$$A_0$$-condensation in quark-gluon plasma with finite baryon density

In the present paper, we return to the problem of spontaneous generation of the $$A_0$$ A 0 -background field in QCD at finite temperature and a quark chemical potential, $$\mu $$ μ . On the lattice, this problem was studied by different approaches where an analytic continuation to the imaginary potential $$i \mu $$ i μ has been used. Here we consider both, real and imaginary chemical potential, analytically within the two-loop gauge-fixing independent effective potential $$W_{eff.}$$ W e f f . . We realize the gauge independence in to ways: (1) on the base of Nielsen’s identity and (2) expressing the potential in terms of Polyakov’s loop. Firstly we reproduce the known expressions in terms of Bernoulli’s polynomials for the gluons and quarks. Then, we calculate the $$\mu $$ μ -dependence, either for small $$\mu $$ μ as expansion or numerically for finite $$\mu $$ μ , real and imaginary. One result is that the chemical potential only weakly changes the values of the condensate fields, but quite strongly deepens the minima of the effective potential. We investigate the dependence of Polyakov’s loop in the minimum of the effective potential, thermodynamic pressure and Debye’s mass on the chemical potential. Comparisons with other results are given.

On the Thermodynamics of Gravity Based on the Equivalence of Energy and Mass and Spacetime

Starting from the assumption of equivalence of energy and mass and spacetime, we explain macroscopic and microscopic gravitational phenomena in terms of thermodynamics. Spacetime is quantized by particles with the minimum mass. We call that particle the spacetime particle. Gravity is represented as a thermodynamic pressure caused by spacetime particles. Then we derived the equation of state of spacetime particles. That equation and so on lead us to conclude the following. Dark matter is spacetime particles composing spacetime. The basic mass of the spacetime particle is 1.05×10^(-62) kg. Spacetime structure is represented as the quantized 3-dimensional sphere of Poincare conjecture. An elementary particle is composed of spacetime particles with energy and charged particles with charges, and it has a radius whose rotational speed is the speed of light. Dark energy is a virtual negative mass by the mass reduction of ordinary matter. Before the birth of the universe, spacetime was the imaginary spacetime caused by one black hole, and spacetime was repeatedly created and annihilated. The universe was born by the collapse of that black hole. Inflation was caused by the expansion of individual matter to their radius at superluminal speed.

Hayward black hole heat engine efficiency in anti-de Sitter space

In this paper, we attempt to further study the heat engine efficiency for the regular black hole (BH) with an anti-de Sitter (AdS) background where the working material is the Hayward–AdS (HAdS) BH. In the extended phase space, we investigate the heat engine efficiency of the HAdS BH by defining the cosmological constant as the thermodynamic pressure P and deriving the mechanical work from the PdV terms. Then, we obtain the relation between the efficiency and the entropy/pressure and plot these function figures. Meanwhile, we compare the relation between the HAdS BH with that of the Bardeen–AdS (BAdS) BH, where it is found that the efficiency of the HAdS BH increases with increase in the magnetic charge q in contrast to that of the BAdS BH decrease with increase in the magnetic charge q. We found that the HAdS BH is more efficient than the BAdS BH, and guess that it is related to the BH structure.

Thermodynamics of de Sitter black holes with conformally coupled scalar fields

We investigate the thermodynamic properties of 3+1 dimensional black holes in asymptotically de Sitter spacetimes, conformally coupled to a real scalar field. We use a Euclidean action approach, where boundary value data is specified at a finite radius ‘cavity’ outside the black hole, working in the extended phase space where the cosmological constant is treated as a thermodynamic pressure. We examine the phase structure of these black holes through their free energy. For the MTZ subclass of solutions, we find Hawking-Page-like phase transitions from a black hole spacetime to thermal de Sitter with a scalar field. In the more general case, Hawking-Page-like phase transitions are also present, whose existence depends further on a particular cosmic censorship bound.

Kinetic Simulations of Compressible Non-Ideal Fluids: From Supercritical Flows to Phase-Change and Exotic Behavior

We investigate a kinetic model for compressible non-ideal fluids. The model imposes the local thermodynamic pressure through a rescaling of the particle’s velocities, which accounts for both long- and short-range effects and hence full thermodynamic consistency. The model is fully Galilean invariant and treats mass, momentum, and energy as local conservation laws. The analysis and derivation of the hydrodynamic limit is followed by the assessment of accuracy and robustness through benchmark simulations ranging from the Joule–Thompson effect to a phase-change and high-speed flows. In particular, we show the direct simulation of the inversion line of a van der Waals gas followed by simulations of phase-change such as the one-dimensional evaporation of a saturated liquid, nucleate, and film boiling and eventually, we investigate the stability of a perturbed strong shock front in two different fluid mediums. In all of the cases, we find excellent agreement with the corresponding theoretical analysis and experimental correlations. We show that our model can operate in the entire phase diagram, including super- as well as sub-critical regimes and inherently captures phase-change phenomena.

Black hole solutions and Euler equation in Rastall and generalized Rastall theories of gravity

Focusing on the special case of generalized Rastall theory, as a subclass of the non-minimal curvature-matter coupling theories in which the field equations are mathematically similar to the Einstein field equations in the presence of cosmological constant, we find two classes of black hole (BH) solutions including (i) conformally flat solutions and (ii) non-singular BHs. Accepting the mass function definition and by using the entropy contents of the solutions along with thermodynamic definitions of temperature and pressure, we study the validity of Euler equation on the corresponding horizons. Our results show that the thermodynamic pressure, meeting the Euler equation, is not always equal to the pressure components appeared in the gravitational field equations and satisfies the first law of thermodynamics, a result which in fact depends on the presumed energy definition. The requirements of having solutions with equal thermodynamic and Hawking temperatures are also studied. Additionally, we study the conformally flat BHs in the Rastall framework. The consequences of employing generalized Misner–Sharp mass in studying the validity of the Euler equation are also addressed.

Generalizing Bogoliubov–Zubarev Theorem to Account for Pressure Fluctuations: Application to Relativistic Gas

The problem of pressure fluctuations in the thermal equilibrium state of some objects is discussed, its solution being suggested via generalizing the Bogoliubov–Zubarev theorem. This theorem relates the thermodynamic pressure with the Hamilton function and its derivatives describing the object in question. It is shown that unlike to other thermodynamic quantities (e.g., the energy or the volume) the pressure fluctuations are described not only by a purely thermodynamic quantity (namely, the corresponding thermodynamic susceptibility) but also by some non-thermodynamic quantities. The attempt is made to apply these results to the relativistic ideal gases, with some numerical results being valid for the limiting ultra-relativistic or high-temperature case.