Thermodynamic Limit Research Articles

Monte Carlo Based Techniques for Quantum Magnets with Long-Range Interactions.

Long-range interactions are relevant for a large variety of quantum systems in quantum optics and condensed matter physics. In particular, the control of quantum-optical platforms promises to gain deep insights into quantum-critical properties induced by the long-range nature of interactions. From a theoretical perspective, long-range interactions are notoriously complicated to treat. Here, we give an overview of recent advancements to investigate quantum magnets with long-range interactions focusing on two techniques based on Monte Carlo integration. First, the method of perturbative continuous unitary transformations where classical Monte Carlo integration is applied within the embedding scheme of white graphs. This linked-cluster expansion allows extracting high-order series expansions of energies and observables in the thermodynamic limit. Second, stochastic series expansion quantum Monte Carlo integration enables calculations on large finite systems. Finite-size scaling can then be used to determine the physical properties of the infinite system. In recent years, both techniques have been applied successfully to one- and two-dimensional quantum magnets involving long-range Ising, XY, and Heisenberg interactions on various bipartite and non-bipartite lattices. Here, we summarise the obtained quantum-critical properties including critical exponents for all these systems in a coherent way. Further, we review how long-range interactions are used to study quantum phase transitions above the upper critical dimension and the scaling techniques to extract these quantum critical properties from the numerical calculations.

Exploring mean field spin models with multiple populations: A theoretical framework

This paper thoroughly investigates the analysis of a modified generalized mean-field Ising model. The thermodynamic limit of free energy is investigated, and both the upper and lower bounds are derived. The lower bound is derived using a standard entropic variational principle, whereas a decoupling method is employed to derive the upper bound. Although the two bounds differ in form, they exhibit the same local maxima. Finally, the impact of a slight external field on the magnetic order is analyzed.

Nanotubes from Lanthanide-Based Misfit-Layered Compounds: Understanding the Growth, Thermodynamic, and Kinetic Stability Limits.

Gaining insights into the kinetics and the thermodynamic limits of nanostructures in high-temperature reactions is crucial for controlling their unique morphology, phase, and structure. Nanotubes from lanthanide-based misfit-layered compounds (MLCs) have been known for more than a decade and were successfully produced mostly via a chemical vapor transport protocol. The MLC nanotubes show diverse structural arrangements and lattice disorders, which could have a salient impact on their properties. Though their structure and charge transfer properties are reasonably well understood, a lack of information on their thermodynamic and kinetic stability limits their scalable synthesis and their applicability in modern technologies. In this study, the growth, thermodynamic stability, and decomposition kinetics of lanthanide-based misfit nanotubes of two model compounds, i.e., (LaS)1.14TaS2 and (SmS)1.19TaS2 are elucidated in detail. The nanotubes were carefully analyzed via atomic resolution electron microscopy imaging and synchrotron-based X-ray and electron diffraction techniques, and the information on their morphology, phase, and structures was deduced. The key insights gained would help to establish the parameters to explore their physio-chemical properties further. Furthermore, this study sheds light on the complex issue of the high-temperature stability of nanotubes and nanostructures in general.

Metal‐Free Organic Dyes for NiO‐Based Dye‐Sensitized Solar Cells: Recent Developments and Future Perspectives

The increasing global demand for energy and growing environmental concerns emphasize the crucial role of solar energy as a sustainable and nondepletable resource. Solar cells, particularly dye‐sensitized solar cells (DSSCs), have gained prominence due to their efficient conversion of solar power, ecofriendly manufacturing processes, and noteworthy stability. Current research in sustainable energy focuses on transitioning from metal‐based to metal‐free organic materials. Tandem solar cells, combining n‐type and p‐type semiconductors sensitized with diverse photoactive dyes, show potential to surpass thermodynamic limits in photon conversion efficiency. Notably, the exploration of n‐type DSSCs as photoanodes in tandem architectures is promising. However, the absence of efficient p‐type photoactive cathodes remains a significant obstacle. Global research efforts are dedicated to addressing charge recombination issues in NiO‐based devices to enhance the efficiency of p‐type DSSCs. The success of any DSSC hinges on the selection of dyes/sensitizers with suitable anchoring groups, wide absorption in the visible–NIR region, and a high extinction coefficient. This article comprehensively reviews advancements in developing highly efficient p‐type sensitizers, emphasizing their pivotal role in unlocking the full potential of tandem solar cells.

Flat-Histogram Monte Carlo Simulation of Water Adsorption in Metal-Organic Frameworks.

Molecular simulations of water adsorption in porous materials often converge slowly due to sampling bottlenecks that follow from hydrogen bonding and, in many cases, the formation of water clusters. These effects may be exacerbated in metal-organic framework (MOF) adsorbents, due to the presence of pore spaces (cages) that promote the formation of discrete-size clusters and hydrophobic effects (if present), among other reasons. In Grand Canonical Monte Carlo (MC) simulations, these sampling challenges are typically manifested by low MC acceptance ratios, a tendency for the simulation to become stuck in a particular loading state (i.e., macrostates), and the persistence of specific clusters for long periods of the simulation. We present simulation strategies to address these sampling challenges, by applying flat-histogram MC (FHMC) methods and specialized MC move types to simulations of water adsorption. FHMC, in both Transition-matrix and Wang-Landau forms, drives the simulation to sample relevant macrostates by incorporating weights that are self-consistently adjusted throughout the simulation and generate the macrostate probability distribution (MPD). Specialized MC moves, based on aggregation-volume bias and configurational bias methods, separately address low acceptance ratios for basic MC trial moves and specifically target water molecules in clusters; in turn, the specialized MC moves improve the efficiency of generating new configurations which is ultimately reflected in improved statistics collected by FHMC. The combined strategies are applied to study the adsorption of water in CuBTC and ZIF-8 at 300 K, through examination of the MPD and the adsorption isotherm generated by histogram reweighting. A key result is the appearance of nontrivial oscillations in the MPD, which we show to be associated with water clusters in the adsorption system. Additionally, we show that the probabilities of certain clusters become similar in value near the boundaries of the isotherm hysteresis loop, indicating a strong connection between cluster formation/destruction and the thermodynamic limits of stability. For a hydrophobic MOF, the FHMC results show that the phase transition from low density to high density is suppressed to water pressure far above the bulk-fluid saturation pressure; this is consistent with results presented elsewhere. We also compare our FHMC simulation isotherm to one measured by a different technique but with ostensibly the same molecular interactions and comment on observed differences and the need for follow-up work. The simulation strategies presented here can be applied to the simulation of water in other MOFs using heuristic guidelines laid out in our text, which should facilitate the more consistent and efficient simulation of water adsorption in porous materials in future applications.

Canonical vs. Grand Canonical Ensemble for Bosonic Gases under Harmonic Confinement.

We analyze the general relation between canonical and grand canonical ensembles in the thermodynamic limit. We begin our discussion by deriving, with an alternative approach, some standard results first obtained by Kac and coworkers in the late 1970s. Then, motivated by the Bose-Einstein condensation (BEC) of trapped gases with a fixed number of atoms, which is well described by the canonical ensemble and by the recent groundbreaking experimental realization of BEC with photons in a dye-filled optical microcavity under genuine grand canonical conditions, we apply our formalism to a system of non-interacting Bose particles confined in a two-dimensional harmonic trap. We discuss in detail the mathematical origin of the inequivalence of ensembles observed in the condensed phase, giving place to the so-called grand canonical catastrophe of density fluctuations. We also provide explicit analytical expressions for the internal energy and specific heat and compare them with available experimental data. For these quantities, we show the equivalence of ensembles in the thermodynamic limit.

Unmasking quantum effects in the surface thermodynamics of fluid nanodrops.

The focus of our study is an in-depth investigation of the quantum effects associated with the surface tension and other thermodynamic properties of nanoscopic liquid drops. The behavior of drops of quantum Lennard-Jones fluids is investigated with path-integral Monte Carlo simulations, and the test-area method is used to determine the surface tension of the spherical vapor-liquid interface. As the thermal de Broglie wavelength, λB, becomes more significant, the average density of the liquid drop decreases, with the drop becoming mechanically unstable at large wavelengths. As a consequence, the surface tension is found to decrease monotonically with λB, vanishing altogether for dominant quantum interactions. Quantum effects can be significant, leading to values that are notably lower than the classical thermodynamic limit, particularly for smaller drops. For planar interfaces (with infinite periodicity in the direction parallel to the interface), quantum effects are much less significant with the same values of λB but are, nevertheless, consequential for values representative of hydrogen or helium-4 at low temperatures corresponding to vapor-liquid coexistence. Large quantum effects are found for small drops of molecules with quantum interactions corresponding to water, ethane, methanol, and carbon dioxide, even at ambient conditions. The notable decrease in the density and tension has important consequences in reducing the Gibbs free-energy barrier of a nucleating cluster, enhancing the nucleation kinetics of liquid drops and of bubble formation. This implies that drops would form at a much greater rate than is predicted by classical nucleation theory.

Three-stage thermalization of a quasi-integrable system

We consider a system of classical hard rods or billiard balls in one dimension, initially prepared in a Bragg-pulse state at a given temperature and subjected to external periodic fields. We show that at late times the system thermalizes in the thermodynamic limit via a three-stages process characterized by: an early phase where the dynamics is well described by Euler hydrodynamics, a subsequent phase where a (weak) turbulent phase is observed and where hydrodynamic gradient expansion can be broken, and a final one where the gas thermalizes according to viscous hydrodynamics. As the hard rod gas shares the same large-scale hydrodynamics as other quantum and classical integrable systems, we expect these features to universally characterize all many-body integrable systems in generic external potentials. Published by the American Physical Society 2024

Process intensification for production of dispersants via integration of reaction and separation in a horizontal thin film evaporator

Process intensification can be achieved in specialty chemicals manufacturing via transition from batch-to-continuous processing. However, the absence of headspace in a continuous tubular reactor limits the ability to remove volatile byproducts from the reacting liquid flow. Previous studies showed that the production of succinimide dispersants follows a two-step amidation-dehydration pathway in which water is formed as a by-product. The inability to remove this water imposed a thermodynamic equilibrium limitation on the dehydration step, and hence necessitated a downstream drying step to obtain a dehydrated dispersant product within commercial specifications. In the present study, the use of an agitated, horizontal thin film evaporator (TFE) was investigated as a continuously operated reactive separator which combines reaction and dehydration into a single operating unit, reducing the overall cost and physical footprint of the process. The continuous TFE unit was first experimentally investigated as a stand-alone, integrated reactor-separator. Using this configuration, the obtained imide yield consistently exceeded the maximum thermodynamic yield at each operating temperature, confirming the efficiency of the integrated reaction and separation steps in the TFE. Next, the unit was modeled by integrating reaction kinetics with mass and energy balance equations, using appropriate correlations for heat and mass transfer from the literature which were verified for the experimental set-up. This model provided insights into the system behavior across different operating conditions, including the role of forward and reverse reactions along the TFE unit length. The model was then used to confirm the feasibility of replacing the two-step tubular reactor-evaporator process with a single TFE unit as an intensified reactive separator, further reducing the physical footprint of the process by enabling compact modular process designs.

Linear response of molecular polaritons.

In this article, we show that the collective light-matter strong coupling regime where N molecular emitters couple to the photon mode of an optical cavity can be mapped to a quantum impurity model where the photon is the impurity that is coupled to a bath of anharmonic transitions. In the thermodynamic limit where N ≫ 1, we argue that the bath can be replaced with an effective harmonic bath, leading to a dramatic simplification of the problem into one of the coupled harmonic oscillators. We derive simple analytical expressions for linear optical spectra (transmission, reflection, and absorption) where the only molecular input required is the molecular linear susceptibility. This formalism is applied to a series of illustrative examples, showing the role of temperature, disorder, vibronic coupling, and optical saturation of the molecular ensemble, explaining that it is useful even when describing an important class of nonlinear optical experiments. For completeness, we provide Appendixes A-C that include a self-contained derivation of the relevant spectroscopic observables for arbitrary anharmonic systems (for both large and small N) within the rotating-wave approximation. While some of the presented results herein have already been reported in the literature, we provide a unified presentation of the results as well as new interpretations that connect powerful concepts in open quantum systems and linear response theory with molecular polaritonics.

Effective Hamiltonian approach to kinetic Ising models: Application to an infinitely long-range Husimi-Temperley model.

The probability distribution (PD) of spin configurations in kinetic Ising models has been cast in the form of the canonical Boltzmann PD with a time-dependent effective Hamiltonian (EH). It has been argued that in systems with extensive energy EH depends linearly on the number of spins N leading to the exponential dependence of PD on the system size. In macroscopic systems the argument of the exponential function may reach values of the order of the Avogadro number which is impossible to deal with computationally, thus making unusable the linear master equation (ME) governing the PD evolution. To overcome the difficulty, it has been suggested to use instead the nonlinear ME (NLME) for the EH density per spin. It has been shown that in spatially homogeneous systems NLME contains only terms of order unity even in the thermodynamic limit. The approach has been illustrated with the kinetic Husimi-Temperley model (HTM) evolving under the Glauber dynamics. At finite N the known numerical results has been reproduced and extended to broader parameter ranges. In the thermodynamic limit an exact nonlinear partial differential equationof the Hamilton-Jacobi type for EH has been derived. It has been shown that the average magnetization in HTM evolves according to the conventional kinetic mean field equation.

Diphenyl Carbonate: Recent Progress on Its Catalytic Synthesis by Transesterification

Diphenyl carbonate is one of the raw materials used for the synthesis of polycarbonate, and its green and clean production is of great importance to the non-phosgene process for polycarbonate. The production of diphenyl carbonate by transesterification is its representative process route and is considered to be one of the typical examples of a green and sustainable process for chemicals. Since the discovery of the transesterification catalyst for diphenyl carbonate in the 1970s, researchers have been committed to improving its catalytic activity and selectivity and, correspondingly, the reaction engineering process. However, thermodynamic limitations, low activity, low selectivity, and limited stability have been bottlenecks that the transesterification catalyst has not been able to completely overcome, and the improvement of the catalyst is still ongoing. Therefore, this review takes the transesterification reaction of dimethyl carbonate and phenol as a model reaction and, based on a review of the progress in catalyst research on catalytic reaction processes, tries to clarify the structure–activity relationship between catalytic active sites and catalytic performance in homogeneous and heterogeneous catalytic processes and provides an overview of the progress in catalyst synthesis and modification.

Dynamically selected steady states and criticality in non-reciprocal networks

We consider a simple neural network model, evolving via non-linear coupled stochastic differential equations, where neural couplings are random Gaussian variables with non-zero mean and arbitrary degree of reciprocity. Using a path-integral approach, we analyse the dynamics, averaged over the network ensemble, in the thermodynamic limit. Our results show that for any degree of reciprocity in the couplings, two types of criticality emerge, corresponding to ferromagnetic and spin-glass order, respectively. The critical lines separating the disordered from the ordered phases is consistent with spectral properties of the coupling matrix, as derived from random matrix theory. As the non-reciprocity (or asymmetry) in the couplings increases, both ordered phases diminish in size, ultimately resulting in the disappearance of the spin-glass phase when the couplings become anti-symmetric. We investigate non-fixed point steady-state solutions for uncorrelated interactions. For such solutions the time-lagged correlation function evolves according to a gradient-descent dynamics on a potential, which depends on the stationary variance. Our analysis shows that in the spin-glass region, the variance dynamically selected by the system leads the correlation function to evolve on the separatrix curve, limiting different realizable steady states, whereas in the ferromagnetic region, a fixed point solution is selected as the only realizable steady state. In the spin-glass region, stationary solutions are unstable against perturbations that break time-translation invariance, indicating chaotic behaviour in large single network instances. Numerical analysis of Lyapunov exponents confirms that chaotic behaviour emerges throughout the spin-glass region, for any value of the coupling correlations. While negative correlations increase the strength of chaos, positive ones reduce it, with chaos disappearing for reciprocal (i.e. symmetric) couplings, where marginal stability is attained. On the other hand, in finite size non-reciprocal networks, fixed points and limit cycles can arise in the spin-glass region, especially close to the critical line. Finally, we show that chaos is suppressed when the strength of external noise exceeds a certain threshold. Intriguing analogies between chaotic phases in non-equilibrium systems and spin-glass phases in equilibrium are put forward.

Effect of temperature on the dissolution of the lead (II) carbonate hydrocerussite for varying pH and dissolved inorganic carbon conditions

The effect of temperature on the solubility of lead-bearing solid phases in water distribution systems for different water chemistry conditions remains unclear although lead concentrations are known to vary seasonally. The study objective is to explore the effect of temperature on the solubility of the lead(II) carbonate hydrocerussite under varying pH and DIC conditions. This is achieved through batch dissolution experiments conducted at multiple pHs (6–10) and DIC concentrations (20–200 mg CL−1) at temperatures ranging from 5 to 40 °C. A thermodynamic model was also applied to evaluate the model’s ability to predict temperature effects on lead(II) carbonate solubility including solid phase transformations. In general, increasing temperature increased total dissolved lead at high pHs and the effect of temperature was greater for high DIC conditions, particularly for pH > 8. Temperature also influenced the pH at which the dominant lead(II) solid phase switched from hydrocerussite to cerussite (occurred between pH 7.25 to 10). Finally, the model was able to capture the overall trends observed despite thermodynamic data limitations. While this study focuses on a simple lead solid-aqueous system, findings provide important insights regarding the way in which temperature and water chemistry interact to affect lead concentrations.

Temperature fluctuations in mesoscopic systems.

Temperature is a fundamental concept in thermodynamics. In macroscopic thermodynamics, systems possess their own intrinsic temperature which equals the reservoir temperature when they equilibrate. In stochastic thermodynamics for simple systems at the microscopic level, thermodynamic quantities other than temperature (a deterministic parameter of the reservoir) are stochastic. To bridge the disparity in the perspectives about temperature between the micro- and macroregimes, we assign a generic mesoscopic N-body system an intrinsic fluctuating temperature T in this work. We simplify the complicated dynamics of numerous particles to one stochastic differential equationwith respect to T, where the noise term accounts for finite-size effects arising from random energy transfer between the system and the reservoir. Our analysis reveals that these fluctuations make the extensive quantities (in the thermodynamic limit) deviate from being extensive. Moreover, we derive finite-size corrections, characterized by heat capacity of the system, to the Jarzynski equality. A possible violation of the principle of maximum work that scales with N^{-1} is also discussed. Additionally, we examine the impact of temperature fluctuations in a finite-size Carnot engine. We show that irreversible entropy production resulting from the temperature fluctuations of the working substance diminishes the average efficiency of the cycle as η_{C}-〈η〉∼N^{-1}, highlighting the unattainability of the Carnot efficiency η_{C} for mesoscopic heat engines even under the quasistatic limit. Our general framework paves the way for further exploration of nonequilibrium thermodynamics and the corresponding finite-size effects in a mesoscopic regime.

Random graphs and real networks with weak geometric coupling

Geometry can be used to explain many properties commonly observed in real networks. It is therefore often assumed that real networks, especially those with high average local clustering, live in an underlying hidden geometric space. However, it has been shown that finite-size effects can also induce substantial clustering, even when the coupling to this space is weak or nonexistent. In this paper, we study the weakly geometric regime, where clustering is absent in the thermodynamic limit but present in finite systems. Extending Mercator, a network embedding tool based on the popularity×similarity S1/H2 static geometric network model, we show that, even when the coupling to the geometric space is weak, geometric information can be recovered from the connectivity alone for networks of any size. The fact that several real networks are best described in this quasigeometric regime suggests that the transition between nongeometric and geometric networks is not a sharp one. Published by the American Physical Society 2024

When correlations exceed system size: finite-size scaling in free boundary conditions above the upper critical dimension

We progress finite-size scaling in systems with free boundary conditions above their upper critical dimension, where in the thermodynamic limit critical scaling is described by mean-field theory. Recent works show that the correlation length is not bound by the system's physical size, a belief that long held sway. Instead, two scaling regimes can be observed — at the critical and pseudo-critical temperatures. We demonstrate that both are manifest for free boundaries. We use numerical simulations of the d = 5 Ising model to analyse the magnetization, susceptibility, magnetization Fourier modes and the partition function zeros. While some of the response functions hide the dual finite-size scaling, the precision enabled by the analysis of Lee–Yang zeros allows this be brought to the fore. In particular, finite-size scaling of leading zeros at the pseudo-critical point confirms recent predictions coming from correlations exceeding the system size. This paper is dedicated to Jaroslav Ilnytskyi on the occasion of his 60th birthday.

Continuum limit of the mobility edge and taste-degeneracy effects in high-temperature lattice QCD with staggered quarks

We study the effects of taste degeneracy on the continuum scaling of the localization properties of the staggered Dirac operator in high-temperature QCD using numerical simulations on the lattice, focusing in particular on the position of the mobility edge separating localized and delocalized modes at the low end of the spectrum. We find that, if the continuum limit is approached at fixed spatial volume, the restoration of taste symmetry leads to sizeable systematic effects on estimates for the mobility edge obtained from spectral statistics, which become larger and larger as the lattice spacing is decreased. Such systematics, however, are found to decrease if the volume is increased at fixed lattice spacing. We argue that spectral statistics estimate correctly the position of the mobility edge in the thermodynamic limit at fixed spacing, and support this with an independent numerical analysis based directly on the properties of the Dirac eigenvectors, that are unaffected by taste degeneracy. We then provide a theoretical argument justifying the exchange of the thermodynamic and continuum limits when studying localization. This allows us to use spectral statistics to determine the position of the mobility edge, and to obtain a controlled continuum extrapolation of the mobility edge for the first time. Published by the American Physical Society 2024

Lattice Oxygen Redox Mechanisms in the Alkaline Oxygen Evolution Reaction

AbstractUnderstanding of fundamental mechanism and kinetics of the oxygen evolution reaction (OER) is pivotal for designing efficient OER electrocatalysts owing to its key role in electrochemical energy conversion devices. In the past few years, the lattice oxygen oxidation mechanism (LOM) arising from the anodic redox chemistry has attracted significant attention as it involves a direct O─O coupling and thus bypasses thermodynamic limitations in the traditional adsorbate evolution mechanism (AEM). Transition metal‐based oxyhydroxides are generally acknowledged as the real catalytic phase in alkaline media. In particular, their low‐dimensional layered structures offer sufficient structural flexibility to trigger the LOM. Herein, a comprehensive overview is provided for recent advances in anion redox from LOM‐based electrocatalysts. Based on analyses of electronic structure of electrocatalysts and LOM, a strategy is proposed to activate LOM. Possible identification techniques for corroboration of the oxygen redox are also reviewed. In addition, the structural reconstruction process induced by the LOM is focused and the importance of multiple in situ/operando characterizations is highlighted to unveil the structural and chemical origins of the LOM. To conclude, a prospect on the remaining challenges and future opportunities for LOM electrocatalysts is presented.

Water-Hydrocarbon Interactions in Anionic Pyrene Monohydrate.

Interactions between water and polycyclic aromatic hydrocarbons are essential in many aspects of chemistry, from interstellar and atmospheric processes to interfacial hydrophobicity and wetting phenomena. Despite their growing importance, the intermolecular potentials of the water-hydrocarbon interactions are underdeveloped compared to the water-water potentials, and there are similarly few experimental probes that are sensitive to the details of the water-hydrocarbon potential. We present a combined experimental and computational study of anionic pyrene monohydrate, one of the simplest water/hydrocarbon clusters. The action spectrum in the OH region of the mass-selected cluster ion provides a rigorous benchmark for intermolecular potentials and computational methodologies. We identify missing intermolecular interactions and shortcomings in conventional dynamics calculations by comparing experimental data to density functional theory and classical molecular dynamics calculations. Kinetic trapping is prevalent, even for one water molecule and one pyrene molecule, leading to slow equilibration in conventional molecular dynamics calculations, even on nanosecond time scales and at low temperatures (50 K). At constant energy, temperature fluctuations for the pair of molecules are substantial. Immersing the system in a bath of soft spheres and employing parallel tempering alleviates kinetic trapping and dampens temperature fluctuations, bringing the system closer to the thermodynamic limit. With such augmented sampling, a simple, flexible water model reproduces the line width and the asymmetric broadening of the symmetric OH stretching mode, which we assign to spectral diffusion. In the OH stretching region, dynamics calculations predict a more intense antisymmetric peak than experiments observe but do not predict the bimodal split symmetric peak that the experiments show. Our work suggests that electronic polarization, missing in the empirical force field, is responsible for the first discrepancy and that quantum nuclear effects, captured neither in density functional theory nor in classical dynamics, may be responsible for the second.