Thermal Equilibrium State Research Articles

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

Quantum Carnot thermal machines reexamined: Definition of efficiency and the effects of strong coupling.

Whether the strong coupling to thermal baths can improve the performance of quantum thermal machines remains an open issue under active debate. Here we revisit quantum thermal machines operating with the quasistatic Carnot cycle and aim to unveil the role of strong coupling in maximum efficiency. Our analysis builds upon definitions of excess work and heat derived from an exact formulation of the first law of thermodynamics for the working substance, which captures the non-Gibbsian thermal equilibrium state that emerges at strong couplings during quasistatic isothermal processes. These excess definitions differ from conventional ones by an energetic cost for maintaining the non-Gibbsian characteristics. With this distinction, we point out that one can introduce two different yet thermodynamically allowed definitions for efficiency of both the heat engine and refrigerator modes. We dub them excess and hybrid definitions, which differ in the way of defining the gain for the thermal machines at strong couplings by either just analyzing the energetics of the working substance or instead evaluating the performance from an external system upon which the thermal machine acts, respectively. We analytically demonstrate that the excess definition predicts that the Carnot limit remains the upper bound for both operation modes at strong couplings, whereas the hybrid one reveals that strong coupling can suppress the maximum efficiency rendering the Carnot limit unattainable. These seemingly incompatible predictions thus indicate that it is imperative to first gauge the definition for efficiency before elucidating the exact role of strong coupling, thereby shedding light on the ongoing investigation on strong-coupling quantum thermal machines.

Molecular Dynamics Simulation of Thermal Nonequilibrium and Chemical Reaction Processes in Hydrogen Combustion.

Using reactive force field (ReaxFF) and molecular dynamics simulation, we investigate the combustion process of hydrogen-oxygen systems in initial thermal nonequilibrium states with different translational and rovibrational temperatures for oxygen. The system studied in this work contains 300 oxygen molecules and 700 hydrogen molecules with a density of 7 times the air density. For this system, the characteristic relaxation times of oxygen and hydrogen vibrational energies are 0.173 and 0.249 ns, respectively. 0.6% of hydrogen undergoes a chemical reaction with oxygen during the thermal nonequilibrium relaxation stage. For the distribution of translational energy and vibrational energy of oxygen in the thermal nonequilibrium state, the maximum mean error of the statistical distribution in the simulation and the Boltzmann distribution at temperature calculated from the average kinetic energy of molecules is about 2.25 × 10-5. At the same time, it was observed in the simulation that many-body interactions play a certain role in the combustion process. Furthermore, we compare the ignition time and temperature rise behavior of different combustion mechanisms and molecular dynamics simulations starting from the thermal equilibrium state. These results will provide meaningful references for the construction of thermal nonequilibrium combustion chemical reaction mechanisms.

Dalton's law of partial optical thermodynamic pressures in highly multimoded nonlinear photonic systems.

We show that in highly multimoded nonlinear photonic systems, the optical thermodynamic pressures emerging from different species of the optical field obey Dalton's law of partial pressures. In multimode settings, the optical thermodynamic pressure is defined as the conjugate to the extensive variable associated with the system's total number of modes and is directly related to the actual electrodynamic radiation forces exerted at the physical boundaries of the system. Here, we extend this notion to photonic configuration supporting different species of the optical field. Under thermal equilibrium conditions, we formally derive an equation that establishes a direct link between the partial thermodynamic pressures and the electrodynamic radiation pressures exerted by each polarization species. Our theoretical framework provides a straightforward approach for quantifying the total radiation pressures through the system's thermodynamic variables without invoking the Maxwell stress tensor formalism. In essence, we show that the total electrodynamic pressure in such arrangements can be obtained in an effortless manner from initial excitation conditions, thus avoiding time-consuming simulations of the utterly complex multimode dynamics. To illustrate the validity of our results, we carry out numerical simulations in multimoded nonlinear optical structures supporting two polarization species and demonstrate excellent agreement with the Maxwell stress tensor method.

Thermal equilibrium time as a novel characteristic of nanofluid evaluation: An experimental investigation of distilled water-based binary and ternary nanofluids

Nanofluids enhance thermal energy transfer in energy storage applications. Proper nanoparticles are crucial, especially regarding their thermophysical properties. This work fabricated a novel instrument to evaluate a mixture of distilled water-based ternary and binary nanofluids. This work prepared novel ternary and binary nanofluids by mixing multi-wall carbon nanotubes (MWCNTs), magnesium oxide (MgO), and boron nitride (BN) into distilled water at various volume concentrations. The instrument that has been fabricated measures the time taken by the nanofluids to reach a thermal equilibrium state as a new characteristic to evaluate and compare the thermal potential of nanofluids, which alleviates the dependence on other instruments that are occasionally inaccessible or costly for researchers. Thermodynamically, this instrument enables the assessment of nano-energy, manifested as the heat transferred to the nanofluid while reaching an equilibrium state. The results verified the purpose of the proposed instrument; the novel characteristic was affected perfectly by increasing the volume concentration of the nanoparticles in the base fluid. All nanofluids prepared with a concentration of 0.5 % emerged as the most effective in achieving thermal equilibrium in a shorter time than the other concentrations. The ternary hybrid nanofluid MWCNTs–MgO–BN with a volume concentration of 0.5 % had the shortest thermal equilibrium time, 157 s. MWCNTs–MgO–BN ternary hybrid nanofluids transferred 8.3, 5.8, and 11.8 % more heat than MWCNTs–MgO, MWCNTs–BN, and MgO–BN binary hybrid nanofluids. The thermophysical essence behind the result obtained by the created instrument lies in the fact that it generated a new approach to evaluating the nanofluids, thanks to which it was possible to evaluate and find out which fluid has the highest thermal conductivity. The uncertainty analysis showed error acceptability in the experimental instrument, with an average uncertainty value percentage for all presented composites of ± 0.936 %.

On the Statistical Regime, Coherence versus Incoherence and Ergodicity of Quantum Vibrational Trajectories in Soft Condensed Molecular Systems.

A theoretical-computational procedure, recently proposed for modelling Vibrational Energy Relaxation (VER) processes of a molecule (Quantum Center, QC) embedded in a complex atomic-molecular system, is extended and applied for analyzing in detail the features of the QC density matrix (DM) temporal evolution. The results, obtained using aqueous azide ion as a case study, show the total lack of coherence in the DM, when the system is prepared to be initially in a pure vibrational eigenstate. This finding is fully in line with the statistical interpretation of the process typically adopted also in the experimental studies where the relaxation processes are all described within the typical schemes of chemical kinetics. Consistently, when the initial vibrational state corresponds to an eigenstate mixture, although initially coherent, the DM relaxes to a fully incoherent condition with a mean lifetime related to the one of the diagonal elements relaxation. These specific DM features turn out to be essentially governed by the thermal equilibrium condition of the atomic-molecular classical coordinates which drive the ensemble of the quantum-trajectories toward the observed statistical regime. Finally, from the analysis of a single long timescale quantum vibrational trajectory it also clearly emerges its ergodic behaviour.

Enhance the coherence of open two-level system through the superposition of environments

Dynamics of a two-level system in the superposition of two dephasing environments with Ohmic-like spectral density is studied when considering initial system-environment correlations. The quantum system and one environment are treated as whole thermal equilibrium state, while the other environment is at thermal equilibrium state alone. Which environment the system interacts with is determined by an ancillary two-level system. When the system interacts with mixture of two sub-Ohmic environments, initial correlations can make the mixed dynamics non-Markovian. For two identical sub-Ohmic environments, if performing the projective measurement on the ancillary two-level system at the special time points, whatever the initial state of the system is, the coherence can be enhanced. For two different environments with βħω0/2>>, we get the approximate expression about the coherence of the system when measuring the ancillary two-level system.

Adiabatic Evolution of Low-Temperature Many-Body Systems

We consider finite-range, many-body fermionic lattice models and we study the evolution of their thermal equilibrium state after introducing a weak and slowly varying time-dependent perturbation. Under suitable assumptions on the external driving, we derive a representation for the average of the evolution of local observables via a convergent expansion in the perturbation, for small enough temperatures. Convergence holds for a range of parameters that is uniform in the size of the system. Under a spectral gap assumption on the unperturbed Hamiltonian, convergence is also uniform in temperature. As an application, our expansion allows us to prove closeness of the time-evolved state to the instantaneous Gibbs state of the perturbed system, in the sense of expectation of local observables, at zero and at small temperatures. As a corollary, we also establish the validity of linear response. Our strategy is based on a rigorous version of the Wick rotation, which allows us to represent the Duhamel expansion for the real-time dynamics in terms of Euclidean correlation functions, for which precise decay estimates are proved using fermionic cluster expansion.

Exact numerical analysis of EMEC mode instability in more realistic Cairns distributed non-thermal plasmas

Non-thermal plasma systems beyond the state of thermal equilibrium must have non-thermality dependent effective temperatures. These particle populations cannot have Maxwellian temperatures T∥,⊥e(M) which are typically considered at thermal equilibrium in the context of Maxwellian plasmas. Previously, in such dilute environments, numerous non-thermal distributions incorporating the concept of Maxwellian temperature T∥,⊥e(M) have been utilized, one of them is Cairns distribution (here termed as type-A). To ameliorate this inconsistency, we propose a more realistic form of Cairns distribution (type-B) with the vigorous definition of effective temperature and effective thermal velocity. Both Cairns distributions (A and B) are utilized to calculate the transverse dielectric response function (TDERF) of electromagnetic electron cyclotron (EMEC) mode. The exact numerical solution of TDERFs of EMEC instability reveals interesting and more promising repercussions in the case of Cairns-B i.e. an augmentation in the behavior of oscillatory and imaginary frequencies of the instability.

Reduced probability densities of long-lived metastable states as those of distributed thermal systems: Possible experimental implications for supercooled fluids

When liquids are cooled sufficiently rapidly below their melting temperature, they may bypass crystalization and, instead, enter a long-lived metastable supercooled state that has long been the focus of intense research. Although they exhibit strikingly different properties, both the (i) long-lived supercooled liquid state and (ii) truly equilibrated (i.e., conventional equilibrium fluid or crystalline) phases of the same material share an identical Hamiltonian. This suggests a mapping between dynamical and other observables in these two different arenas. We formalize these notions via a simple theorem applicable to general systems and illustrate that given a Hamiltonian defining the dynamics: (1) the reduced probability densities of all possible stationary states are linear combinations of reduced probability densities associated with thermal equilibria at different temperatures, chemical potentials, etc. (2) Excusing special cases, amongst all of these stationary states, a clustering of correlations is only consistent with conventional thermal equilibrium states (associated with a sharp distribution of the above state variables). (3) Other stationary states may be modified so as to have local correlations. These deformations concomitantly lead to metastable (yet possibly very long-lived) states. Since the lifetime of the supercooled state is exceptionally long relative to the natural microscopic time scales, their reduced probability densities may be close to those that we find for exact stationary states (i.e., a weighted average of equilibrium probability densities at different state variables). This form suggests several new predictions such as the existence of dynamical heterogeneity stronger than probed for thus far and a relation between the specific heat peak and viscosities. Our theorem may further place constraints on the putative “ideal glass” phase.

Evaluating different geothermal heat-flow maps as basal boundary conditions during spin-up of the Greenland ice sheet

Abstract. There is currently poor scientific agreement on whether the ice–bed interface is frozen or thawed beneath approximately one third of the Greenland ice sheet. This disagreement in basal thermal state results, at least partly, from differences in the subglacial geothermal heat-flow basal boundary condition used in different ice-flow models. Here, we employ seven widely used Greenland geothermal heat-flow maps in 10 000-year spin-ups of the Community Ice Sheet Model (CISM). We perform two spin-ups: one nudged toward thickness observations and the other unconstrained. Across the seven heat-flow maps, and regardless of unconstrained or nudged spin-up, the spread in basal ice temperatures exceeds 10 ∘C over large areas of the ice–bed interface. For a given heat-flow map, the thawed-bed ice-sheet area is consistently larger under unconstrained spin-ups than nudged spin-ups. Under the unconstrained spin-up, thawed-bed area ranges from 33.5 % to 60.0 % across the seven heat-flow maps. Perhaps counterintuitively, the highest iceberg calving fluxes are associated with the lowest heat flows (and vice versa) for both unconstrained and nudged spin-ups. These results highlight the direct, and non-trivial, influence of the heat-flow boundary condition on the simulated equilibrium thermal state of the ice sheet. We suggest that future ice-flow model intercomparisons should employ a range of basal heat-flow maps, and limit direct intercomparisons with simulations using a common heat-flow map.

Numerical study on mixed convection heat transfer of copper-water nanofluid in a porous cavity with an isothermal solid block in local thermal non-equilibrium

This manuscript reports a numerical study on mixed convection heat transfer of Cu-water nanofluid in a porous cavity with an isothermal solid block in the state of local thermal non equilibrium. The set of governing equations are solved by finite volume method combined with SIMPLE algorithm. Through streamlines and isothermal contour plots as well as the average Nusselt number, the impact of various parameters like the nanoparticle concentration, Richardson number, Darcy number, and inter phase heat transfer coefficient is highlighted. The main findings indicate that the Local thermal non-equilibrium state (H = 1, 10) produces the maximum heat transfer rate than the local thermal equilibrium state (H = 1000).

The Entropy of the Quark Gluon Plasma at Finite Temperature

In this paper we have calculated the thermal partition function of the thermo- dynamical system of Quark Gluon Plasma and also we have calculated the entropy of quark gluon plasma for the zero chemical potential at the thermal equilibrium condition.

Computed Rotational Collision Rate Coefficients for Recently Detected Anionic Cyanopolyynes

We report new results from quantum calculations of energy-transfer processes taking place in interstellar environments and involving two newly observed molecular species: C5N− and C7N− in collision with He atoms and p–H2 molecules. These species are part of the anionic molecular chains labeled as cyanopolyynes, which have been observed over the years in molecule-rich circumstellar envelopes and in molecular clouds. In the present work, we first carry out new ab initio calculations for the C7N− interaction potential with He atoms and then obtain state-to-state rotationally inelastic cross sections and rate coefficients involving the same transitions, which have been observed experimentally by emission in the interstellar medium (ISM) from both of these linear species. For the C5N−/He system, we extend the calculations already published in Biwas et al. to compare more directly the two molecular anions. We extend further the quantum calculations by also computing in this work collision rate coefficients for the hydrogen molecule interacting with C5N−, using our previously computed interaction potential. Additionally, we obtain the same rate coefficients for the C7N−/H2 system by using a scaling procedure that makes use of the new C7N−/He rate coefficients, as discussed in detail in the present paper. Their significance in affecting internal state populations in ISM environments where the anionic cyanopolyynes have been found is analyzed by using the concept of critical density indicators. Finally, similarities and differences between such species and the comparative efficiency of their collision rate coefficients are discussed. These new calculations suggest that, at least for the case of these longer chains, the rotational populations could reach local thermal equilibrium conditions within their observational environments.

Does canonical quantization lead to GKSL dynamics?

We introduce a generalized classical model of Brownian motion for describing thermal relaxation processes which is thermodynamically consistent. Applying the canonical quantization to this model, a quantum equation for the density operator is obtained. This equation has a thermal equilibrium state as its stationary solution, but the time evolution is not necessarily a Completely Positive and Trace-Preserving (CPTP) map. In the application to the harmonic oscillator potential, however, the requirement of the CPTP map is shown to be satisfied by choosing parameters appropriately and then our equation reproduces a Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) equation satisfying the detailed balance condition. This result suggests a quantum-classical correspondence in thermal relaxation processes and will provide a new insight to the study of decoherence.

Influence of mineral composition on thermal equilibrium state during laser perforation

Energy consumption during laser rock perforation is controlled by conductive losses and latent heats during the phase transitions of melting and evaporation. To understand then improve the efficiency of laser perforation, the influence of rock mineral composition on these processes is investigated, and a theoretical model of laser rock breaking under steady-state heat conduction is developed. The findings reveal that the melting properties of mineral components primarily control thermal equilibrium during laser perforation. The key minerals, namely feldspar, quartz, and clay, were used to study the melt response in both pure samples and synthetic rock composites composed of these minerals. When feldspar is dominant, the thermal equilibrium temperature remains stable after reaching the feldspar gas phase boundary. While in situations where quartz dominates, the thermal equilibrium temperature is slightly below the melting point of pure quartz. The findings highlight the relationship between laser rock perforation efficiency and melting properties of minerals.

Improvements in bonding through ultrasonic additive manufacturing of titanium by stabilizing displacive phase transformations

The development of advanced materials to operate in extreme environments (temperature, pressure, strain rate, irradiation, etc.) is essential to meet future energy challenges. In addition to being an advanced solid state bonding technique, ultrasonic additive manufacturing (UAM) can be considered as a type of extreme environment due to the high strain and high strain rate deformation that is created. Understanding the physical processes that occur in this extreme environment can be valuable to creating new desirable microstructures and/or phase changes. Although UAM has demonstrated great success in bonding a variety of materials, the underlying science mechanisms controlling the bonding are not well quantified. We observed crystal structure changes from hexagonal closed packed (HCP) to body centered cubic (BCC) in Ti and Ti alloy specimens occurring within ∼0.5 s following UAM bonding with an estimated peak temperature of ∼400 °C. Extensive interdiffusion of elements (0.2 µm – 2 µm depending on location) occurred that does not conform to thermal equilibrium bulk or grain boundary diffusion. We present evidence that a significant concentration of deformation induced vacancies Xv (between 10−4 - 10−6 atomic fraction) was created during UAM, approximately ten orders of magnitude higher than the Xv value of ∼10−15 expected for thermal equilibrium conditions. This caused pronounced metallurgical changes including rapid elemental diffusion, strain induced phase transformation, and bonding. We examined this UAM-induced severe plastic deformation on a variety of materials and performed uncertainty calculations from the measurements.

Improved Quantum-Classical Treatment of N2-N2 Inelastic Collisions: Effect of the Potentials and Complete Rate Coefficient Data Sets.

In this study, complete (i.e., including all vibrational quantum numbers in an N2 vibrational ladder) data sets of vibration-to-vibration and vibration-to-translation rate coefficients for N2-N2 collisions are explicitly computed along with transport properties (shear and bulk viscosity, thermal conductivity, and self-diffusion) in the temperature range 100-9000 K. To reach this goal, we improved a mixed quantum-classical (MQC) dynamics approach by lifting the constraint of a Morse treatment of the vibrational wave function and intramolecular potential and permitting the use of more realistic and flexible representations. The new formulation has also allowed us to separately analyze the role of intra- and intermolecular potentials on the calculated rates and properties. Ab initio intramolecular potentials are indispensable for highly excited vibrational states, though the Morse potential still gives reasonable values up to v = 20. An accurate description of the long-range interaction and the van der Waals well is a requisite for the correct reproduction of qualitative and quantitative rate coefficients, particularly at low temperatures, making physically meaningful analytical representations still the best choice compared to currently available ab initio potential energy surfaces. These settings were used to directly compute the MQC rates corresponding to a large number of initial vibrational quantum numbers, and the missing intermediate values were predicted using a machine learning technique (i.e., the Gaussian process regression approach). The obtained values are reliable in the wide temperature range employed and are therefore valuable data for many communities dealing with nonlocal thermal equilibrium conditions in different environments.