Basic Thermodynamic Quantities Research Articles

Dimensionally continued black holes sourced by a conformally coupled scalar field and Chaplygin-like dark fluid

In this paper, we study the higher dimensional black holes of Lovelock gravity coupled with a conformal scalar field. The matter source of gravity is suggested to come from the Chaplygin-like dark fluid, i.e., the hybrid of a dark matter and dark energy. We primarily focus on dimensionally continued gravity where the coupling parameters are reduced into two independent parameters, i.e., the Newtonian and cosmological constants. In this specific case of Lovelock gravity, we derive the metric function that describes the hairy black holes surrounded by dark fluid. For these objects, the basic thermodynamic quantities are worked out. We discuss how the unified dark fluid affects both local and global thermodynamic stabilities. We also demonstrate that the radiation spectrum is proportional to the change in entropy of the hairy black holes. Lastly, the hairy black holes in the presence of Chaplygin-like dark fluid are briefly investigated within the context of generic Lovelock gravity.

Calculating the classical virial expansion using automated algebra.

Using schematic model potentials, we calculate exactly the virial coefficients of a classical gas up to sixth order and use them to calculate the virial expansion of basic thermodynamic quantities such as pressure, density, and compressibility. At sufficiently strong couplings, as expected, the virial expansion fails to converge. However, at least for the interactions and parameter ranges we explored, we find that Padé-Borel resummation methods are very effective in improving the convergence of the expansion.

Effect of modified gravity on the Hawking evaporation of charged AdS black holes

We study the impact of rainbow and Einstein bumblebee modified theories of gravity on the Hawking evaporation process of the black holes. After evaluating the basic thermodynamical quantities, we find out impact parameter b = (angular momentum )/(energy of the emitted particles), which control the emission of the particles and the photon orbit of the black hole in modified theories of gravity. We utilize the well-known Stefan-Boltzmann law to obtain the relationship of black hole mass M against its lifetime t. The numerical results of black hole mass versus lifetime t show that initially the mass of black hole in modified gravity decreases rapidly and later evaporation process becomes slower when temperature reduces to zero. The black hole requires huge time to fully evaporate which is consistent result with 3rd law of thermodynamics for black holes. We observe that increasing values of AdS length l increases evaporation time and increasing value of rainbow parameter η results in slowing down the evaporation process. Moreover, we analyze that uncharged black holes evaporate quickly as compared to charged black hole and black hole in higher dimensions required huge time to fully evaporate as compared to black hole in small dimensions.

Quasitopological electromagnetism, conformal scalar field and Lovelock black holes

In this work, we present the new higher dimensional dyonic black hole solutions of the Lovelock-scalar gravity coupled with quasitopological electromagnetism. First, we concentrate on the dimensionally continued gravity and construct the solution that describes the dyonic black holes with conformal scalar hair in diverse dimensions. We study the physical properties and discuss the effects of the quasitopological electromagnetism and conformal scalar field on the local thermodynamic stability of these dimensionally continued black holes. Next, we derive the solutions that describe the conformal hairy black holes of the Gauss–Bonnet and third order Lovelock gravities in the presence of quasitopological electromagnetism. The basic thermodynamic quantities of these black holes are calculated as well.

Machine learning interatomic potentials for aluminium: application to solidification phenomena

In studying solidification process by simulations on the atomic scale, the modeling of crystal nucleation or amorphization requires the construction of interatomic interactions that are able to reproduce the properties of both the solid and the liquid states. Taking into account rare nucleation events or structural relaxation under deep undercooling conditions requires much larger length scales and longer time scales than those achievable by ab initio molecular dynamics (AIMD). This problem is addressed by means of classical molecular dynamics simulations using a well established high dimensional neural network potential trained on a set of configurations generated by AIMD relevant for solidification phenomena. Our dataset contains various crystalline structures and liquid states at different pressures, including their time fluctuations in a wide range of temperatures. Applied to elemental aluminium, the resulting potential is shown to be efficient to reproduce the basic structural, dynamics and thermodynamic quantities in the liquid and undercooled states. Early stages of crystallization are further investigated on a much larger scale with one million atoms, allowing us to unravel features of the homogeneous nucleation mechanisms in the fcc phase at ambient pressure as well as in the bcc phase at high pressure with unprecedented accuracy close to the ab initio one. In both cases, a single step nucleation process is observed.

МЕТОДИЧНІ ОСОБЛИВОСТІ ВИВЧЕННЯ ОСНОВ ТЕОРІЇ ФЛУКТУАЦІЙ У КУРСІ ТЕОРЕТИЧНОЇ ФІЗИКИ ПЕДАГОГІЧНОГО УНІВЕРСИТЕТУ

The article deals with the theoretical aspects and practical implementation of the author's methodological approach in teaching the basics of fluctuation theory of the course of theoretical physics in Pedagogical University, which is important in the fundamental training of pre-service physics teachers. It is noted that despite the availability of various literary sources, methodological value and originality of the author's approaches in covering the main issues of the course, the need to improve the methodology of its teaching in modern conditions of modernization of higher pedagogical education in the context of European requirements and realities is quite obvious and natural. It is noted that the effective mastery of the basic principles of the theory of fluctuations of theoretical physics, taking into account the principles of fundamentality and professional orientation will contribute to the maximum conciseness of the mathematical apparatus, content compactness, unity, clarity and consistency of teaching material. The author proposes to study the fluctuations of the basic thermodynamic quantities of a macrosystem (energy, volume, density, temperature, entropy, pressure) using two Gibbs lemmas. Molecular scattering of light and its consequences are elucidated according to Rayleigh's law, in conditions when the dimensions of the inhomogeneities of the strucure due to the thermal motion of particles is small in comparison with the wavelength of light. The derivation of the Einstein-Smolukhovsky formula for Brownian motion is proposed according to primary sources with emphasis on the analysis of its physical essence, connection with the second law of thermodynamics, experimental determination based on it in the early twentieth century Boltzmann's constant as a decisive argument in favour of the molecular kinetic theory of the structure of matter and the whole concept of statistical physics. The organization of the educational process on the basis of the methodological approach that was proposed by the author testifies to its effectiveness, which is confirmed by the level of cognitive activity and the results of the final modular control of applicants in recent years. Key words: professional competence of pre-service physics teacher, theoretical physics, theory of fluctuations.

Quantum correlated heat engine in XY chain with Dzyaloshinskii\u2013Moriya interactions

In this paper, we consider a heat engines composed of two interactional qubits with spin-orbit interaction (Dzyaloshinskii–Moriya (DM)) subject to an external magnetic field, so that each qubit is coupled with cold or hot source. One intention of this work is to investigate the following question: is it possible the effects of DM lead to improve basic thermodynamic quantities in this heat engine are coupled to local environments that are not necessarily at equilibrium? Moreover, we study whether or not quantum correlations can be helpful in the performance of quantum work engines. For this end, we investigate the effects of the temperature and the interaction rate of each qubit with its surrounding environment on quantum correlations such as quantum coherence and quantum discord and quantum entanglements, as well as the generated work. Finally we compare three quantum correlations (entanglement, discord, and coherence) with thermodynamic parameters and show that the output work is positive for what values of the magnetic field so that this cycle can be considered as a thermal machine.

Charged black holes in 4D Einstein–Gauss–Bonnet gravity coupled to nonlinear electrodynamics with maximum allowable symmetries

Recently a new model of nonlinear Maxwell electrodynamics which preserves both conformal and SO(2) duality-rotational invariance has been proposed. In this work, we consider this model as a source of gravitational field and study black holes of novel four-dimensional Einstein–Gauss–Bonnet gravity. In this framework we solve the gravitational field equations and work out the metric function that describe a black hole which generalizes the Maxwellian charged black hole of four-dimensional Einstein–Gauss–Bonnet gravity. Some basic thermodynamic quantities corresponding to the new black hole solution are computed and thermodynamic stability as well as thermal phase transitions are investigated.

Nonlinearly charged black holes surrounded by cloud of strings and quintessence in Einstein-Massive gravity

In this work, a new model of double-Logarithmic electrodynamics has been minimally coupled to Einstein-massive gravity and the nonlinearly charged black holes in the presence of quintessential cosmic dark energy and string cloud background are investigated. In this set up, new magnetically charged black hole solution has been derived. Thermodynamics of these black holes are also analyzed and different thermodynamic quantities are computed. Basic thermodynamic quantities such as heat capacity and Hawking temperature have been plotted and the regions corresponding to thermodynamic stability and instability are pointed out. The generalized first law of thermodynamics and the associated Smarr’s relation have also been written down in this context of massive gravity and matter sources. At last, the nonlinearly electrically charged black holes are also briefly studied.

Free energy and entropy for finite temperature quantum field theory under the influence of periodic backgrounds

The basic thermodynamic quantities for a non-interacting scalar field in a periodic potential composed of either a one-dimensional chain of Dirac delta -delta ^prime functions or a specific potential with extended compact support are calculated. First, we consider the representation in terms of real frequencies (or one-particle energies). Then we turn the axis of frequency integration towards the imaginary axis by a finite angle, which allows for easy numerical evaluation, and finally turn completely to the imaginary frequencies and derive the corresponding Matsubara representation, which this way appears also for systems with band structure. In the limit case T rightarrow 0 we confirm earlier results on the vacuum energy. We calculate for the mentioned examples the free energy and the entropy and generalize earlier results on negative entropy.

Black holes and other exact spherical solutions in quadratic gravity

We study static, spherically symmetric vacuum solutions to Quadratic Gravity, extending considerably our previous Rapid Communication [Phys. Rev. D 98, 021502(R) (2018)] on this topic. Using a conformal-to-Kundt metric ansatz, we arrive at a much simpler form of the field equations in comparison with their expression in the standard spherically symmetric coordinates. We present details of the derivation of this compact form of two ordinary differential field equations for two metric functions. Next, we apply analytical methods and express their solutions as infinite power series expansions. We systematically derive all possible cases admitted by such an ansatz, arriving at six main classes of solutions, and provide recurrent formulas for all the series coefficients. These results allow us to identify the classes containing the Schwarzschild black hole as a special case. It turns out that one class contains only the Schwarzschild black hole, three classes admit the Schwarzschild solution as a special subcase, and two classes are not compatible with the Schwarzschild solution at all since they have strictly nonzero Bach tensor. In our analysis, we naturally focus on the classes containing the Schwarzschild spacetime, in particular on a new family of the Schwarzschild-Bach black holes which possesses one additional non-Schwarzschild parameter corresponding to the value of the Bach tensor invariant on the horizon. We study its geometrical and physical properties, such as basic thermodynamical quantities and tidal effects on free test particles induced by the presence of the Bach tensor. We also compare our results with previous findings in the literature obtained using the standard spherically symmetric coordinates.

Thermodynamical properties of bosons and fermions for a lattice motivated dispersion relationship

In this paper we calculate the basic thermodynamical quantities for a system of bosonic simple harmonic oscillators (BSHOs) and the corresponding system of fermionic simple harmonic oscillators (FSHOs) using a dispersion relationship similar to cases in general relativity and condensed matter physics. In the FSHO, we see negative temperatures, and in both cases we obtain finally a system of oscillators with only one effective frequency of vibration. Also we see that pressure is less than zero for T[Formula: see text][Formula: see text][Formula: see text]Tc where Tc is the critical temperature for bosons.

Computational study on thermodynamic properties of Fischer-Tropsch synthesis process

Using the highly accurate G4 method, we computed the thermodynamic data of 1287 possible reaction products under a wide range of reaction conditions in the Fischer-Tropcsh synthesis (FTS) process. These accurate thermodynamic data provide basic thermodynamic quantities for the actual chemical engineering process and are useful in analyzing product distribution because FTS demonstrates many features of an equilibrium-controlled system. Our results show that the number of thermodynamically allowed products to increase when lowering temperature, raising pressure, and raising H2/CO ratio. At low temperature, high pressure and high H2/CO ratio, many products are thermodynamically allowed and the selectivity of product has to be controlled by kinetic factors. On the other hand, high selectivity of lighter products can be realized in thermodynamics by raising temperature and lowering pressure. We found that the equilibrium product yield will reach a maximum and remain unchanged when lowering temperature, raising pressure, and raising H2/CO ratio to some limits, implying that optimizing reaction conditions has no effect on equilibrium product yields beyond these limits. The thermodynamic analysis is also useful in designing and evaluating FTS reaction mechanisms. We found that reaction pathways through formaldehyde should be discarded because of its extremely low equilibrium yield. Recently, in the FTS process using metal-oxide-zeolite catalysts for the highly selective production of C2—C4 olefins and aromatic hydrocarbons, there are several guesses on the possible reaction intermediates entering the zeolite channel. Our results show that ketene, methanol, and dimethyl ether are three possible reaction intermediates.

Structural, mechanical, and thermodynamic properties of R-3m ReB4 under high pressure

The structural, mechanical, and thermodynamic properties of R-3m ReB4 under high pressure were investigated by using the density functional theory in combination with the quasi-harmonic Debye model in this work. The calculated structure parameters and bulk moduli of R-3m ReB4 at zero pressure are in good agreement with previous theoretical data. The calculated single crystal elastic constants and phonon spectra revealed that R-3m ReB4 is mechanically and dynamically stable at least 100 GPa. The pressure dependence of elastic constants and elastic modulus (B, G, and E) have been determined. Based on the obtained elastic modulus, two theoretical models were used to predict the Vickers hardness of R-3m ReB4. Furthermore, through plotting the directional dependent of bulk moduli, Young’s moduli, and shear moduli, the elastic anisotropy has been investigated in detail. Moreover, using the quasi-harmonic Debye model, some basic thermodynamical quantities such as the heat capacity, Gruneisen parameter, and the thermal expansion coefficients of R-3m ReB4 were explored under high temperature and high pressure. The obtained results can provide valuable reference for future synthesis and application R-3m ReB4 material.

Exact Black Holes in Quadratic Gravity with any Cosmological Constant.

We present a new explicit class of black holes in general quadratic gravity with a cosmological constant. These spherically symmetric Schwarzschild-Bach-(anti-)de Sitter geometries, derived under the assumption of constant scalar curvature, form a three-parameter family determined by the black-hole horizon position, the value of the Bach invariant on the horizon, and the cosmological constant. Using a conformal to Kundt metric ansatz, the fourth-order field equations simplify to a compact autonomous system. Its solutions are found as power series, enabling us to directly set the Bach parameter and/or cosmological constant equal to zero. To interpret these spacetimes, we analyze the metric functions. In particular, we demonstrate that for a certain range of positive cosmological constant there are both black-hole and cosmological horizons, with a static region between them. The tidal effects on free test particles and basic thermodynamic quantities are also determined.

On the Electrochemistry of Lipon Breakdown

Solid electrolytes are considered a necessary step for Li-ion ions to surpass the practical limit of 800Wh/L. Next to safety aspects, solid-state electrolytes could enable more compact batteries thus increasing their volumetric storage capacity. A main driver, however, is the potential for solid-electrolytes to increase the electrochemical window to accommodate high voltage positive electrodes (5V cathodes) and stability against metallic lithium as negative electrode. As such, solid-state batteries could enable high energy density through increased cell voltage. Numerous Li-ion conducting solids are known today, however most do not have the broad electrochemical window and stability against lithium yet. Nitrogen doped lithium phosphate glass or LiPON is a well known solid electrolyte material attributed with excellent electrochemical stability above 5V and stable against metallic lithium [1]. However, due to its limited ionic conductivity (~10-6 S/cm) it is only applicable in thin-film batteries for use for medical implants and various sensor systems. It has also been evaluated as solid-electrolyte coatings on electrode particles as buffer layer between active material and the bulk electrolyte. In a thin-film stack, it is an ideal model system for electrochemical study. In this paper, we report on the electrochemistry of RF-sputtered LiPON thin films and studied the out plating of lithium until break down. The LiPON thin-films had ionic conductivities ranging between 1x10-7 and 1x10-6 S/cm [2]. The decomposition potential was calculated from basic thermodynamic quantities and was linked to current-voltage (I-V) measurements with great consistency. The reported I-V measurements were conducted on metal-electrolyte-metal or MEM structures. The decomposition of LiPON was shown to occur at a potential of 4.8 V and proceeds in a diffusion limited way. It could be shown that LiPON breakdown is rather determined by the time needed for the decomposition reactions to complete, rather than being solely driven by the electric field. From the diffusion limited Li-ion current, the Li+ diffusion coefficient was extracted and found to be 2x10-11 cm2/s. This value is in excellent agreement with literature reports [3]. Ultimately hard breakdown was shown by TOF-SIMS imaging experiments and occurs through the formation of metallic lithium filaments. In the present work, we have for the first time formulated a breakdown mechanism for LiPON layers based on experimental measurements and thermodynamic considerations. The presented work provides a detailed evaluation of a solid electrolyte's breakdown and stability using I-V measurements. As such these measurements allow determination of ion transport phenomena as well as of the electrochemical stability window. It can also provide insight in the breakdown mechanism of RRAM devices.

(Compactified) black branes in four dimensional f(R)-gravity

A new family of analytical solutions in a four dimensional static spacetime is presented for f(R)-gravity. In contrast to General Relativity, we find that a non trivial black brane/string solution is supported in vacuum power law f(R)-gravity for appropriate values of the parameters characterizing the model and when axisymmetry is introduced in the line element. For the aforementioned solution, we perform a brief investigation over its basic thermodynamic quantities.

Entangled quantum Otto heat engines based on two-spin systems with the Dzyaloshinski–Moriya interaction

We construct an entangled quantum Otto engine based on spin-1/2 systems undergoing Dzyaloshinski-Moriya (DM) interaction within a varying magnetic field. We investigate the influence of the DM interaction on basic thermodynamic quantities, including heat transfer, work done, and efficiency and find that the DM interaction importantly influences the engine's thermodynamics. We obtain an expression for engine efficiency, finding it to yield the same efficiency for antiferromagnetic and ferromagnetic coupling. A new upper bound, nontrivially consistent with the second law of thermodynamics, is derived for engine efficiency in the case of non-zero DM interaction.

Redefining solubility parameters: Bulk and surface properties from unified molecular descriptors

The central objective of this work is to revisit the development of the widely used solubility parameters and linear solvation energy relationships (LSER) and seek interconnections and possibilities for secure exchange of information. Partial solvation parameters (PSP) are used as the reference concept through which the unification is attempted and extended to surface tension components. Simple expressions are reported interrelating solubility parameters with LSER molecular descriptors. The fundamental differences of the various approaches to hydrogen bonding interactions are discussed in an effort to explain incompatibilities and similarities. Simple QSPR-type expressions are proposed for fast solvent screening and related properties. Predictions of drug solubilities and wetting properties of solid surfaces are reported. The developments are made by having in mind their implementation in a thermodynamic equation-of-state framework for the reliable estimation of all basic thermodynamic quantities of compounds over a broad range of external conditions. The challenges and the perspectives of this unification are critically discussed.

QCD equation of state to O(μB6) from lattice QCD

We calculated the QCD equation of state using Taylor expansions that include contributions from up to sixth order in the baryon, strangeness and electric charge chemical potentials. Calculations have been performed with the Highly Improved Staggered Quark action in the temperature range $T\in [135~{\rm MeV}, 330~{\rm MeV}]$ using up to four different sets of lattice cut-offs corresponding to lattices of size $N_\sigma^3\times N_\tau$ with aspect ratio $N_\sigma/N_\tau=4$ and $N_\tau =6-16$. The strange quark mass is tuned to its physical value and we use two strange to light quark mass ratios $m_s/m_l=20$ and $27$, which in the continuum limit correspond to a pion mass of about $160$ MeV and $140$ MeV espectively. Sixth-order results for Taylor expansion coefficients are used to estimate truncation errors of the fourth-order expansion. We show that truncation errors are small for baryon chemical potentials less then twice the temperature ($\mu_B\le 2T$). The fourth-order equation of state thus is suitable for the modeling of dense matter created in heavy ion collisions with center-of-mass energies down to $\sqrt{s_{NN}}\sim 12$ GeV. We provide a parametrization of basic thermodynamic quantities that can be readily used in hydrodynamic simulation codes. The results on up to sixth order expansion coefficients of bulk thermodynamics are used for the calculation of lines of constant pressure, energy and entropy densities in the $T$-$\mu_B$ plane and are compared with the crossover line for the QCD chiral transition as well as with experimental results on freeze-out parameters in heavy ion collisions. These coefficients also provide estimates for the location of a possible critical point. We argue that results on sixth order expansion coefficients disfavor the existence of a critical point in the QCD phase diagram for $\mu_B/T\le 2$ and $T/T_c(\mu_B=0) > 0.9$.