Thermal Equilibrium State Research Articles

Entropy analysis of mixed convective electro-magnetohydrodynamic couple-stress hybrid nanofluid flow with variable electrical conductivity in a porous channel

The paper presents a novel study to examine the irreversibility of quadratically mixed convective electro-magnetohydrodynamic (EMHD) flow of a couple-stress hybrid nanofluid (CSHNF) with variable properties in a vertical porous channel. The channel walls are exposed to an applied electric field effect and a uniform transverse magnetic field. The hybrid nanofluid considered is an ethylene glycol (C 2 H 6 O 2) base mixed with multi-walled carbon nanotubes (MWCNT) and silver (Ag) nanoparticles (NPs), assuming the base fluid and nanoparticles to be in a state of thermal equilibrium following the Tiwari-Das nanofluid model. The potential applications of the study can be in microfluidics to nanofluidics, particularly in developing cooling technologies, EMHD pumps, high-end microelectromechanical systems (MEMS), and lab-on-a-chip (LOC) devices used in bioengineering. A constant pressure gradient acting in the flow direction and the buoyancy effect under the quadratic Boussinesq approximation drive the flow. The governing momentum and energy equations are nondimensionalized using pertinent dimensionless parameters and solved by the semi-analytical homotopy analysis method (HAM). The entropy generation and the Bejan numbers are derived to examine the irreversibilities in the system. To investigate the rate of shear stresses and heat transfer, skin friction coefficients and Nusselt numbers on the channel walls are determined. The analysis emphasizes the influence of nanoparticle concentration and electromagnetic field on the flow dynamics, temperature distribution, and system irreversibilities in the presence of porous media. It reveals the enhancement of fluid velocity and temperature degradation for higher concentrations. In contrast, both reduce for higher magnetic and electrical strength. With the enhancement of electrical joule heating and quadratic convection, a higher entropy generation rate is attained with a low rate of heat transfer irreversibility. However, it reduces with higher nanoparticle concentration, electrical strength, porosity, and variable electrical conductivity parameters under the dominance of heat transfer irreversibility.

The impact of quantum correlations on parameter estimation in a spin reservoir

We study the impact of quantum correlations existing within the system-environment thermal equilibrium state while estimating the parameters of the spin reservoir. By employing various physical situations of interest, we present results for the reservoir temperature and its coupling strength with the central two-level system. The central system (probe) interacts with the bunch of randomly oriented spin systems and attains a thermal equilibrium state. We consider a projective measurement which prepares the probe’s initial state, and then the global system (probe and reservoir) evolves unitarily. The reduced density operator encapsulates the information about the spin reservoir which can be extracted by doing measurements on the probe. The precision of such measurement is quantified by quantum Fisher information. We repeat this process if the probe-reservoir initial state is not correlated (product state). We compare the estimation results for both with and without the outturn of initial correlations. In the temperature estimation case, our results are promising as one can significantly improve the accuracy of the estimates by including the effect of initial correlations. A similar trend prevails in the case of coupling strength estimation especially at low temperatures.

Time evolutions of information entropies in a one-dimensional Vlasov–Poisson system

A one-dimensional Vlasov–Poisson system is considered to elucidate how the information entropies of the probability distribution functions of the electron position and velocity variables evolve in the Landau damping process. Considering the initial condition given by the Maxwellian velocity distribution with the spatial density perturbation in the form of the cosine function of the position, we derive linear and quasilinear analytical solutions that accurately describe both early and late time behaviors of the distribution function and the electric field. The validity of these solutions is confirmed by comparison with numerical simulations based on contour dynamics. Using the quasilinear analytical solution, the time evolutions of the velocity distribution function and its kurtosis indicating deviation from the Gaussian distribution are evaluated with the accuracy of the squared perturbation amplitude. We also determine the time evolutions of the information entropies of the electron position and velocity variables and their mutual information. We further consider Coulomb collisions that relax the state in the late-time limit in the collisionless process to the thermal equilibrium state. In this collisional relaxation process, the mutual information of the position and velocity variables decreases to zero, while the total information entropy of the phase-space distribution function increases by the decrease in the mutual information and demonstrates the validity of Boltzmann's H-theorem.

Many body gravity and the galaxy rotation curves

A novel theory was proposed earlier to model systems with thermal gradients, based on the postulate that the spatial and temporal variation in temperature can be recast as a variation in the metric. Combining the variation in the metric due to the thermal variations and gravity, leads to the concept of thermal gravity in a 5-D space-time-temperature setting. When the 5-D Einstein field equations are projected on to a 4-D space, they result in additional terms in the field equations. This may lead to unique phenomena such as the spontaneous symmetry breaking of scalar particles in the presence of a strong gravitational field. This theory, originally conceived in a quantum mechanical framework, is now adapted to explain the galaxy rotation curves. A galaxy is not in a state of thermal equilibrium. A parameter called the “degree of thermalization” is introduced to model partially thermalized systems. The generalization of thermal gravity to partially thermalized systems, leads to the theory of many-body gravity. The theory of many-body gravity is now shown to be able to explain the rotation curves of the Milky Way and the M31 (Andromeda) galaxies, to a fair extent. The radial acceleration relation (RAR) for 63 galaxies, with their galactic masses spanning three orders of magnitude, has been replicated. Finally, the wide binary star (WBS) system is touched upon.

Heat capacity and quantum compressibility of dynamical spacetimes with thermal particle creation

This work continues the investigation in two recent papers on the quantum thermodynamics of spacetimes, (1) placing what was studied in [] for thermal quantum fields in the context of early universe cosmology, and (2) extending the considerations of vacuum compressibility of dynamical spaces treated in [] to dynamical spacetimes with thermal quantum fields. We begin with a warning that thermal equilibrium condition is not guaranteed to exist or maintained in a dynamical setting and thus finite temperature quantum field theory in cosmological spacetimes needs more careful considerations than what is often described in textbooks. A full description requires nonequilibrium quantum field theory in dynamical spacetimes using “in-in” techniques. A more manageable subclass of dynamics is where thermal equilibrium conditions are established at both the beginning and the end of evolution, where the in-thermal state and the out-thermal state are both well defined. Particle creation in the full history can then be calculated in this in-out asymptotically-stationary setup via the S-matrix transition amplitudes. Here we shall assume an in-vacuum state. It has been shown that if the intervening dynamics has an initial period of exponential expansion, such as in inflationary cosmology, particles created from the parametric amplification of the vacuum fluctuations in the initial vacuum will have a thermal spectrum measured at the out-state. Under these conditions finite temperature field theory can be applied to calculate the quantum thermodynamic quantities. Here we consider a massive conformal scalar field in a closed four-dimensional Friedmann-Lemaître-Robertson-Walker universe based on the simple analytically solvable Bernard-Duncan model. We calculate the energy density of particles created from an in-vacuum and derive the partition function. From the free energy we then derive the heat capacity and the quantum compressibility of these spacetimes with thermal particle creation. We end with some discussions and suggestions for further work in this program of studies. Published by the American Physical Society 2024

Doping dependence of boron–hydrogen dynamics in crystalline silicon

In this contribution, we investigate the formation and dissociation of boron–hydrogen (BH) pairs in crystalline silicon under thermal equilibrium conditions. Our samples span doping concentrations of nearly two orders of magnitude and are passivated with a layer stack consisting of thin aluminum oxide and hydrogen-rich silicon nitride (Al2O3/SiNx:H). This layer stack acts as a hydrogen source during a following rapid thermal annealing. We characterize the samples using low-temperature Fourier-transform infrared spectroscopy and four-point-probe resistivity measurements. Our findings show that the proportion of hydrogen atoms initially bound to boron (BH pairs) rises with increasing boron concentration. Upon isothermal dark annealing at (163 ± 2) °C, hydrogen present in molecular form, H2, dissociates at a rate directly proportional to the concentration of boron atoms, ∝ [B−], leading to the formation of BH pairs. With prolonged annealing, an unknown hydrogen complex is formed at a rate that is inversely proportional to the square of the boron concentration, ∝ 1/[B−]2, resulting in the disappearance of BH pairs. Based on experimental observations, we derive a kinetic model in which we describe the formation of the unknown complex through neutral hydrogen H0 binding to a sink. Additionally, we investigate the temperature dependence of the reaction rates and find that the H2 dissociation process has an activation energy of (1.11 ± 0.05) eV, which is in close agreement with theoretical predictions.

Single droplet or bubble and its stability: Kinetic theory and dynamical system approaches.

Steady solutions of a single droplet or bubble in the van der Waals fluid are investigated on the basis of the kinetic model equationthat has been recently proposed by Miyauchi etal. [Gas Dynamics with Applications in Industry and Life Sciences (Springer, Cham, 2023), pp. 19-39]. Under the thermal equilibrium condition and isotropic assumption with respect to the origin of the coordinates, the kinetic equationis reduced to an ordinary differential equationfor the density, which can be regarded as a low-dimensional dynamical system. The possible density distribution is studied as a flow in the low-dimensional phase space. It is clarified that a single droplet or bubble can be understood as a flow that goes into a fixed point and that the flow is qualitatively different in the unstable and metastable parameter regions. The features of the obtained density distributions in individual regions are also clarified. Finally, the stability of those solutions is studied by direct numerical experiments of the kinetic equation.

Exploration of microscopic physical processes of Z-pinch by a modified electrostatic direct implicit particle-in-cell algorithm

Abstract For investigating efficiently the stagnation kinetic-process of Z-pinch, we develop a novel modified electrostatic implicit particle-in-cell algorithm in radial one-dimension for Z-pinch simulation in which a small-angle cumulative binary collision algorithm is used. In our algorithm, the electric field in z-direction is solved by a parallel electrode-plate model, the azimuthal magnetic field is obtained by Ampere’s law, and the term for charged particle gyromotion is approximated by the cross product of the averaged velocity and magnetic field. In simulation results of 2 MA deuterium plasma shell Z-pinch, the mass-center implosion trajectory agrees generally with that obtained by one-dimensional MHD simulation, and the plasma current also closely aligns with the external current. The phase space diagrams and radial-velocity probability distributions of ions and electrons are obtained. The main kinetic characteristic of electron motion is thermal equilibrium and oscillation, which should be oscillated around the ions, while that of ion motion is implosion inwards. In the region of stagnation radius, the radial-velocity probability distribution of ions transits from the non-equilibrium to equilibrium state with the current increasing, while of electrons is basically the equilibrium state. When the initial ion density and current peak are not high enough, the ions may not reach their thermal equilibrium state through collisions even in its stagnation phase.

Emergence hour-by-hour of features in the kilonova AT2017gfo

The spectral features in the optical/near-infrared counterparts of neutron star mergers (kilonovae, KNe) evolve dramatically on hourly timescales. To examine the spectral evolution, we compiled a temporal series that was complete at all observed epochs from 0.5 to 9.4\,days of the best optical/near-infrared (NIR) spectra of the gravitational-wave detected kilonova AT2017gfo. Using our analysis of this spectral series, we show that the emergence times of spectral features place strong constraints on line identifications and ejecta properties, while their subsequent evolution probes the structure of the ejecta. We find that the most prominent spectral feature, the 1\ P Cygni line, appears suddenly, with the earliest detection at 1.17\,days. We find evidence in this earliest feature for the fastest yet discovered kilonova ejecta component at 0.40--0.45$c$. Across the observed epochs and wavelengths, the velocities of the line-forming regions span nearly an order of magnitude, down to as low as 0.04--0.07$c$. The time of emergence closely follows the predictions for because combines rapidly under local thermal equilibrium (LTE) conditions. The transition time between the doubly and singly ionised states provides the first direct measurement of the ionisation temperature. This temperature is highly consistent with the temperature of the emitted blackbody radiation field at a level of a few percent. Furthermore, we find the KN to be isotropic in temperature, that is, the polar and equatorial ejecta differ by less than a few hundred Kelvin or \( 5\)<!PCT!>, in the first few days post-merger based on measurements of the reverberation time-delay effect. This suggests that a model with very simple assumptions, with single-temperature LTE conditions, reproduces the early kilonova properties surprisingly well.

Temperature Variations in Deep Thermal Well LZT-1 in Lądek-Zdrój (Bohemian Massif; SW Poland)—Evidence of Geothermal Anomaly and Paleoclimatic Changes

The thermal water deposit in Lądek-Zdrój (SW Poland) occurs in fractured reservoir rocks, and its hydrogeological regime is controlled by the features of the local geology and lithology of the hosting crystalline complexes, mainly impermeable high-grade metamorphosed mica schists and gneisses. The fractured thermal water aquifer is confined by a thrust fault-type aquitard that creates artesian pressure and, therefore, the water intakes and natural springs in Lądek Zdrój provide spontaneous outflow. Classical geothermometers yield an estimation of reservoir temperatures that ranges from 50 to 70 °C, with a maximum of 88 °C. The heat flux (HF) value of the Lądek-Zdrój region is 64 mW/m2. The new borehole, LZT-1, is in the border zone of a local thermal anomaly with a geothermal degree of 25–27 m/°C. The estimated temperature at the bottom of the LZT-1 borehole, under thermal equilibrium conditions, ranges between 70 °C and 80 °C. A stream of heated waters from the deep system flows from the recharge areas, shaping the local geothermal anomaly and thus influencing the thermal conditions in the Lądek-Zdrój area. The activation of this water circulation system occurred in the Pleistocene.

Gas Kinematics and Dynamics of Carina Pillars: A Case Study of G287.76-0.87

We study the kinematics of a pillar, namely G287.76-0.87, using three rotational lines of 12CO(5-4), 12CO(8-7), 12CO(11-10), and a fine structure line of [O i] 63 μm in southern Carina observed by SOFIA/GREAT. This pillar is irradiated by the associated massive star cluster Trumpler 16, which includes η Carina. Our analysis shows that the relative velocity of the pillar with respect to this ionization source is small, ∼1 km s−1, and the gas motion in the tail is more turbulent than in the head. We also performed analytical calculations to estimate the gas column density in local thermal equilibrium (LTE) conditions, which yields N CO as (∼0.2–5) × 1017 cm−2. We further constrain the gas’s physical properties in non-LTE conditions using RADEX. The non-LTE estimations result in nH2≃105cm−3 and N CO ≃ 1016 cm−2. We found that the thermal pressure within the G287.76-0.87 pillar is sufficiently high to make it stable for the surrounding hot gas and radiation feedback if the winds are not active. While they are active, stellar winds from the clustered stars sculpt the surrounding molecular cloud into pillars within the giant bubble around η Carina.

Numerical simulation of Darcy–Forchheimer flow of Casson ternary hybrid nanofluid with melting phenomena and local thermal non-equilibrium effects

The Casson fluid flow over a stretching sheet is studied in this work in the presence of porous media with melting heat transfer and chemical reaction, combining nanoparticles of Ti4Al6V,AA7072 and AA7075 with a base fluid of sodium alginate (NaAlg). The porous medium Darcy Forchheimer effect is included in the momentum equation. Through the effects of melting, the process of heat transfer is described. In order to explore the features of heat transmission in the absenteeism of LTECs (local thermal equilibrium conditions), the current study employs a mathematical model that has been simplified. For both the solid and liquid phases, the LTNE model yields two different fundamental thermal gradients. This proposed model compares the YOM (Yamada-Ota model) and XM (Xue model), two well-known trihybrid nanofluid models, in terms of performance. After applying the proper transformations, modulated non-linear PDEs (partial differential equations) are simplified in ODEs (ordinary differential equations) and the bvp4c method is used to solve them numerically. A graphic discussion of the relevant factors' significance on the pertinent fields has been presented. It is observed that the Casson ternary hybrid nanofluid temperature and velocity distributions predominate at higher melting parameter. The solid phase's heat transport rate rises with an upsurge in the interphase heat transfer parameter.

Rigorous results on approach to thermal equilibrium, entanglement, and nonclassicality of an optical quantum field mode scattering from the elements of a non-equilibrium quantum reservoir

Rigorous derivations of the approach of individual elements of large isolated systems to a state of thermal equilibrium, starting from arbitrary initial states, are exceedingly rare. This is particularly true for quantum mechanical systems. We demonstrate here how, through a mechanism of repeated scattering, an approach to equilibrium of this type actually occurs in a specific quantum system, one that can be viewed as a natural quantum analog of several previously studied classical models. In particular, we consider an optical mode passing through a reservoir composed of a large number of sequentially-encountered modes of the same frequency, each of which it interacts with through a beam splitter. We then analyze the dependence of the asymptotic state of this mode on the assumed stationary common initial state σ of the reservoir modes and on the transmittance τ=cos⁡λ of the beam splitters. These results allow us to establish that at small λ such a mode will, starting from an arbitrary initial system state ρ, approach a state of thermal equilibrium even when the reservoir modes are not themselves initially thermalized. We show in addition that, when the initial states are pure, the asymptotic state of the optical mode is maximally entangled with the reservoir and exhibits less nonclassicality than the state of the reservoir modes.

Statistical mechanics and pressure of composite multimoded weakly nonlinear optical systems.

Statistical mechanics can provide a versatile theoretical framework for investigating the collective dynamics of weakly nonlinear-wave settings that can be utterly complex to describe otherwise. In optics, composite systems arise due to interactions between different frequencies and polarizations. The purpose of this work is to develop a thermodynamic theory that takes into account the synergistic action of multiple components. We find that the type of the nonlinearity involved can have important implications in the thermalization process and, hence, can lead to different thermal equilibrium conditions. Importantly, we derive closed-form expressions for the actual optomechanical pressure that is exerted on the system. In particular, the total optomechanical pressure is the sum of the partial pressures due to each component. Our results can be applied to a variety of weakly nonlinear optical settings such as multimode fibers, bulk waveguides, photonic lattices, and coupled microresonators. We present two specific examples, where two colors interact in a one-waveguide array with either a cubic or quadratic nonlinearity.

A collision operator for describing dissipation in noncanonical phase space

The phase space of a noncanonical Hamiltonian system is partially inaccessible due to dynamical constraints (Casimir invariants) arising from the kernel of the Poisson tensor. When an ensemble of noncanonical Hamiltonian systems is allowed to interact, dissipative processes eventually break the phase space constraints, resulting in a thermodynamic equilibrium described by a Maxwell–Boltzmann distribution. However, the time scale required to reach Maxwell–Boltzmann statistics is often much longer than the time scale over which a given system achieves a state of thermal equilibrium. Examples include diffusion in rigid mechanical systems, as well as collisionless relaxation in magnetized plasmas and stellar systems, where the interval between binary Coulomb or gravitational collisions can be longer than the time scale over which stable structures are self-organized. Here, we focus on self-organizing phenomena over spacetime scales such that particle interactions respect the noncanonical Hamiltonian structure, but yet act to create a state of thermodynamic equilibrium. We derive a collision operator for general noncanonical Hamiltonian systems, applicable to fast, localized interactions. This collision operator depends on the interaction exchanged by colliding particles and on the Poisson tensor encoding the noncanonical phase space structure, is consistent with entropy growth and conservation of particle number and energy, preserves the interior Casimir invariants, reduces to the Landau collision operator in the limit of grazing binary Coulomb collisions in canonical phase space, and exhibits a metriplectic structure. We further show how thermodynamic equilibria depart from Maxwell–Boltzmann statistics due to the noncanonical phase space structure, and how self-organization and collisionless relaxation in magnetized plasmas and stellar systems can be described through the derived collision operator.

Quantum tachyonic preheating, revisited

In certain models of inflation, the postinflationary reheating of the Universe is not primarily due to perturbative decay of the inflaton field into particles, but proceeds through a tachyonic instability. In the process, long-wavelength modes of an unstable field, which is often distinct from the inflaton itself, acquire very large occupation numbers, which are subsequently redistributed into a thermal equilibrium state. We investigate this process numerically through quantum real-time lattice simulations of the Kadanoff-Baym equation, using a 1/N-NLO truncation of the 2PI-effective action. We identify the early-time maximum occupation number, the “classical” momentum range, the validity of the classical approximation and the effective IR temperature, and study the kinetic equilibration of the system and the equation of state.

On the self-assembly of polarization domain observed in the relaxor ferroelectric Pb[(Mg1/3Nb2/3)0.722Ti0.278]O3

Self-assembly of polarization domain in relaxor-ferroelectrics Pb[(Mg1/3Nb2/3)0.722Ti0.278]O3 is discussed based on the observation of the coherent soft X-ray laser reflection. We investigate the autocorrelation of the polarization domain at the early stage of evolution. Local order of the polarization domain become in phase and periodic over 600 μm as the temperature of the crystal cool down to 383 K keeping with almost thermal equilibrium condition. Minimum domain formation free energy is discussed qualitatively.

Simulation study of the electrothermal field in a chloride electrolysis cell with 16 electrode pairs

AbstractThe spatial distribution of the electrothermal field within molten salt electrolytic cells significantly influences the efficiency of the electrolysis process, the quality of the end products, and the overall stability of the system. Enhancing the design of chloride electrolysis cells can lead to marked improvements in both process efficiency and system stability, thereby yielding increased economic benefits. This study introduces a design for a chloride electrolysis cell and examines the thermal budget under elevated electrical current intensities across 16 electrode pairs. It further analyzes the degree to which various parameters affect thermal equilibrium. The findings indicate that the electrolytic cell maintains a small thermal budget discrepancy at a current intensity of 124 kA and is less than 5%, with substantial heat dissipation observed at the surface of the top area of anode exposure and considerable energy consumption at both the anode and the electrolyte. Dimensionless treatment of the different parameterized simulation results has been conducted to develop a nondimensional equation, describing the thermal equilibrium conditions within the electrolytic cell. This foundational work paves the way for further investigations into the interactions between the electrothermal field and other physical fields, as well as for the optimization of the electrolytic cell's geometry and design.

Revised Enskog equation for hard rods

We point out that Percus’s collision integral for one-dimensional hard rods (Percus 1969 Phys. Fluids 12 1560–3) does not preserve the thermal equilibrium state in an external trapping potential. We derive a revised Enskog equation for hard rods and show that it preserves this thermal state exactly. In contrast to recent proposed kinetic equations for dynamics in integrability-breaking traps, both our kinetic equation and its thermal states are explicitly nonlocal in space. Our equation differs from earlier proposals at third order in spatial derivatives and we attribute this discrepancy to the choice of collision integral underlying our approach.

Einstein gravity as the thermal equilibrium state of a nonminimally coupled scalar field geometry

Einstein gravity as the thermal equilibrium state of a nonminimally coupled scalar field geometry