Canonical Ensemble Research Articles

Statistical mechanics of crystal nuclei of hard spheres.

In the study of crystal nucleation via computer simulations, hard spheres are arguably the most extensively explored model system. Nonetheless, even in this simple model system, the complex thermodynamics of crystal nuclei can sometimes give rise to counterintuitive results, such as the recent observation that the pressure inside a critical nucleus is lower than that of the surrounding fluid, seemingly clashing with the strictly positive Young-Laplace pressure we would expect in liquid droplets. Here, we re-derive many of the founding equations associated with crystal nucleation and use the hard-sphere model to demonstrate how they give rise to this negative pressure difference. We exploit the fact that, in the canonical ensemble, a nucleus can be in a (meta)stable equilibrium with the fluid and measure the surface stress for both flat and curved interfaces. Additionally, we explain the effect of defects on the chemical potential inside the crystal nucleus. Finally, we present a simple, fitted thermodynamic model to capture the properties of the nucleus, including the work required to form critical nuclei.

Investigation of hybrid modeling and its transferability in building load prediction used for district heating systems

In the district heating systems, the historical operation data of the buildings in those areas would be partially or entirely missing. The traditional data-driven model is hard to predict the ground truth results because the historical data is not available for model training. However, utilizing the physics-based methods for load calculation takes a long time to process and encounters low accuracy issues. This paper investigates several hybrid models that integrate the data-driven model and the physics-based models with different fusion methods. The physics-based models calculate envelope load and infiltration load, based on Fourier's law and the grand canonical ensemble theory, respectively. After undergoing load processing, features fusion, and residual connection, the best advanced hybrid models generate 21.35%, 16.35%, and 12.73% better prediction results compared with the data-driven model. Moreover, the advanced hybride models also perform strong transferability across all the data quantity groups. In terms of practical application, the advanced hybrid models could be deployed with effective generalization in limited data scenarios and robust transfer capabilities. The selected best model constructed by hybrid modeling displays the highest performance and saves the total training costs with strong transferability.

Riemann surfaces and winding numbers of Rényi phase structure of charged-flat black holes

It’s widely recognized that the free energy landscape captures the essentials of thermodynamic phase transitions. In this work, we extend the findings of [1] by incorporating the nonextensive nature of black hole entropy. Specifically, the connection between black hole phase transitions and the winding number of Riemann surfaces derived through complex analysis is extended to the Rényi entropy framework. This new geometrical and nonextensive formalism is employed to predict the phase portraits of charged-flat black holes within both the canonical and grand canonical ensembles. Furthermore, we elucidate novel relations between the number of sheets comprising the Riemann surface of the Hawking–Page and Van der Waals transitions and the dimensionality of black hole spacetimes. Notably, these new numbers are consistent with those found for charged-AdS black holes in Gibbs–Boltzmann statistics, providing another significant example of the potential connection between the cosmological constant and the nonextensive Rényi parameter.

Topological properties of black holes in five-dimensional gauged supergravity

In this paper, we study the topological properties of five-dimensional rotating charged black holes in different ensembles.The topological numbers for the black holes are gotten in the grand canonical and canonical ensembles, which are 1. When the charge and cosmological constant disappear, their topological numbers are 0. When the pressure is lower than the critical pressure, the phase transition exists in the canonical ensemble. However, the phase transition also exists in the grand canonical ensemble when the pressure is higher than the critical pressure and two independent rotational parameters are a=1 and b=−1. This may be due to the fact that the values of the rotational parameters change the supersymmetry of the black hole and lead to the phase transition.

The utilization of Rutin-loaded lipid nanoparticles as promise carriers to enhance the therapeutic efficacy in ovarian cancer: A computational and experimental study

Since natural chemicals can act as multi-targeted agents in the fight against cancer, recently, highly interested in using them to reduce the adverse effects of cancer treatment, therefore, developing novel and efficient therapeutic methods for cancer is paramount. Studies have demonstrated that Ru exhibits widespread pharmacological properties, such as antioxidant, anti-inflammatory, antiangiogenic, pro-apoptotic, and anti-proliferative activities. These qualities can potentially contribute to the prevention and treatment of cancer. This research aims to develop nano-lipid carriers (NLC) that transport the Ru to OV (SK-OV-3), forcing them to undergo apoptosis and ultimately terminate the cancer cell’s life. First, the molecular structure of water, and other materials were constructed using Material Studio software. Then, the structure of the molecules was optimized through the Forcite module in the software. In sequence, to set the temperature of the system the MD simulations were run under the NVT ensemble with velocity scale as a thermostat and total simulation time equal to 100 ps as the initialization step. We applied the hydrophobic-hydrophobic interactions and micellization process method to encapsulate Ru into NLC. The computational studies showed that in the first 30 ps of the simulation, the system was unstable, but after that, the system reached a stable condition. Moreover, we observed that the density of the system rapidly decreased to a stable mean value equal. Also, the characterizations using DLS and TEM imaging showed that the synthesized NPs have a size lower than 100 nm. The hemolysis evaluation showed that the Ru-micelles are hemocompatible and induced lower than 10 % hemolysis in all tested group. The result shows that the synthesized NLC loading efficiency was 73.63 %, and the particle size was 76 ± 3 nm. The Ru release experiment demonstrated that the loaded sample (Ru-NLC) exhibited a steady release effect, with a total release amount of 84.62 ± 1.61 % of the loaded quantity over 48 h. The findings of in vitro results indicate that Ru-NLC substantially impacts the metabolism of SK-OV-3 cells, and ultimately increases the amount of apoptosis protein levels. Because of these alterations, the cell’s capacity for growth is diminished, and it ultimately dies due to intrinsic apoptosis. The results of the Western blotting experiment indicate that Ru-NLC increases the apoptosis in cancer cells. At long last, we have demonstrated that loading Ru into NLC increased the solubility and bioavailability and could increase the therapeutic efficacy.

On the nonequilibrium dynamics of gravitational algebras

Abstract We explore nonequilibrium features of certain operator algebras which appear in quantum gravity. The algebra of observables in a black hole background is a Type II ∞ von Neumann algebra. We discuss how this algebra can be coupled to the algebra of observable of an infinite reservoir within the canonical ensemble, aiming to induce nonequilibrium dynamics. The resulting dynamics can lead the system towards a nonequilibrium steady state which can be characterized through modular theory. Within this framework we address the definition of entropy production and its relationship to relative entropy, alongside exploring other applications.

Dissociation temperature of gas hydrates through isenthalpic-isobaric molecular dynamics simulations.

Molecular simulations are a powerful tool to understand phenomena and obtain properties of gas hydrate systems. The direct coexistence method (DCM) in the NVT or NPT ensembles, the most commonly used method to determine hydrate dissociation temperatures, can be computationally expensive due to the need for several long simulations. Through an extensive set of simulations, we report here the details of the DCM within the NPH (isobaric-isenthalpic) ensemble, which require fewer and shorter trajectories. The dissociation pressure of methane hydrates is obtained for pressures of 4, 8, 15, 30, and 50 MPa. The values are in agreement with other literature simulations and experimental data. The results are further validated with the calculation of the enthalpy of dissociation, with a value of 50kJ/mol of methane, also in agreement with the literature. The complexity of a multiphase and multicomponent system presents challenges lacking in simpler water/ice systems. These are found to be dependent on energy conservation. The optimal set of parameters to achieve it is also reported, including a smaller time step and the use of double precision, along with an analysis of some factors that could affect the convergence of the method. Although these parameters require more computational cost, the NPH ensemble is successful in providing the dissociation temperature of gas hydrates in fewer simulations than other ensembles and with productions lasting only 500ns.

Phase equilibrium and separation process of byproduct vinyl acrylate in the ethylene vapor phase method producing vinyl acetate

Vinyl acrylate is one of the byproducts in the ethylene vapor phase method for the production of vinyl acetate (VAc), which not only has a toxic effect on the catalyst but also affects the purity of the product. Currently, phase equilibrium data for vinyl acrylate with water are missing, making the destination of vinyl acrylate in the distillation process uncertain. This has led to a lack of effective removal means, which restricts the optimization of the ethylene vapor phase method. This paper uses a method combining quantum chemistry and molecular dynamics simulation (MD) to investigate the existential form of the water molecule. And based on the ab initio calculation of the first principle, the force field parameters of the special water molecular structure are calculated, and the TIP4P-P force field that can describe the special water structure is established. Using the Gibbs Ensemble Monte Carlo (GEMC) method, the reliability of the improved water molecule force field for modeling the phase equilibrium of a binary system is first verified. Further, vapor–liquid phase equilibrium data for the vinyl acrylate-water binary system at 110 kPa and 150 kPa are calculated and the corresponding x-y and T-x-y phase diagrams are plotted. After performing the thermodynamic consistency test, the phase equilibrium data are fitted to obtain the binary interaction parameters of vinyl acrylate with water. The fitted parameters are applied to the process simulation of the VAc refining process to optimize the conditions and obtain an effective separation scheme for vinyl acrylate. The concentration distribution of vinyl acrylate in the distillation column is investigated, thus clarifying the destination of vinyl acrylate in the distillation process and facilitating the optimization of the ethylene vapor phase method.

Accurate and Fast Estimation of the Continuum Limit in Path Integral Simulations of Quantum Oscillators and Crystals.

Convergence of imaginary-time path integral results requires a substantial number of beads (n) when quantum effects are significant. Traditional Trotter scaling approaches estimate the continuum limit (n → ∞) through extrapolation; however, their validity is restricted to the asymptotic domain of large n. We introduce an efficient extrapolation approach for quantum oscillators and crystals with harmonic character. The fitting function is inspired by the analytic solution of the harmonic oscillator (HO), or the Einstein crystal for solids. While the formulation is designed for first derivative properties (energy and pressure), its extension to second derivative properties (e.g., heat capacity) is straightforward. We apply the method to a one-dimensional HO and anharmonic oscillator (AO), as well as a three-dimensional Lennard-Jones crystal. Configurations are sampled using path integral molecular dynamics simulations in the canonical ensemble, at a low temperature of T = 0.1 (simulation units). Compared to Trotter extrapolation approaches, the new method demonstrates a substantial accuracy in estimating the continuum limit, using only a few simulations of relatively small system sizes. This efficiency significantly reduces computational cost, providing a powerful tool to facilitate computations for more complex and challenging systems, such as molecules and crystals modeled using ab initio methods.

Phantom BTZ black holes

Motivated by the impact of the phantom field (or anti-Maxwell field) on the structure of three-dimensional black holes in the presence of the cosmological constant, we present the first extraction of solutions for the phantom BTZ (A)dS black hole. In this study, we analyze the effect of the phantom field on the horizon structure. Furthermore, we compare the BTZ black holes in the presence of both the phantom and Maxwell fields. Additionally, we calculate the conserved and thermodynamic quantities of the phantom BTZ black holes, demonstrating their compliance with the first law of thermodynamics. Subsequently, we assess the effects of the electrical charge and the cosmological constant on the local stability in the canonical ensemble by considering these fields with respect to the heat capacity. We then investigate the global stability area of the BTZ black holes with phantom and Maxwell fields within the grand canonical ensemble using Gibbs free energy. In this analysis, we evaluate the influence of the electrical charge and the cosmological constant on this area.

Critical assessment of diffusion coefficients of benzene and its derivatives in supercritical carbon dioxide: Experimental data, molecular dynamics simulations, and modeling

The tracer diffusion coefficient (D12) is a critical transport property essential for research, design and optimization of industrial processes. However, experimental determination of D12 is often challenging, time-consuming, and frequently exhibits significant variability across different systems and conditions. In this study, a comprehensive assessment of D12 for benzene, phenol, chlorobenzene, anisole, and the three isomers of dichlorobenzene in supercritical carbon dioxide (▪) is presented. The available experimental data was meticulously compiled and analyzed, comparing different data points from various authors to assess consistency and accuracy. The experimental values were then compared with predictions from classical molecular dynamics (MD) simulations carried out in this work, in which three distinct ▪ force fields (EPM2, TraPPE, and Zhu et al.) and the OPLS-AA force field for the solute molecules were tested in combination with NVT and NPT ensembles. Among the evaluated combinations of force field and ensemble, the Zhu et al./NPT pair demonstrated excellent agreement with experimental data, achieving an overall deviation of only 5.63 %.Additionally, the performance of alternative approaches for estimating D12, including phenomenological and semi-empirical models—Wilke-Chang, Lai-Tan, Tracer Liu-Silva-Macedo and He-Yu equations—and machine learning (ML) algorithms was evaluated, highlighting their comparative accuracy while accounting for their inherent limitations. Overall, the ML model proved highly effective, with a deviation of only 2.42 % when applied to compounds within the training dataset. However, for compounds outside this dataset, the reliability, flexibility and accuracy of MD simulations, as demonstrated in this study, strongly suggest their application for D12 estimation in ▪/benzene-derivative systems, with possible additional valuable insights from the analysis of MD trajectories.

Partition function approach to non-Gaussian likelihoods: macrocanonical partitions and replicating Markov-chains

Monte-Carlo techniques are standard numerical tools for exploring non-Gaussian and multivariate likelihoods. Many variants of the original Metropolis-Hastings algorithm have been proposed to increase the sampling efficiency. Motivated by Ensemble Monte Carlo we allow the number of Markov chains to vary by exchanging particles with a reservoir, controlled by a parameter analogous to a chemical potential μ, which effectively establishes a random process that samples microstates from a macrocanonical instead of a canonical ensemble. In this paper, we develop the theory of macrocanonical sampling for statistical inference on the basis of Bayesian macrocanonical partition functions, thereby bringing to light the relations between information-theoretical quantities and thermodynamic properties. Furthermore, we propose an algorithm for macrocanonical sampling, 𝙰𝚟𝚊𝚕𝚊𝚗𝚌𝚑𝚎 𝚂𝚊𝚖𝚙𝚕𝚒𝚗𝚐, and apply it to various toy problems as well as the likelihood on the cosmological parameters Ωm and w on the basis of data from the supernova distance redshift relation.

Generalized hydrodynamics and approach to generalized Gibbs equilibrium for a classical harmonic chain

Abstract We study the evolution of a classical harmonic chain with nearest-neighbor interactions starting from domain wall initial conditions. The initial state is taken to be either a product of two Gibbs ensembles (GEs) with unequal temperatures on the two halves of the chain or a product of two generalized Gibbs ensembles (GGEs) with different parameters in the two halves. For this system, we construct the Wigner function and demonstrate that its evolution defines the generalized hydrodynamics (GHD) describing the evolution of the conserved quantities. We solve the GHD for both finite and infinite chains and compute the evolution of conserved densities and currents. For a finite chain with fixed boundaries, we show that these quantities relax as ∼ 1 / t to their respective steady-state values given by the final expected GE or GGE state, depending on the initial conditions. Exact expressions for the Lagrange multipliers of the final expected GGE state are obtained in terms of the steady-state densities. In the case of an infinite chain, we find that the conserved densities and currents at any finite time exhibit ballistic scaling while, at infinite time, any finite segment of the system can be described by a current-carrying non-equilibrium steady state (NESS). We compute the scaling functions analytically and show that the relaxation to the NESS occurs as ∼ 1 / t for the densities and as ∼ 1 / t 2 for the currents. We compare the analytical results from hydrodynamics with those from exact microscopic numerics and find excellent agreement.

Phase behavior analysis of methane confined in nanopores using molecular simulation

Interest in the phase behavior of hydrocarbons in shale reservoirs has grown in recent years. Petroleum fluid phase behavior has been observed to differ significantly between conventional reservoirs and shale reservoirs. Within shale reservoirs, notable surface-fluid interactions can lead to non-uniform molecule distribution and an alteration in fluid phase behavior, primarily caused by the existence of nano-scale porous materials. In this work, we study the phase behavior of methane in single cylindrical pore models. We apply the gauge Gibbs ensemble Monte Carlo (gauge-GEMC) simulation technique to investigate the phase behavior of methane in 4–10 nm single nanopores and calculate the saturation pressures at various temperatures using the grand canonical Monte Carlo (GCMC) simulation technique. A shift in the phase diagram has been found for methane in nanopores. As pore size decreases, the shift becomes more significant.

MEDOC: A fast, scalable and mathematically exact algorithm for the site-specific prediction of the protonation degree in large disordered proteins.

Intrinsically disordered regions are found in most eukaryotic proteins and are enriched in positively and negatively charged residues. While it is often convenient to assume these residues follow their model-compound pK a values, recent work has shown that local charge effects (charge regulation) can upshift or downshift sidechain pK a values with major consequences for molecular function. Despite this, charge regulation is rarely considered when investigating disordered regions. The number of potential charge microstates that can be populated through acid/base regulation of a given number of ionizable residues in a sequence, N , scales as ∼2 N . This exponential scaling makes the assessment of the full charge landscape of most proteins computationally intractable. To address this problem, we developed MEDOC (Multisite Extent of Deprotonation Originating from Context) to determine the degree of protonation of a protein based on the local sequence context of each ionizable residue. We show that we can drastically reduce the number of parameters necessary to determine the full, analytic, Boltzmann partition function of the charge landscape at both global and site-specific levels. Our algorithm applies the structure of the q -canonical ensemble, combined with novel strategies to rapidly obtain the minimal set of parameters, thereby circumventing the combinatorial explosion of the number of charge microstates even for proteins containing a large number of ionizable amino acids. We apply MEDOC to several sequences, including a global analysis of the distribution of pK a values across the entire DisProt database. Our results show differences in the distribution of predicted pK a values for different amino acids, in agreement with NMR-measured distributions in proteins.

Dephasing dynamics of a central spin interacting with a classical Ising spin bath

We study the effect of interaction between bath spins on central spin dynamics. For this end, we consider various types of interactions among the bath fluctuators. We give an analytical relation for the dephasing dynamics of a central spin homogeneously interacting with a bath of classically interacting spins in thermal equilibrium. The obtained exact relation for the central spin dynamics depends on the average of the number of bath spins N in the canonical ensemble. We find the relation of dephasing time with bath's temperature and strength of interaction between bath spins. We show that if the classically interacting bath is large enough, off-diagonal coherence will decay into Gaussian form. This Gaussian decay is valid for temperatures higher than critical temperature. Moreover, we analytically prove the equivalence of dephasing dynamics for central spin models with classical Ising spin bath and quantum flip-flop spin bath interactions. Therefore, the dephasing dynamics for central spin models with quantum spin bath interactions can be reproduced with much less expensive classical spin bath interaction model instead. Our results can be applied in a number of quantum systems used in quantum sensing such as color centers in solids or quantum dots manuscript.

Robust finite-temperature many-body scarring on a quantum computer

Mechanisms for suppressing thermalization in disorder-free many-body systems, such as Hilbert space fragmentation and quantum many-body scars, have recently attracted much interest in foundations of quantum statistical physics and potential quantum information processing applications. However, their sensitivity to realistic effects such as finite temperature remains largely unexplored. Here, we have utilized IBM's Kolkata quantum processor to demonstrate an unexpected robustness of quantum many-body scars at finite temperatures when the system is prepared in a thermal Gibbs ensemble. We identify such robustness in the PXP model, which describes quantum many-body scars in experimental systems of Rydberg atom arrays and ultracold atoms in tilted Bose-Hubbard optical lattices. By contrast, other theoretical models which host exact quantum many-body scars are found to lack such robustness and their scarring properties quickly decay with temperature. Our study sheds light on the important differences between scarred models in terms of their algebraic structures, which impacts their resilience to finite temperature. Published by the American Physical Society 2024

Li diffusion in oxygen-chlorine mixed anion borosilicate glasses using a machine-learning simulation.

Lithium-ion conducting borate glasses are suitable for solid-state batteries as an interfacial material between a crystalline electrolyte and an electrode, thanks to their superior formability. Chlorine has been known to improve the electron conductivity of borate glasses as a secondary anion. To examine the impact of chlorine on lithium dynamics, molecular dynamics (MD) simulations were performed with a machine-learning interatomic potential (MLIP). The accuracy of the MLIP in modeling chlorine-doped lithium borate (LBCl) and borosilicate (LBSCl) glasses was verified by comparing with available experimental data on density, neutron diffraction S(q), and glass transition temperatures (Tg). While the MLIP-MD simulations underestimated the density when an isobaric-isothermal (NPT) ensemble was used, the glass models relaxed using the NPT ensemble after a melt-quench simulation employing a canonical (NVT) ensemble possessed reasonable density. The LBCl and LBSCl glass models exhibited increased lithium ion diffusion, and the ions were found to travel longer distances with an increase in the chlorine content. According to the structural analyses, it was observed that chlorine ions primarily interacted with lithium ions rather than the network formers. Consequently, lithium ions that interacted with a higher amount of chlorine showed a moderate increase in mobility. In summary, the MLIP demonstrated reasonable accuracy in modeling chlorine-containing borate glasses and enabled the investigation of the effect of chlorine on electron conductivity. In contrast, the first sharp diffraction peaks in S(q) deviated from the experimental diffractions, suggesting that additional efforts are required to accurately model the middle-range structure of the glasses.

Thermo-Magnetic properties of non-relativistic particles under the effect of energy-dependent Hellmann potential

This manuscript presents an analysis of the thermal and magnetic properties of particles moving in two dimensions under the influence of an external magnetic field and Aharanov-Bohm flux, considering an energy-dependent Hellmann potential. The energy eigenvalue is obtained using the asymptotic iteration method. Next, we model the system as a canonical ensemble and derive the partition function to acquire analytical expressions for the Helmholtz free energy, entropy, mean energy, and specific heat. We observe that an increase in the external magnetic field and AB flux generally increases the energy eigenvalues, with a stronger effect at lower flux values, while energy eigenvalues decrease with an increase in the screening parameter. Additionally, Helmholtz free energy and entropy functions are sensitive to temperature, particularly in the low-temperature regime, while specific heat exhibits a Schottky anomaly. We also compute the magnetisation and susceptibility functions, finding that both magnetisation and susceptibility increase with the external magnetic field strength and the AB flux.

Pseudogap Effects in the Strongly Correlated Regime of the Two-Dimensional Fermi Gas.

The two-species Fermi gas with attractive short-range interactions in two spatial dimensions provides a paradigmatic system for the understanding of strongly correlated Fermi superfluids in two dimensions. It is known to exhibit a BEC to BCS crossover as a function of ln(k_{F}a), where a is the scattering length, and to undergo a Berezinskii-Kosterlitz-Thouless superfluid transition below a critical temperature T_{c}. However, the extent of a pseudogap regime in the strongly correlated regime of ln(k_{F}a)∼1, in which pairing correlations persist above T_{c}, remains largely unexplored with controlled theoretical methods. Here, we use finite-temperature auxiliary-field quantum MonteCarlo methods on discrete lattices in the canonical ensemble formalism to calculate thermodynamical observables in the strongly correlated regime. We extrapolate to continuous time and the continuum limit to eliminate systematic errors and present results for particle numbers ranging from N=42 to N=162. We estimate T_{c} by a finite-size scaling analysis, and observe clear pseudogap signatures above T_{c} and below a temperature T^{*} in both the spin susceptibility and free-energy gap. We also present results for the contact, a fundamental thermodynamic property of quantum many-body systems with short-range interactions.