We consider classes of translationally invariant black hole solutions whose equations of state closely resemble that of QCD at zero chemical potential. We use these backgrounds to compute the ratio zeta/s of bulk viscosity to entropy density. For a class of black holes that exhibits a first order transition, we observe a sharp rise in zeta/s near T_c. For constructions that exhibit a smooth cross-over, like QCD does, the rise in zeta/s is more modest. We conjecture that divergences in zeta/s for black hole horizons are related to extrema of the entropy density as a function of temperature.
In higher dimensions, we study Degenerate-Higher-Order-Scalar-Tensor theories and we derive solutions that resemble the Schwarzschild Anti-de Sitter black holes. We compute their thermodynamic quantities following the Wald formalism, satisfying the First Law of Thermodynamics and a higher dimensional Smarr relation. Constructing a Noether charge with a suitable choice of a space-like Killing vector, we obtain the shear viscosity of the non-gravitational dual field theory, where for a suitable choice of the couplings functions, the Kovtun-Son-Starinets bound is violated. These results are corro…
In higher dimensions, we explore planar hairy black hole configurations for a special subclass of the Horndeski theory, defined by two coupling functions depending on the kinetic term and enjoying shift symmetry and reflection symmetry. For this analysis, we derive a set of new solutions, given by time-dependent as well as time independent scalar field configurations. Additionally, we calculate their thermodynamic quantities by using Wald formalism, satisfying the First Law of Thermodynamics as well as a Smarr relation. Together with the above, the Wald procedure allows us to compute the shear…
A finite temperature extension of the effective holographic models for QCD (EHQCD), proposed in Ref.[1], is investigated in the present work. EHQCD models are characterized by two parameters, the conformal dimension of the relevant operator that deforms the CFT and the associated coupling. We find that black hole solutions appear at temperatures higher than some temperature $T_{min}$ and can be categorized in two classes: large and small black holes. A large black hole is thermally stable and it is therefore interpreted as the gravity dual of a non-conformal plasma. A small black hole, on the …
We extend an earlier investigation of the thermodynamics of static black holes in an Einstein-Horndeski theory of gravity coupled to a scalar field, by including now an elec- tromagnetic field as well. By studying the two-parameter families of charged static black holes, we obtain much more powerful constraints on the thermodynamics since, unlike in the uncharged one-parameter case, now the right-hand side of the first law is not automatically integrable. In fact, this allows us to demonstrate that there must be an additional contribution in the first law, over and above the usual terms expect…
A relativistic version of the rational extended thermodynamics of polyatomic gases based on a new hierarchy of moments that takes into account the total energy composed by the rest energy and the energy of the molecular internal mode is proposed. The moment equations associated with the Boltzmann-Chernikov equation are derived, and the system for the first $15$ equations is closed by the procedure of the maximum entropy principle and by using an appropriate BGK model for the collisional term. The entropy principle with a convex entropy density is proved in a neighborhood of equilibrium state, …
In nonzero magnetic field, the magnetic properties and thermodynamics of the quantum-chromodynamic (QCD) matter is studied in the hadron resonance gas and the Polyakov linear-sigma models and compared with recent lattice calculations. Both models are fairly suited to describe the degrees of freedom in the hadronic phase. The partonic ones are only accessible by the second model. It is found that the QCD matter has paramagnetic properties, which monotonically depend on the temperature and are not affected by the hadron-quark phase-transition. Furthermore, raising the magnetic field strength inc…
We develop analytic techniques to construct the leading dissipative terms in a derivative expansion of holographic fluids. Our basic ingredient is the Crnkovic-Witten symplectic current of classical gravity which we use to extract the dissipative transport coefficients of holographic fluids, assuming knowledge of the thermodynamics and the near horizon geometries of the bulk black hole geometries. We apply our techniques to non-conformal neutral fluids to reproduce previous results on the shear viscosity and generalise a known expression for the bulk viscosity.
We study in detail the thermodynamics of the quantum chromodynamics (QCD) matter utilizing two different statistics, extensive and non-extensive. The thermodynamics such as (pressure, number density, energy density , entropy and magnetization) are determined from both statistics at zero and non-zero magnetic field, eB = 0; 0:2; 0:3GeV^2. The magnetic field effect appears by adding a vacuum contribution to the free energy along side the thermal contribution. The extensive thermodynamics can be emerged from the resonance hadron gas model which is incorporated in the present work. Accordingly, we…
The interest in the thermodynamics of supersymmetric Yang-Mills started after Maldacena proposed the duality between string theory on AdS backgrounds and the large-N limit of SYM theories. One of the motivations to study the thermal properties of ${\cal N}=4$ supersymmetric Yang-Mills in four dimensions (SYM$_{4,4}$) is that at high temperatures, the weak-coupling limit of this theory has many similarities with high temperature quantum chromodynamics (QCD). In this proceedings contribution, we review recent calculations of the resummed perturbative free energy of ${\cal N}=4$ supersymmetric Ya…
We consider thermodynamic properties of a quark-gluon plasma related to quasiparticles having the internal structure. For this purpose, we employ a possible analogy between quantum chromodynamics and non-Abelian Proca-Dirac-Higgs theory. The influence of characteristic sizes of the quasiparticles on such thermodynamic properties of the quark-gluon plasma like the internal energy and pressure is studied. Sizes of the quasiparticles are taken into account in the spirit of the van der Waals equation but we take into consideration that the quasiparticles have different sizes, and the average value…
In this paper, we analyze the effects of thermal fluctuations on a STU black hole. We observe that these thermal fluctuations can affect the stability of a STU black hole. We will also analyze the effects of these thermal fluctuations on the thermodynamic of STU black hole. Furthermore, in the Jacobson formalism such a modification will produce a deformation of the geometry of the STU black hole. Hence, we use the AdS/CFT correspondence to analyze the effect of such a deformation on the dual quark-gluon plasma. So, we explicitly analyze the effect of thermal fluctuations on the shear viscosity…
Previously, the Einstein equation has been described as an equation of state, general relativity as the equilibrium state of gravity, and $f({\cal R})$ gravity as a non-equilibrium one. We apply Eckart's first order thermodynamics to the effective dissipative fluid describing scalar-tensor gravity. Surprisingly, we obtain simple expressions for the effective heat flux, "temperature of gravity", shear and bulk viscosity, and entropy density, plus a generalized Fourier law in a consistent Eckart thermodynamical picture. Well-defined notions of temperature and approach to equilibrium, missing in …
We study the equilibrium and near-equilibrium properties of a holographic five-dimensional model consisting of Einstein gravity coupled to a scalar field with a non-trivial potential. The dual four-dimensional gauge theory is not conformal and, at zero temperature, exhibits a renormalisation group flow between two different fixed points. We quantify the deviations from conformality both in terms of thermodynamic observables and in terms of the bulk viscosity of the theory. The ratio of bulk over shear viscosity violates Buchel's bound. We study relaxation of small-amplitude, homogeneous pertur…
The thermodynamics of quantum chromodynamics at low temperatures and in sufficiently strong magnetic fields is governed by neutral pions. We analyze the interacting system of neutral pions and photons at zero baryon chemical potential using effective field theory. As a consequence of the axial anomaly and the external magnetic field, the pions and photons mix with one another. The resulting spectrum contains one usual, relativistic photon state, and two nonrelativistic modes, one of which is gapless and the other gapped. Furthermore, we calculate the leading, one-loop contribution to the press…
Soon after the formulation of Quantum Chromodynamics in 1972 its regularization on Euclidean space-time lattices had been introduced by Kenneth Wilson. This paved ground for numerical studies of non-perturbative aspects of QCD, first shown by Michael Creutz. Ever since these first lattice QCD calculations the exploration of the QCD phase diagram and the thermodynamics of strong-interaction matter at non-zero temperature and density was pursued vigorously. In this brief review I try to highlight some of the results on QCD thermodynamics obtain during the last 42 years through lattice QCD calcul…
We show how a Hall viscosity induced by a magnetic field can be generated in strongly coupled theories with a holographic dual. This is achieved by considering parity-breaking higher derivative terms in the gravity dual. These terms couple the Riemann curvature tensor to the field strength of a gauge field dual to the charge current, and have an analog in the field theory side as a coupling between the "Euler current" and the electromagnetic field. As a concrete example, we study the effect of the new terms in the thermodynamic and transport properties of a strongly coupled magnetized plasma d…
Thermodynamics of the Heisenberg XXX chain with negative spin
Institute of Modern Physics, Northwest University（西北大学现代物理研究所）；C.N. Yang Institute for Theoretical Physics, Stony Brook University（纽约州立大学石溪分校杨振宁理论物理研究所）
