NC scale introduced in the model. Our findings indicate that the non-comm…
It is well known that entropy can be used to holographically establish a connection between geometry, thermodynamics and information theory. In this paper, we will use complexity to holographically establish a connection between geometry, thermodynamics and information theory. Thus, we will analyse the relation between holographic complexity, fidelity susceptibility, and thermodynamics in extended phase space. We will demonstrate that fidelity susceptibility (which is the informational complexity dual to a maximum volume in AdS) can be related to the thermodynamical volume (which is conjugate …
For a general maximally symmetric (spherically, plane or hyperbola symmetric) holographic screen, we rewrite the equations of motion of general Lovelock gravity into the form of some generalized first law of thermodynamics, under certain ansatz. With this observation together with other two independent ways, exactly the same temperature and entropy on the screen are obtained. So it is argued that the thermodynamic interpretation of gravity is physically meaningful not only on the horizon, but also on a general maximally symmetric screen. Moreover, the formula of entropy is further checked in t…
In the present paper we consider the interacting holographic model of dark energy to investigate the validity of the generalized second laws of thermodynamics in non-flat (closed) universe enclosed by the event horizon measured from the sphere of the horizon named $L$. We show that for $L$ as the system's IR cut-off the generalized second law is respected for the special range of the deceleration parameter.
In this work, we have analytically analyzed the insulator/superconductor phase transition in the presence of a 5-dimensional $AdS$ soliton background using matching method and thermodynamic geometry approach. We have first employed the matching method to obtain the critical chemical potential. We then move on to investigate the free energy and thermodynamic geometry of this model in 3+1 dimensions. This investigation of the thermodynamic geometry leads to the critical chemical potential of the system from the condition of the divergence of the scalar curvature. We have then compared the value …
We explore the thermodynamics of AdS$_5$ black holes in two models: i) an improved holographic QCD model with a simple dilaton potential, and ii) the Stückelberg model in 5D. In the former case, by applying techniques of singular perturbation theory, we obtain a resummation of the naive expansion at high temperatures, providing a good fit to the lattice data for the trace anomaly. In the latter, we find a solution of the equations of motion by considering an expansion in the conformal dimension of the current associated to the gauge field.
The area of a future holographic screen increases monotonically. Associating this area with entropy results in a generalized second law for Cosmology (GSLC). Unlike black hole horizons, screens relevant to Cosmology have no thermodynamical interpretation. We suggest relating the entropy of the screens to spacetime degrees of freedom surface density derived from a (seemingly) phase space. This construction enables us to identify the entropy of any holographic screen as the entropy detected by accelerating observers due to their acceleration. Using Unruh's temperature and the equivalence princip…
Using a reasonable choice in normalizing the timelike Killing vector, we investigate the thermodynamic properties of charged accelerating Anti-de Sitter (AdS) black holes. We find that the expression of the thermodynamic mass in the first law of thermodynamics displays an inextricably intertwining behavior with the charge due to the unusual asymptotic structure of the accelerating black holes. Meanwhile, the thermodynamic length as a potential conjugate to the varying cosmic string tension is introduced and analyzed in detail, and the possible phase behavior of the charged accelerating black h…
A holographic model of probe quarkonia is presented, where the dynamical gravity-dilaton background is adjusted to the thermodynamics of 2 +1 flavor QCD with physical quark masses. The quarkonia action is modified to account for a systematic study of the heavy-quark mass dependence. We focus on the $J/ψ$ and $Υ$ spectral functions and relate our model to heavy quarkonia formation as a special aspect of hadron phenomenology in heavy-ion collisions at LHC.
The thermodynamic Euler equation for high-energy states of large-$N$ gauge theories is derived from the dependence of the extensive quantities on the number of colors $N$. This Euler equation relates the energy of the state to the temperature, entropy, number of degrees of freedom and its chemical potential, but not to the volume or pressure. In the context of the gauge/gravity duality we show that the Euler equation is dual to the generalized Smarr formula for black holes in the presence of a negative cosmological constant. We also match the fundamental variational equation of thermodynamics …
The holographic entanglement entropy of an infinite strip subsystem on the asymptotic AdS boundary is used as a probe to study the thermodynamic instabilities of planar R-charged black holes (or their dual field theories). We focus on the single-charge AdS black holes in $D=5$, which correspond to spinning D3-branes with one non-vanishing angular momentum. Our results show that the holographic entanglement entropy indeed exhibits the thermodynamic instability associated with the divergence of the specific heat. When the width of the strip is large enough, the finite part of the holographic ent…
We study the first law of thermodynamics in IR modified Hǒrava-Lifshitz spacetime. Based on the Bekenstein-Hawking entropy, we obtain the integral formula and the differential formula of the first law of thermodynamics for the Kehagias-Sfetsos black hole by treating $ω$ as a new state parameter and redefining a mass that is just equal to $M_{ADM}$ obtained by Myung\cite{YSM2} if we take $α=3π/8$.
We explore the thermodynamics of a black-hole solution in improved holographic QCD with a simple dilaton potential having two parameters. By applying techniques of singular perturbation theory, we get uniform approximations for the metric and the dilaton field in the two regimes of big and small black-holes. These techniques lead to a resummation of the naive expansion at high temperatures, providing an important theoretical improvement with respect to previous results in the literature. By using this technique, it is shown how a quadratic dependence at low enough temperatures can naturally ap…
Generalized second law of thermodynamics in the Bianchi type I universe with the generalized holographic Ricci dark energy model is studied in this paper. The behavior of dark energy's equation of state parameter indicates that it is matter-like in the early time of the universe but phantom-like in the future. By analysing the evolution of the deviations of state parameter and the total pressure of the universe, we find that for an anisotropic Bianchi type I universe, it transits from a high anisotropy stage to a more homogeneous stage in the near past. Using the normal entropy given by Gibbs'…
The cosmological Friedmann equation sourced by the trace anomaly of a conformal field theory that is dual to the five-dimensional Schwarzschild-AdS geometry can be derived from the first law of thermodynamics if the apparent horizon of the boundary spacetime acquires a logarithmically-corrected Bekenstein-Hawking entropy. It is shown that such a correction to the entropy can arise when the generalized uncertainty principle (GUP) is invoked. The necessary condition for such a thermodynamic derivation directly relates the GUP parameter to the conformal anomaly. It is consistent with the existenc…
Einstein gravities in general dimensions coupled to a cosmological constant and extended with quadratic curvature invariants admit a variety of black holes that may asymptote to Minkowski, anti-de Sitter or Lifshitz spacetimes. We adopt the Wald formalism to derive an explicit formula for calculating the thermodynamical first law for the static black holes with spherical/toric/hyperbolic isometries in these theories. This allows us to derive/rederive the first laws for a wide range of black holes in literature. Furthermore, we construct many new exact solutions and obtain their first laws.
We have considered a cosmological model of holographic dark energy interacting with dark matter and another unknown component of dark energy of the universe. We have assumed two interaction terms $Q$ and $Q'$ in order to include the scenario in which the mutual interaction between the two principal components (i.e., holographic dark energy and dark matter) of the universe leads to some loss in other forms of cosmic constituents. Our model is valid for any sign of $Q$ and $Q'$. If $Q<Q'$, then part of the dark energy density decays into dark matter and the rest in the other unknown energy densi…
We study the thermodynamics of a self-gravitating system of neutral fermions at finite temperature and analyze its backreaction in an asymptotically AdS space. We evaluate numerically the free entropy as a function of temperature, and perform a stability analysis applying the simple and powerful graphical method referred as the Katz criterion. We found that for highly-enough degenerate fermionic solutions, the onset of thermodynamic instability arises, though prior to the turning point on the mass as a function of the central density. Our results for finite temperature fermions provide a novel…
We study thermodynamics of flat space/boson star systems enclosed in a scalar reflecting box with St$\ddot{u}$ckelberg mechanism. We also disclose effects of model parameters on transitions and the properties appear to be qualitatively the same as those in holographic St$\ddot{u}$ckelberg transitions. Moreover, we obtain a relation $\barζ\thickapprox 2 \tildeζ$ and the second order characteristic exponent, which also hold in holographic superconductor theories. The similarity between quasi-local thermodynamic transitions and holographic transitions provides additional evidences that holographi…
We consider the brane universe in the bulk background of the topological Reissner-Nordström de Sitter black holes. We show that the thermodynamic quantities (including entropy) of the dual CFT take usual special forms expressed in terms of Hubble parameter and its time derivative at the moment, when the brane crosses the black hole horizon or the cosmological horizon. We obtain the generalized Cardy-Verlinde formula for the CFT with an charge and cosmological constant, for any values of the curvature parameter $k$ in the Friedmann equations.
A new conception is proposed in Ref.\cite{Verlinde:2010hp,Padmanabhan:2009kr} that gravity is one kind of entropic force. In this letter, we try to discuss its applications to the modified gravities by using three different corrections to the area law of entropy which are derived from the quantum effects and extra dimensions. According to the assumption of holographic principle, the number of bits $N$ which is related to the equipartition law of energy is modified. Then, the modified law of Newton's gravity and the modified Friedmann equations are obtained by using the new notion. By choosing …
In this paper we study the Wiedemann-Franz laws for transport in 2+1 dimensions, and the action of $Sl(2,\mathbb{Z})$ on this transport, for theories with an AdS/CMT dual. We find that $Sl(2,\mathbb{Z})$ restricts the RG-like flow of conductivities and that the Wiedemann-Franz law is $\bar L =\barκ/(Tσ)=cg_4^2π/3$, from the weakly coupled} gravity dual. In a self-dual theory this value is also the value of $L =κ/(Tσ)$ in the weakly coupled field theory description. Using the formalism of a 0+1 dimensional effective action for both generalized $SYK_q$ models and the $AdS_4$ gravity dual, we cal…
This dissertation investigates thermodynamic, emergent and holographic aspects of gravity in the context of causal diamonds. We obtain a gravitational first law for causal diamonds in maximally symmetric spacetimes and argue that these diamonds are in thermodynamic equilibrium at negative temperature. Further, gravitational field equations, including higher curvature corrections, are derived from an equilibrium condition on the generalized entropy of small maximally symmetric diamonds. Finally, we assign three holographic microscopic quantities to causal diamonds in spherically symmetric space…
Using the solution phase space method, we investigate the thermodynamics of black holes in Einstein-aether-Maxwell theory, for which the traditional Wald method (covariant phase space method) fails. We show the first laws of thermodynamics and definitive entropy expressions at both Killing and universal horizons for some examples of exact black hole solutions, including 3-dimensional static charged quasi-BTZ black hole, two 4-dimensional static charged black holes and 3-dimensional rotating solution. At Killing horizons the entropies are exactly one quarter of the horizon area, but at universa…
