Quantum fluctuations and thermal dissipation in higher derivative gravity

We construct a proof of the second law of thermodynamics in an arbitrary diffeomorphism invariant theory of gravity working within the approximation of linearized dynamical fluctuations around stationary black holes. We achieve this by establishing the existence of an entropy current defined on the horizon of the dynamically perturbed black hole in such theories. By construction, this entropy current has non-negative divergence, suggestive of a mechanism for the dynamical black hole to approach a final equilibrium configuration via entropy production as well as the spatial flow of it on the null horizon. This enables us to argue for the second law in its strongest possible form, which has a manifest locality at each space-time point. We explicitly check that the form of the entropy current that we construct in this paper exactly matches with previously reported expressions computed considering specific four derivative theories of higher curvature gravity. Using the same set up we also provide an alternative proof of the physical process version of the first law applicable to arbitrary higher derivative theories of gravity.

Thermodynamics of five-dimensional Schwarzschild Anti-de Sitter (SAdS) and SdS black holes in the particular model of higher derivative gravity is considered. The free energy, mass (thermodynamical energy) and entropy are evaluated. There exists the parameters region where BH entropy is zero or negative. The arguments are given that corresponding BH solutions are not stable. We also present the FRW-equations of motion of time (space)-like branes in SAdS or SdS BH background. The properties of dual CFT are discussed and it is shown that it has zero Casimir energy when BH entropy (effective gravitational constant) is zero. The Cardy-Verlinde formula for CFT dual to SAdS or SdS BH is found in the universal form.

Thermodynamics of black holes in anti de Sitter (AdS) spacetimes typically contains critical points in the phase diagram, some of which correspond to the first order transition ending in a second order one. Following the recent proposal in [arXiv:2112.01706] on using Duan's $\phi$-mapping theory, we classify the critical points of six dimensional charged Gauss-Bonnet black holes in AdS spacetime. We find that the higher derivative corrections from Gauss-Bonnet gravity do not change the topological class of critical points in charged black holes in AdS, unlike the case of Born-Infeld corrections noted earlier. The connection between the topological nature of critical points and existence of first order phase transitions breaks down in a certain parameter regime. A resolution is proposed by treating the novel and conventional critical points as phase creation and phase annihilation points, respectively. Examples are provided to support the proposal.

We figure out the explicit expression for the trace of the field equations associated to generic higher derivative theories of gravity endowed with Lagrangians depending upon the metric and its Riemann tensor, together with arbitrary order covariant derivatives of the Riemann tensor. Then an equality linking the Lagrangian density with the covariant divergence of a vector field is put forward in terms of the trace of the field equations. As a significant application, we particularly concentrate on a broad range of higher derivative theories of gravity with the Lagrangian density constructed from the contraction of the product for metric tensors with the product of the Riemann tensors and the arbitrary order covariant derivatives of the Riemann tensor. By utilizing the trace for the equations of motion, such a type of Lagrangian density is expressed as the covariant divergence of a vector field.

Quantum fluctuations at absolute zero may push a system into a different phase or state. The 'quantum critical point' at which this happens in certain materials has now been probed in greater detail.

A quantum critical point (QCP) is currently being conjectured for the BaFe2(As1−xPx)2 system at the critical value xc ≈ 0.3. In the proximity of a QCP, all thermodynamic and transport properties are expected to scale with a single characteristic energy, given by the quantum fluctuations. Such a universal behavior has not, however, been found in the superconducting upper critical field Hc2. Here we report Hc2 data for epitaxial thin films extracted from the electrical resistance measured in very high magnetic fields up to 67 Tesla. Using a multi-band analysis we find that Hc2 is sensitive to the QCP, implying a significant charge carrier effective mass enhancement at the doping-induced QCP that is essentially band-dependent. Our results point to two qualitatively different groups of electrons in BaFe2(As1−xPx)2. The first one (possibly associated to hot spots or whole Fermi sheets) has a strong mass enhancement at the QCP, and the second one is insensitive to the QCP. The observed duality could also be present in many other quantum critical systems.

The superconductor-insulator transition (SIT) is an excellent example of a quantum phase transition at zero temperature, dominated by quantum fluctuations. These are expected to be very prominent close to the quantum critical point. So far, most of the experimental studies of the SIT have concentrated on transport properties and tunneling experiments that provide indirect information on criticality close to the transition. Here we present an experiment uniquely designed to study the evolution of quantum fluctuations through the quantum critical point. We utilize the Nernst effect, which has been shown to be effective in probing superconducting fluctuation. We measure the Nernst coefficient in amorphous indium oxide films tuned through the SIT and find a large signal on both the superconducting and the insulating sides, which peaks close to the critical point. The transverse Peltier coefficient α_{xy}, which is the thermodynamic quantity extracted from these measurements, follows quantum critical scaling with critical exponents ν∼0.7 and z∼1. These exponents are consistent with a clean X-Y model in 2+1 dimensions.

Quantum liquid, in the form of a self-bound droplet, is stabilized by a subtle balance between the mean-field contribution and quantum fluctuations. While a liquid-gas transition is expected when such a balance is broken, it remains elusive whether liquid-gas critical points exist in the quantum regime. Here, we study the quantum criticality in a binary Bose mixture undergoing the liquid-gas transition. We show that, beyond a narrow stability window of the self-bound liquid, a liquid-gas coexistence persists, which eventually transits into a homogeneous mixture. Importantly, we identify two distinct critical points where the liquid-gas coexistence terminates. These critical points are characterized by rich critical behaviors in their vicinity, including divergent susceptibility, unique phonon-mode softening, and enhanced density correlations. The liquid-gas transition and the critical points can be readily explored in ultracold atoms confined to a box potential. Our work highlights the thermodynamic approach as a powerful tool in revealing the quantum liquid-gas criticality, and paves the way for further studies of critical phenomena in quantum liquids.

Quantum critical phenomena are widely studied across various materials families, from high-temperature superconductors to magnetic insulators. They occur when a thermodynamic phase transition is suppressed to zero temperature as a function of some tuning parameter such as pressure or magnetic field. This generally yields a point of instability—a so-called quantum critical point—at which the phase transition is driven exclusively by quantum fluctuations. Here, we show that the heavy fermion metamagnet UTe2 possesses a quantum phase transition at extreme magnetic field strengths of over 70 T. Rather than terminating at one singular point, we find that the phase boundary is sensitive to magnetic field components in each of the three Cartesian axes of magnetic field space. This results in the transition surface being bounded by a continuous ring of quantum critical points, the locus of which forms an extended line of quantum criticality—a novel form of quantum critical phase boundary. Within this quantum critical line sits a magnetic field-induced superconducting state in a toroidal shape, which persists to fields over 70 T. We model our data by a phenomenological free energy expansion and show how a quantum critical line—rather than a more conventional singular point of instability—anchors the remarkable high magnetic field phase landscape of UTe2. Published by the American Physical Society 2025

We study the greybody factor of charged hairy black holes (BHs) that arise due to the presence of an axion coupled to the electromagnetic field. Specifically, we consider spin-0 and spin-1 test particles propagating in the background of BHs with axion hair, where the spacetime geometry is modified compared to that of the Reissner-Nordstrom (RN) BH. In contrast to the RN solution, with a given total BH charge, the effective potential for test particles depends on the ratio of electric to magnetic charges. In other words, charged BHs with axion hair breaks the electric-magnetic duality present in the RN solution. We compute the transmission coefficient of test particles plunging into the charged hairy BH and find that the deviation from the RN solution is particularly evident for higher multipole moments. Precise measurements of greybody factors can thus serve as probes for the possible existence of axions coupled to the electromagnetic field, as well as potential signatures of magnetic monopoles.

We study the thermodynamics and the chemical potential for a five-dimensional charged AdS black hole by treating the cosmological constant as the number of colors $N$ in the boundary gauge theory and its conjugate quantity as the associated chemical potential $\mu$. It is found that there exists a small-large black hole phase transition. The critical phenomena are investigated in the $N^{2}$-$\mu$ chart. In particular, in the reduced parameter space, all the thermodynamic quantities can be rescaled with the black hole charge such that these reduced quantities are charge-independent. Then we obtain the coexistence curve and the phase diagram. The latent heat is also numerically calculated. Moreover, the heat capacity and the thermodynamic scalar are studied. The result indicates that the information of the first-order black hole phase transition is encoded in the heat capacity and scalar. However, the phase transition point cannot be directly calculated with them. Nevertheless, the critical point linked to a second-order phase transition can be determined by either the heat capacity or the scalar. In addition, we calculate the critical exponents of the heat capacity and the scalar for the saturated small and large black holes near the critical point.

We study static spherically symmetric solutions of Einstein gravity plus an action polynomial in the Ricci scalar, $R$, of arbitrary degree, $n$, in arbitrary dimension, $D$. The global properties of all such solutions are derived by studying the phase space of field equations in the equivalent theory of gravity coupled to a scalar field, which is obtained by a field redefinition and conformal transformation. The following uniqueness theorem is obtained: provided that the coefficient of the $R^2$ term in the Lagrangian polynomial is positive then the only static spherically symmetric asymptotically flat solution with a regular horizon in these models is the Schwarzschild solution. Other branches of solutions with regular horizons, which are asymptotically anti-de Sitter, or de Sitter, are also found. An exact Schwarzschild-de Sitter type solution is found to exist in the $R+aR^2$ if $D>4$. If terms of cubic or higher order in $R$ are included in the action, then such solutions also exist in four dimensions. The general Schwarzschild-de Sitter type solution for arbitrary $D$ and $n$ is given. The fact that the Schwarzschild solution in these models does not coincide with the exterior solution of physical bodies such as stars has important physical implications which we discuss. As a byproduct, we classify all static spherically symmetric solutions of $D$-dimensional gravity coupled to a scalar field with a potential consisting of a finite sum of exponential terms.

In this paper, new electrically charged asymptotically flat black hole solutions are numerically derived in the context of higher derivative gravity. These solutions can be interpreted as generalizations of two different classes of non-charged asymptotically flat spacetimes: Schwarzschild and non-Schwarzschild solutions. Extreme black hole solutions and black holes with negative mass were found.

The behaviour of the finite-temperature C-function, defined by Neto and Fradkin (1993 Nucl. Phys. B 400 525), is analysed within a d -dimensional exactly solvable lattice model, recently considered by Vojta (1996 Phys. Rev. B 53 710), which is of the same universality class as the quantum nonlinear O(n) sigma model in the limit n. The scaling functions of C for the cases d = 1 (absence of long-range order), d = 2 (existence of a quantum critical point), d = 4 (existence of a line of finite-temperature critical points that ends up with a quantum critical point) are derived and analysed. The locations of regions where C is monotonically increasing (which depend significantly on d) are exactly determined. The results are interpreted within the finite-size scaling theory that has to be modified for d = 4.

In this paper, we devote to investigate the energy-momentum problem of higher dimensional black holes in the general theory of relativity. The energy and momentum complex of Moller has been used for the calculations. Also, total energy and total momentum of some special cases for higher dimensional black holes such as Schwarzschild-like black holes, Reissner-Nordstrom-like charged black holes, AdS-like black holes, topological black holes, BTZ-like and charged BTZ-like black holes were obtained. It is invented that the momentum of black holes vanishes everywhere while the energy of black holes are not equal to zero in higher dimension. Also the results agree with Yang and Radinschi or Vagenas results in three and four dimensional black holes, respectively (Jang and Radinschi in AIP Conf. Proc. 895, 325, 2007; Vagenas in Mod. Phys. Lett. A 21, 1947, 2006).