High-temperature Limit Research Articles

Power and efficient power optimization of one-qubit Novikov quantum heat engines with an external dissipative heat leak

Abstract We optimize one-qubit Novikov quantum heat engines with a dissipative heat leak using the formalisms of open-system Quantum Mechanics and the Finite-Time Thermodynamics. We show that the leak changes the power-efficiency and the efficient-power-efficiency curves, reduces the maximum efficiency of the machine and does not change its power. We also discuss the effects of the leak on the power that is rejected from the machine to the environment. Finally, we study the high-temperature limit to check that the engine reduces in this limit to a classic Novikov heat engine.

Rationality in four dimensions

By leveraging the physics of the Higgs branch, we argue that the conformal central charges a and c of an arbitrary 4D N=2 superconformal field theory (SCFT) are rational numbers. Our proof of the rationality of c is conditioned on a well-supported conjecture about how the Higgs branch of an SCFT is encoded in its protected chiral algebra. To establish the rationality of a, we further rely on a widely believed technical assumption on the high-temperature limit of the superconformal index. Published by the American Physical Society 2024

Thermal Radiation Annealing for Overcoming Processing Temperature Limitation of Flexible Perovskite Solar Cells.

Common polymeric conductive electrodes, such as polyethylene terephthalate (PET) coated with indium tin oxide, face a major challenge due to their low processing-temperature limits, attributed to PET's low glass transition temperature (Tg) of (70-80°C). This limitation significantly narrows the scope of material selection, limits the processing techniques applicable to the low Tg, and hinders the ripened technology transfer from glass substrates to them. Addressing the temperature constraints of the flexible substrates is impactful yet underexplored, with broader implications for fields beyond photovoltaics. Here, a new thermal radiation annealing methodology is introduced to address this issue. By applying the above Tg radiation annealing in conjunction with thermoelectric cooling, highly ordered molecular packing on PET substrates is successfully created, which is exclusively unachievable due to PET's low thermal tolerance. As a result, in the context of perovskite solar cells, this approach enables the circumvention of high-temperature annealing limitations of PET substrates, leading to a remarkable flexible device efficiency of 22.61% and a record fill factor of 83.42%. This approach proves especially advantageous for advancing the field of flexible optoelectronic devices.

Universal asymptotics for high energy CFT data

Equilibrium finite temperature observables of a CFT can be described by a local effective action for background fields — a “thermal effective action”. This effective action determines the asymptotic density of states of a CFT as a detailed function of dimension and spin. We discuss subleading perturbative and nonperturbative corrections to the density, comparing with free and holographic examples. We furthermore show how to use the thermal effective action on more complicated geometries at special locations called “hot spots”. The hot spot idea makes a prediction for a CFT partition function on a higher-dimensional version of a genus-2 Riemann surface, in a particular high temperature limit. By decomposing the partition function into a novel higher-dimensional version of genus-2 conformal blocks (which we compute at large scaling dimension), we extract the asymptotic density of heavy-heavy-heavy OPE coefficients in a higher-dimensional CFT. We also compute asymptotics of thermal 1-point functions using the same techniques.

Spin Drude weight for the integrable XXZ chain with arbitrary spin

Using generalized hydrodynamics (GHD), we exactly evaluate the finite-temperature spin Drude weight at zero magnetic field for the integrable XXZ chain with arbitrary spin and easy-plane anisotropy. First, we construct the fusion hierarchy of the quantum transfer matrices (T-functions) and derive functional relations (T- and Y-systems) satisfied by the T-functions and certain combinations of them (Y-functions). Through analytical arguments, the Y-system is reduced to a set of non-linear integral equations, equivalent to the thermodynamic Bethe ansatz (TBA) equations. Then, employing GHD, we calculate the spin Drude weight at arbitrary finite temperatures. As a result, a characteristic fractal-like structure of the Drude weight is observed at arbitrary spin, similar to the spin-1/2 case. In our approach, the solutions to the TBA equations (i.e. the Y-functions) can be explicitly written in terms of the T-functions, thus allowing for a systematic calculation of the high-temperature limit of the Drude weight.

Systematic approaches to assessing high-temperature limits to fertility in animals.

Critical thermal limits (CTLs) gauge the physiological impact of temperature on survival or critical biological function, aiding predictions of species range shifts and climatic resilience. Two recent Drosophila species studies, using similar approaches to determine temperatures that induce sterility (thermal fertility limits [TFLs]), reveal that TFLs are often lower than CTLs and that TFLs better predict both current species distributions and extinction probability. Moreover, many studies show fertility is more sensitive at less extreme temperatures than survival (thermal sensitivity of fertility [TSF]). These results present a more pessimistic outlook on the consequences of climate change. However, unlike CTLs, TFL data are limited to Drosophila, and variability in TSF methods poses challenges in predicting species responses to increasing temperature. To address these data and methodological gaps, we propose 3 standardized approaches for assessing thermal impacts on fertility. We focus on adult obligate sexual terrestrial invertebrates but also provide modifications for other animal groups and life-history stages. We first outline a "gold-standard" protocol for determining TFLs, focussing on the effects of short-term heat shocks and simulating more frequent extreme heat events predicted by climate models. As this approach may be difficult to apply to some organisms, we then provide a standardized TSF protocol. Finally, we provide a framework to quantify fertility loss in response to extreme heat events in nature, given the limitations in laboratory approaches. Applying these standardized approaches across many taxa, similar to CTLs, will allow robust tests of the impact of fertility loss on species responses to increasing temperatures.

Entanglement and Chaos near critical point in strongly coupled Gauge theory

We perform a holographic study of the high and low temperature behaviours of logarithmic negativity (LN) and entanglement wedge cross section (EWCS) in a large N strongly coupled thermal field theory with critical point, having a well defined gravity dual known as 1RC black hole. The bulk theory accommodates a dimensionless parameter ξ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\xi $$\\end{document}, proportional to the charge of the 1RC black hole. Holographically, ξ→2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\xi \\rightarrow 2$$\\end{document} limit ensures an existence of a critical point in the dual boundary theory. We show that the logarithmic negativity in low and high temperature limits enhances with increasing ξ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\xi $$\\end{document}. We analytically compute the EWCS in low and high temperature limits and find an agreement with the previously reported numerical results. We holographically explore the correlation between two identical copies of thermal field theory with critical point forming a thermofield double state (TFD) by computing the thermo mutual information (TMI). TMI shows an increasing behaviour with respect to the width of the boundary region. Furthermore, we study the chaotic behaviour of the field theory by analyzing a shock wave in the dual eternal 1 RC black hole and then estimate the degradation of TMI. The rate of such disruption of TMI slows down as the value of critical parameter ξ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\xi $$\\end{document} takes higher values.

The quantum Carnot-like heat engine: The level degenerate case

The two-level quantum heat engines have been studied extensively. Before that, the optimization of most heat engines was mainly concentrated in non-degenerate cases. We consider the level degeneracy, then calculate the maximum operation time and the irreversible dissipation coefficient of the two-level system under the scheme of linear tuned levels. In the high-temperature limit, we find that the level degeneracy affects the maximum power of the two-level heat engine. Especially in the case of the same degeneracy of the ground state and the excited state, the influence is the greatest. In addition, we also show that the degeneracy does not affect the efficiency at maximum power and the consistent relation of the two-level Carnot-like heat engine.

Griffiths phase in a facilitated Rydberg gas at low temperatures

The spread of excitations by Rydberg facilitation bears many similarities to epidemics. Such systems can be modeled with Monte Carlo simulations of classical rate equations to great accuracy as a result of high dephasing. Motivated by experiments, we theoretically analyze the dynamics of a Rydberg many-body system in the facilitation regime in the limits of high and low temperatures. In the high-temperature limit, a homogeneous mean-field behavior is recovered, while characteristic effects of heterogeneity can be seen in a frozen gas. At high temperatures, the system displays an absorbing-state phase transition and, in the presence of an additional loss channel, self-organized criticality. In a frozen or low-temperature gas, excitations are constrained to a network resembling an Erdős-Rényi graph. We show that the absorbing-state phase transition is replaced with an extended Griffiths phase, which we accurately describe by a susceptible-infected-susceptible model on the Erdős-Rényi network taking into account Rydberg blockade. Published by the American Physical Society 2024

Climate acts as an environmental filter to plant pathogens.

Climate shapes the distribution of plant-associated microbes such as mycorrhizal and endophytic fungi. However, the role of climate in plant pathogen community assembly is less understood. Here, we explored the role of climate in the assembly of Phytophthora communities at >250 sites along a latitudinal gradient from Spain to northern Sweden and an altitudinal gradient from the Spanish Pyrenees to lowland areas. Communities were detected by ITS sequencing of river filtrates. Mediation analysis supported the role of climate in the biogeography of Phytophthora and ruled out other environmental factors such as geography or tree diversity. Comparisons of functional and species diversity showed that environmental filtering dominated over competitive exclusion in Europe. Temperature and precipitation acted as environmental filters at different extremes of the gradients. In northern regions, winter temperatures acted as an environmental filter on Phytophthora community assembly, selecting species adapted to survive low minimum temperatures. In southern latitudes, a hot dry climate was the main environmental filter, resulting in communities dominated by drought-tolerant Phytophthora species with thick oospore walls, a high optimum temperature for growth, and a high maximum temperature limit for growth. By taking a community ecology approach, we show that the establishment of Phytophthora plant pathogens in Europe is mainly restricted by cold temperatures.

The effect of Ficoll 70 on thermally-induced and chemically-induced conformational transitions of an RTX protein is quantitatively accounted for by a unified excluded volume model.

A unified excluded volume model based upon the effective hard particle approximation is developed and used to quantitatively model previously published experimental measurements of the effect of adding high concentrations of an "inert" polymer, Ficoll 70, on conformational transitions of the toxin protein RCL that are induced by addition of calcium at constant temperature or by increasing temperature in the absence and presence of high calcium concentrations. The best-fit of this model, which accounts quantitatively for all of the published data to within experimental precision, yields an estimate of the volume of solution excluded to Ficoll by each of four identified conformational states of RCL: H - the most compact conformation adopted in the limits of high calcium concentration and low temperature, H* - the conformation adopted in the limits of high calcium concentration and high temperature, A - the conformation adopted in the limits of low (or no) calcium at low temperature, and A* - the conformation adopted in the limits of low calcium and high temperature. Ficoll exclusion volumes increase in the order H < H* < A < A*. These results are discussed in the context of the physiological functions of the RTX proteins, which are involved in the secretion process and the calcium-induced folding of bacterial virulence factors.

Thermal-insulating ceramic fiber aerogels reinforced by fusing knots of overlapping fibers for superelasticity and high compression resistance

A ceramic SiZrOC fiber aerogel reinforced by fusing knots of overlapping fibers exhibits superelasticity, high compression resistance and a very high-temperature resistance limit.

Harmonic models and molecular dynamics simulations of isomorph behavior of Lennard-Jones fluids: Excess entropy and high temperature limiting behavior

Henchman’s approximate harmonic model of liquids is extended to predict the thermodynamic behavior along lines of constant excess entropy (“isomorphs”) in the liquid and supercritical fluid regimes of the Lennard-Jones (LJ) potential phase diagram. Simple analytic expressions based on harmonic cell models of fluids are derived for the isomorph lines, one accurate version of which only requires as input parameters the average repulsive and attractive parts of the potential energy per particle at a single reference state point on the isomorph. The new harmonic cell routes for generating the isomorph lines are compared with those predicted by the literature molecular dynamics (MD) methods, the small step MD method giving typically the best agreement over a wide density and temperature range. Four routes to calculate the excess entropy in the MD simulations are compared, which includes employing Henchman’s formulation, Widom’s particle insertion method, thermodynamic integration, and parameterized LJ equations of state. The thermodynamic integration method proves to be the most computationally efficient. The excess entropy is resolved into contributions from the repulsive and attractive parts of the potential. The repulsive and attractive components of the potential energy, excess Helmholtz free energy, and excess entropy along a fluid isomorph are predicted to vary as ∼T−1/2 in the high temperature limit by an extension of classical inverse power potential perturbation theory statistical mechanics, trends that are confirmed by the MD simulations.

Perturbation theory in a microcanonical ensemble

The microcanonical ensemble is a natural starting point of statistical mechanics. However, when it comes to perturbation theory in statistical mechanics, mainly the canonical and grand canonical ensembles have been used. In this article we show how the microcanonical ensemble can be directly used to carry out perturbation theory for both non-interacting and interacting systems. We obtain the first non-trivial order answers for the specific heat of anharmonic oscillators and for the virial expansion in real gases. They are in exact agreement with the results obtained from the canonical ensemble. In addition, we show how crossover functions for the specific heat of anharmonic oscillators can be constructed using a microcanonical ensemble and also how the subsequent terms of the virial expansion can be obtained. We find that if we consider quantum free particles in a one-dimensional box of extension L, then both the ensembles give an unusual result for the first correction to the specific heat in the high temperature limit.

Holographic thermal correlators for hyperbolic CFTs

We use holography to compute the exact form of retarded Green’s functions for a scalar operator with conformal dimension ∆ in a thermal CFT and in its related counterpart with chemical potential in R1 × H3. In our analysis, we recast the wave equation of a scalar field in the normal form of Heun’s equation in the dual gravity theories described by the AdS hyperbolic blackhole and its charged version. Heun’s equation is identified to the semiclassical limit of the BPZ equation for a five-point correlator with one degenerate field insertion in the Liouville theory on the Riemann sphere. The crossing symmetry of conformal block in the Liouville theory eventually gives rise to a set of connection formulas among the solutions of Heun’s equation evaluated at different regular singularities. We use the connection formula to reproduce the leading order behaviors of the scalar field near the horizon as well as near the boundary and achieve the exact form of the retarded thermal Green’s function. We show a recipe to obtain the exact retarded Green’s function for a thermal CFT dual to AdS blackbrane from a high-temperature limit accompanied by a complex mapping on AdS hyperbolic blackhole. Moreover, we show the retarded Green’s function for the boundary CFT of Rindler AdS spacetime admits a free integer parameter.

Experimental analysis and multi-objective optimization of flame dynamics and combustion performance in methane-fueled slit-type combustors

Achieving a high wall temperature and wide flame stability limit is of extreme significance for the maximization of power generation in hydrocarbon fuel-driven micro-thermophotovoltaic and thermoelectric devices. For this, detailed experimental investigations are conducted on variable channel height combustors, with the emphasis on analyzing the flame dynamics and thermal performance. A preliminary understanding of the multiple flame morphologies in the combustors is developed by varying the input working conditions and wall materials. The basic types of unstable flames are clarified. The pinch-off phenomenon of a weak flame in a slit combustor is observed for the first time, and the cell tends to decrease and emerge with an increase in the flow rate. The combustible range is shown to be extended with increasing the channel height, while it exhibits a non-monotonic changing trend with the combustor thermal conductivity which highlights the importance of the balance between heat transfer due to the flame-wall coupling and heat losses. Furthermore, a Kriging-NSGA-II optimization model is also developed to obtain the optimal characteristics in terms of radiation efficiency, standard deviation and volume power density. A Pareto-optimal front solution is determined to identify three distinct regions of thermal conductivities, which is crucially useful in guiding the design of practical micro-power systems based on different working requirements.

Black holes and hot shells in the Euclidean path integral approach to quantum gravity

We study a spherical black hole surrounded by a hot self-gravitating thin shell in the canonical ensemble, i.e. a black hole and a hot thin shell inside a heat reservoir acting as a boundary with its area and temperature fixed. To work out the quantum statistical mechanics partition function of this matter-black hole system, from which the thermodynamics of the system follows, we use the Euclidean path integral approach to quantum gravity that identifies the path integral of the gravitational system with the partition function itself. In a semiclassical evaluation of the path integral, one needs to compute the classical action of the system. From the action, one finds the result that the total entropy, given by the sum of black hole and matter entropies, is a function of the gravitational radius of the system alone. So, the black hole inside the shell has no direct influence on the total entropy. One also finds the free energy which is equal to the action times the temperature, the thermodynamic energy, and the temperature stratification along the system. Another important result is that the heat reservoir temperature is composed of a free function of the gravitational radius of the system, which acts as a reduced temperature equation of state, divided by the redshift function at the reservoir. Upon the specification of the reduced temperature, the solutions for the gravitational radii of the system compatible with the boundary data can be found. In addition, it is found that the black hole inside the shell has two possible horizon radii. The first law of thermodynamics is then identified, and it is shown that the first law is satisfied by the system as whole, it is realized by the matter in the hot shell, and it is also applicable to the black hole. The thermodynamic stability analysis is performed through the calculation of the system’s heat capacity. By specifying the available temperature free function as the Hawking temperature equation of state of the gravitational radius of the system, which itself is not a black hole, one finds a remarkable exact mechanical and thermodynamic solution. With the exact solution in hand one establishes that pure black hole spaces, hot shell with a black hole spaces, pure hot shell spaces, and hot flat spaces are phases that cohabit in the ensemble, with some of them acting as thermodynamic mimickers. This exact thermodynamic solution for a black hole with a self-gravitating hot shell is not only of interest in itself, but can also be seen as a model to situations involving black holes interacting with hot gravitons and other hot particles. The study of the high temperature limits for the system also reveals several important aspects.

Thermodynamics of ultrarefractory condensates: Implications for the high-temperature limit of the inner dust rim of the early solar protoplanetary disk

Ultrarefractory (UR) condensates found in refractory inclusions in chondrites contain records of the early nebular thermochemistry that prevailed in the high-temperature region close to the protosun. Recent reports of the UR phases such as allendeite (Sc4Zr3O12), tazheranite ((Zr,Ti,Ca)O2−x), and kangite ((Sc,Ti,Al,Zr,Mg,Ca,□)2O3) imply, respectively, nebular condensation temperatures and origins higher than and inward of those previously deduced from calcium-aluminum-rich inclusions. However, knowledge gaps on their thermochemistry have precluded a quantitative understanding of temperatures and chemical pathways that led to their origins in the early solar protoplanetary disk. Here we use density functional theory to determine the thermochemistry of these materials for the first time. We find that allendeite is a stable phase under equilibrium conditions with its condensation temperature (1643 K at 10−4 bar) in the same range as that of nominal hibonite (CaAl12O19, 1637 K at 10−4 bar). Among the UR oxides, tetragonal ZrO2 exhibits the highest condensation temperature (1739 K at 10−4 bar) and potentially reveals the high-temperature limits at which solid dust could have survived in the inner region of the disk. In comparison, we find that pure cubic ZrO2 does not form from a cooling gas of solar composition undergoing equilibrium condensation. Similarly, we find that the stoichiometric endmember of kangite, Sc2O3 does not condense under equilibrium conditions, and moreover, the role of Ti and Zr as solutes is crucial to modeling its stability and origins.

Leading quantum correction to the classical free energy

The quantum free energy of a system governed by a standard Hamiltonian is larger than its classical counterpart. The lowest-order correction, first calculated by Wigner, is proportional to ℏ2 and involves the sum of the mean squared forces. We present an elementary derivation of this result by drawing upon the Zassenhaus formula, an operator-generalization for the main functional relation of the exponential map. Our approach highlights the central role of non-commutativity between kinetic and potential energy and is more direct than Wigner's original calculation, or even streamlined variations thereof found in modern textbooks. We illustrate the quality of the correction for the simple harmonic oscillator (analytically) and the purely quartic oscillator (numerically) in the limit of high temperature. We also demonstrate that the Wigner correction fails in situations with sufficiently rapidly changing potentials, for instance, the particle in a box.

Casimir free energy for massive scalars: A comparative study of various approaches

We compute the Casimir thermodynamic quantities for a massive real scalar field between two parallel plates with the Dirichlet boundary conditions, using three different general approaches and present explicit solutions for each. The Casimir thermodynamic quantities include the Casimir Helmholtz free energy, pressure, energy, and entropy. The three general approaches that we use are based on the fundamental definition of Casimir thermodynamic quantities, the analytic continuation method, and the zero temperature subtraction method. Within the analytic continuation approach, we use two distinct methods which are based on the utilization of the zeta function and the Schlömilch summation formula. We include the renormalized versions of the latter two approaches as well, whereas the first approach does not require one. Within each general approach, we obtain the same results in a few different ways to ascertain the selected cancellations of infinities have been done correctly. We show that, as expected, the results based on the zeta function and the Schlömilch summation formula are equivalent. We then do a comparative study of the three different general approaches and their results and show that they are in principle not equivalent to each other, and they yield equivalent results only in the massless case. In particular, we show that the Casimir energy calculated only by the first approach has all three properties of going to zero as the temperature, mass of the field or the distance between the plates increases. Moreover, we show that in this approach the Casimir entropy reaches a positive constant in the high temperature limit, which can explain the linear term in the Casimir free energy. We use the results obtained by the fundamental approach as our reference for the correct results.