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Recent interest in parallelizing flat-histogram transition-matrix Monte Carlo simulations in the grand canonical ensemble, due to its demonstrated effectiveness in studying phase behavior, self-assembly and adsorption, has led to the most extreme case of single-macrostate simulations, where each macrostate is simulated independently with ghost particle insertions and deletions. Despite their use in several studies, no efficiency comparisons of these single-macrostate simulations have been made with multiple-macrostate simulations. We show that multiple-macrostate simulations are up to 3 orders of magnitude more efficient than single-macrostate simulations, which demonstrates the remarkable efficiency of flat-histogram biased insertions and deletions, even with low acceptance probabilities. Efficiency comparisons were made for supercritical fluids and vapor–liquid equilibrium of bulk Lennard-Jones and a three-site water model, self-assembling patchy trimer particles and adsorption of a Lennard-Jones fluid confined in a purely repulsive porous network, using the open source simulation toolkit FEASST. By directly comparing with a variety of Monte Carlo trial move sets, this efficiency loss in single-macrostate simulations is attributed to three related reasons. First, ghost particle insertions and deletions in single-macrostate simulations incur the same computational expense as grand canonical ensemble trials in multiple-macrostate simulations, yet ghost trials do not reap the sampling benefit from propagating the Markov chain to a new microstate. Second, single-macrostate simulations lack macrostate change trials that are biased by the self-consistently converging relative macrostate probability, which is a major component of flat histogram simulations. Third, limiting a Markov chain to a single macrostate reduces sampling possibilities. Existing parallelization methods for multiple-macrostate flat-histogram simulations are shown to be more efficient than parallel single-macrostate simulations by approximately an order of magnitude or more in all systems investigated.

2022 APR 2 (NewsRx) -- By a News Reporter-Staff News Editor at Obesity, Fitness & Wellness Week -- United States Government (Silver Spring, Maryland, United States) has been issued patent [...]

The bulk viscosity, a transport coefficient in the Navier–Stokes equation, is often neglected in the continuum mechanics of Newtonian fluids. Recently, however, the role of the bulk viscosity is highlighted in the area of surface and interface-related phenomena, in systematic model up-scaling and as an important quantity for the interpretation of acoustic sensor data. The prediction of the bulk viscosity usually employs molecular dynamics and the Green–Kubo linear response theory, which is used to sample transport properties in general from molecular trajectories. Since simulations are usually carried out at specified state points in concert with the evaluation of other thermodynamic properties, the role of thermostats in molecular dynamics needs to be explored systematically. In this work, we carefully investigate the role of thermostatting schemes and numerical implementations of the Green–Kubo formalism, in particular in the canonical ensemble, using two popular water force field models. It turns out that the sampling of the bulk and shear viscosities is a delicate challenge since details of thermostatting and numerical subtleties may have an influence on the results beyond statistical uncertainties. Based on the present findings, we conclude with hints on how to construct robust sampling in the canonical ensemble for the bulk viscosity.

Disordered biopolymer gels, such as those synthesized from polysaccharide and gelatin, play an important role in biomedical applications, particularly in tissue engineering. During the gelation process of these gels, polymer chains associate in the presence of gelling agents, forming physical cross-links known as the junction zones. In contrast to rubber-like networks, the resulting network comprises two main regions: the ordered region due to the junction zones and the amorphous region due to the unassociated chains. Under thermal fluctuations and/or external loading, the number and locations of junction zones can change leading to "zipping" (lengthening, i.e., expansion of the junction zones) and "unzipping" (shortening, i.e., shrinkage of the junction zones). This gives rise to intriguing features in biopolymer gels such as healing and damage-like energy dissipation. Despite the recognition of zipping and unzipping in such gels, the development of mathematical models that incorporate the microscopic mechanisms into the material's macroscopic mechanical properties is still in its early stages. In this paper, we provide a systematic framework for such multiscale modeling. Several critical steps are taken to equip the eight-chain network model with a previously developed micromechanics model for a coil–rod structure, where the coil represents an unassociated chain and the rod represents a junction zone. Most importantly, for a network of coil–rod structures under zero stress, the rigidity induced by the rod leads to an end-to-end distance (r 0) for the coil–rod which is different from a classical result for a Gaussian coil: n b where b is the Kuhn length and n is the number of Kuhn segments in the coil. By relaxing the incompressible assumption in the original eight-chain model, r 0 is determined for the gel network, which depends on the length of the junction zone. Consequently, as the junction zone extends/shrinks following zipping/unzipping under an external load, an irreversible deformation can occur after unloading, consistent with experimentally observed "permanent set". The extension/shrinkage of the junction zone is captured by statistical mechanics analysis in the grand canonical ensemble, which allows the exchange of segments between the coil and the rod, driven by the binding energy of polymer chain association. The model also includes explicit consideration of swelling and the influence of solvent molecules as a result of their mixing with the polymer chains in the gel network. With physically reasonable parameters, the proposed model is shown to provide good matching with experimental data on the uniaxial testing of alginate gels, revealing progressive unzipping during loading and partial re-zipping during unloading leading to the appearance of a permanent set. This formulation not only paves the way for more advanced studies of disordered biopolymer gels but also lays the groundwork for modeling hybrid gels that contain coil–rod structures as a component. [ABSTRACT FROM AUTHOR]

In electrochemical experiments, the number of electrons of the electrode immersed in the electrolyte is usually variable. Additionally, the numbers of adsorbed substances on the surface of the electrode, the solvent molecules, and counter charge ions in the near-surface region can also vary. Treating electrochemical solid–liquid interfaces with the typical fixed electron number density functional theory (DFT) approach tends to be a challenge. This can be addressed by using grand canonical ensemble approaches. We present the implementation of two grand canonical ensemble approaches in the open-source computational chemistry software CP2K that go beyond the existing canonical ensemble paradigm. The first approach is based on implicit solvent models and explicit atomistic solute (electrode with/without adsorbed species) models, and includes two recent developments: (a) grand canonical self-consistent field (GC-SCF) method (J. Chem. Phys.2017,146,114104) allowing the electron number of the system to fluctuate naturally and accordingly with the experimental electrode potential, (b) planar counter charge (J. Chem. Phys.2019,150,041722, Phys. Rev. B2003,68,245416) salt model completely screening the net charge of the electrode model. In contrast with previous studies, in our implementation, the work function (WF) (absolute electrode potential if the potential drop at the electrolyte–vacuum interface is omitted) is the constrained quantity during an SCF optimization instead of the Fermi energy. The chemical potential of electrons (negative WF) is a natural variable of the grand potential in the GC ensemble of electronic states, and this method can easily achieve stable SCF convergence and obtain an electronic structure that precisely corresponds to a user-specified WF. The second approach referred to as the GC DFT molecular dynamics (DFT-MD) simulation scheme (Phys. Rev. Lett.2002,88,213002, J. Chem. Phys.2005,122,234505, J. Am. Chem. Soc.2004,126(12),3928–3938) is based on fully explicit modeling the solvent molecules and the ions and is used to calculate the electron chemical potential corresponding to an equilibrium electrochemical half-reaction (M(n+m)++ ne–⇌ Mm+) which involves DFT-MD, by allowing the number of electrons to vary during the DFT-MD simulation process. This opens the way for forefront electrochemical calculations in CP2K for a broad range of systems.

Quantum Monte Carlo methods are powerful techniques for studying strongly interacting Fermi systems. However, implementing these methods on computers with finite-precision arithmetic requires careful attention to numerical stability. In the auxiliary-field Monte Carlo (AFMC) method, low-temperature or large-model-space calculations require numerically stabilized matrix multiplication. When adapting methods used in the grand-canonical ensemble to the canonical ensemble of fixed particle number, the numerical stabilization increases the number of required floating-point operations for computing observables by a factor of the size of the single-particle model space, and thus can greatly limit the systems that can be studied. We describe an improved method for stabilizing canonical-ensemble calculations in AFMC that exhibits better scaling, and present numerical tests that demonstrate the accuracy and improved performance of the method. [ABSTRACT FROM AUTHOR]

In order to enable large-scale molecular simulations, algorithms must efficiently utilize multicore processors that continue to increase in total core count over time with relatively stagnant clock speeds. Although parallelized molecular dynamics (MD) software has taken advantage of this trend in computer hardware, single-particle perturbations with Monte Carlo (MC) are more difficult to parallelize than system-wide updates in MD using domain decomposition. Instead, prefetching reconstructs the serial Markov chain after computing multiple MC trials in parallel. Canonical ensemble MC simulations of a Lennard-Jones fluid with prefetching resulted in up to a factor of 1.7 speedup using 2 threads, and a factor of 3 speedup using 4 threads. Strategies for maximizing efficiency of prefetching simulations are discussed, including the potentially counterintuitive benefit of reduced acceptance probabilities. Determination of the optimal acceptance probability for a parallel simulation is simplified by theoretical prediction from serial simulation data. Finally, complete open-source code for parallel prefetch simulations was made available in the Free Energy and Advance Sampling Simulation Toolkit (FEASST).

In order to enable large-scale molecular simulations, algorithms must efficiently utilize multi-core processors that continue to increase in total core count over time with relatively stagnant clock speeds. Although parallelized molecular dynamics (MD) software has taken advantage of this trend in computer hardware, single-particle perturbations with Monte Carlo (MC) are more difficult to parallelize than system-wide updates in MD using domain decomposition. Instead, prefetching reconstructs the serial Markov chain after computing multiple MC trials in parallel. Canonical ensemble simulations of a Lennard-Jones fluid with prefetching resulted in up to a factor of 1.7 speedup using 2 threads, and a factor of 3 speedup using 4 threads. Strategies for maximizing efficiency of prefetching simulations are discussed, including the potentially counter-intuitive benefit of reduced acceptance probabilities. Determination of the optimal acceptance probability for a parallel simulation is simplified by theoretical prediction from serial simulation data. Finally, complete open-source code for parallel prefetch simulations was made available in the Free Energy and Advance Sampling Simulation Toolkit (FEASST).

The potentials of redox systems involving nitrogen, oxygen, and metal ions of the first-row transition series have been computed according to the general approach of the grand canonical ensemble, which leads to the equilibrium value of the reduction potential via a (complete) sampling of configuration space at a given temperature. The approach is a single configuration approach in the sense that identical molecular structures are sampled for both the oxidized and reduced species considered in water solution. In this study, the solute and a cluster of 11–12 water molecules are treated explicitly at the same level of theory and embedded in a continuum solvent. The molecular energies are computed in the framework of the density functional theory. Our approach is basically different from the approach based on the ThermoDynamic Cycle involving gas-phase calculations of the electron affinity of the oxidized species, corrected by the differential hydration energy (obtained from continuum solvent models only) between oxidized and reduced forms. The calculated redox potentials are in agreement with the available experimental data much closer than other results so far presented in the literature. Our results are very satisfactory also in the case of the 3+/2+ redox states of the first-row transition metals, i.e., systems with a high positive charge for which enhanced effects of the solvent are expected.

We have recently proposed a new unified theoretical scheme (the “middle” scheme) for thermostat algorithms for efficient and accurate configurational sampling of the canonical ensemble. In this paper, we extend the “middle” scheme to molecular dynamics algorithms for configurational sampling in systems subject to constraints. Holonomic constraints and isokinetic constraints are used for demonstration. Numerical examples indicate that the “middle” scheme presents a promising approach to calculate configuration-dependent thermodynamic properties and their thermal fluctuations.

Grand canonical ensemble (GCE) modeling of electrochemical interfaces, in which the electrochemical potential is converged to a preset constant, is essential for understanding electrochemistry and electrocatalysis at the electrodes. However, it requires developing efficient and robust algorithms to perform practical and effective GCE modeling with density functional theory (DFT) calculations. Herein, we developed an efficient and robust fully converged constant-potential (FCP) algorithm based on Newton’s method and a polynomial fitting to calculate the necessary derivative for DFT calculations. We demonstrated with the constant-potential geometry optimization and Born–Oppenheimer molecular dynamics (BOMD) calculations that our FCP algorithm is resistant to the numerical instability that plagues other algorithms, and it delivers efficient convergence to the preset electrochemical potential and renders accurate forces for updating the nuclear positions of an electronically open system, outperforming other algorithms. The implementation of our FCP algorithm enables flexibility in using various computational codes and versatility in performing advanced tasks including the constant-potential enhanced-sampling BOMD simulations that we showcased with the modeling of the electrochemical hydrogenation of CO, and it is thus expected to find a wide spectrum of applications in the modeling of chemistry at electrochemical interfaces.

We study the thermodynamics of a d-dimensional Schwarzschild black hole, also known as a Schwarzschild-Tangherlini black hole, in the canonical ensemble. This generalizes York's formalism, which has been initially applied to four dimensions and later to five dimensions, to any number d of dimensions. The canonical ensemble, characterized by a cavity of fixed radius r and fixed temperature T at the boundary, allows for two possible black hole solutions in thermal equilibrium, a smaller black hole and a larger black hole. In four and five dimensions, these solutions have a direct exact form, whereas in an arbitrary number of dimensions, one is compelled to resort to approximation schemes or numerical calculations. From the Euclidean action and the path integral approach, we obtain the free energy, the thermodynamic energy, the thermodynamic pressure, and the entropy, of the black hole plus cavity system. The entropy of the system is given by the Bekenstein-Hawking area law. The analysis of the heat capacity of the system shows that the smaller black hole is in unstable equilibrium and the larger black hole is in stable equilibrium. The d-dimensional photon sphere radius divides the stability criterion. Indeed, if the cavity's radius is larger than the photon sphere radius, and so the black hole is small, the system is unstable, if the cavity's radius is smaller than the photon sphere radius, and so the black hole is large, the system is stable. To study perturbations on the system, a generalized free energy function is obtained that also allows one to understand the possible phase transitions between classical hot flat space and the black holes. The Buchdahl radius, that appears naturally in the general relativistic study of star structure, also shows up in our context; the free energy is zero when the cavity's radius has the d-dimensional Buchdahl radius value. Then, if the cavity's radius is larger than the Buchdahl radius, classical hot flat space phase cannot make a phase transition to a black hole phase, and if smaller, classical hot flat space can nucleate a black hole. The roles of both the photon sphere and the Buchdahl limit are present for every dimension d, indicating that, besides their known role in dynamics, these radii also play a role in the thermodynamics of gravitational systems. The close link between the canonical analysis performed and the direct perturbation of the path integral is also pointed out. Since hot flat space is a quantum system made purely of gravitons, if only gravitation is considered, it is of great interest to compare the d-dimensional free energies of quantum hot flat space and the stable black hole to find for which ranges of r and T, the quantities that characterize the canonical ensemble, one phase predominates over the other. Phase diagrams for a few different dimensions are displayed. The density of states at a given energy is found through an inverse Laplace transformation giving back the entropy of the stable black hole. Several side calculations and further deliberations are performed, namely, the calculation for the approximate expressions for the canonical ensemble black hole horizon radii, a brief study of the photon orbit radius and the Buchdahl radius in the d-dimensional Schwarzschild solution, a connection to the thermodynamics of thin shells in d spacetime dimensions which are systems that are also apt to a rigorous thermodynamic study, a presentation of quantum hot flat space in d spacetime dimensions as a thermodynamic system, an analysis of classical hot flat space in d spacetime dimensions as a product of quantum hot flat space with the black hole transitions and the corresponding phase diagrams for a few different dimensions, and a synopsis with the relevance of the work. It is still worth mentioning that the comparison of the thermodynamics of d-dimensional Schwarzschild black holes and classical hot flat space in the canonical ensemble with the thermodynamics of spherical thin shells in d dimensions yields a striking direct matching between the two systems, most notably that the photon sphere radius appears here as a thermodynamic stability divisor in both systems, and the Buchdahl radius that appears on thermodynamic grounds for canonical black holes appears also as a thermodynamic and as a dynamical radius for thin shells. [ABSTRACT FROM AUTHOR]

In this paper, we study the small-large black hole phase transition and construct the Ruppeiner geometry for the five-dimensional charged Gauss-Bonnet-AdS black hole in the grand canonical ensemble. By making use of the equal area law, we obtain the analytical coexistence curve of the small and large black holes. Then the phase diagrams are examined. We also calculate the change of the thermodynamic volume during the small-large phase transition, which indicates that there exists a sudden change among the black hole microstructures. The corresponding normalized scalar curvature of the Ruppeiner geometry is also calculated. Combing with the empirical observation of scalar curvature, we find that for low electric potential, the attractive interaction dominates among the microstructures, while a high electric potential produces repulsive interactions. In the reduced parameter space, we observe that only attractive interaction is allowed when the coexistence region is excluded. The normalized scalar curvature also admits a critical exponent 2 and a universal constant -1/8. In particular, the value of the normalized scalar curvature keeps the same along the coexistence small and large black hole curves. So in the grand canonical ensemble, the interaction can keep constant at the phase transition where the black hole microstructures change. These results disclose the intriguing microstructures for the charged AdS black hole in the Gauss-Bonnet gravity. [ABSTRACT FROM AUTHOR]

We study the thermodynamics of a five-dimensional Schwarzschild black hole, also known as a five-dimensional Schwarzschild-Tangherlini black hole, in the canonical ensemble using York's formalism. Inside a cavity of fixed size r and fixed temperature T, we find that there is a threshold at πrT=1 above which a black hole can be in thermal equilibrium with the cavity's boundary. Moreover, this thermal equilibrium can only be achieved for two specific types of black holes. One is a small black hole (compared with the cavity size r) of horizon radius r+1, while the other is a large black hole (of the order of the cavity size r) of horizon radius r+2. In five dimensions, the radii r+1 and r+2 have an exact expression. Through the path integral formalism, which directly yields the partition function of the system, one obtains the action and thus the free energy for the black hole in the canonical ensemble. The procedure leads naturally to the thermal energy and entropy of the canonical system, the latter turning out to be given by the Bekenstein-Hawking area law S=A+4, where the black hole's surface area in five dimensions is A+=2π2r3+ and r+ stands for both r+1 and r+2. We also calculate the heat capacity and find that it is positive when the heat bath is placed at a radius r that is equal or less than the photonic orbit, implying in this case thermodynamic stability, and instability otherwise. This means that the small black hole r+1 is unstable and the large one r+2 is stable. A generalized free energy is used to compare the possible thermodynamic phase transitions relative to classical hot flat space which has zero free energy, and we show that it is feasible in certain instances that classical hot flat space transits through r+1 to settle at the stable r+2, with the free energy of the unstable smaller black hole r+1 acting as the potential barrier between the two states. It is also shown that, remarkably, the free energy of the larger r+2 black hole is zero when the cavity radius is equal to the Buchdahl radius. The relation to the instabilities that arise due to perturbations in the path integral in the instanton solution is mentioned. Hot flat space is made of gravitons and it should be treated quantum mechanically rather than classically. Quantum hot flat space has negative free energy and we find the conditions for which the large black hole phase, quantum hot flat space phase, or both are the ground state of the canonical ensemble. The corresponding phase diagram is displayed in a r×T plot showing clearly the three possible phases. Using the density of states ν at a given energy E we also find that the entropy of the large black hole r+2 is S=A+2/4. In addition, we make the connection between the five-dimensional thermodynamics and York's four-dimensional results. [ABSTRACT FROM AUTHOR]

Abstract: This paper aims to investigate the peripheral mechanism of taste perception by the use of the grand canonical ensemble in statistical physics. It allows a better understanding of this process and its interpretation at a microscopic level. The experimental part allowed us to obtain psychophysical curves relative to four nutritive sweeteners (sucrose, fructose, glucose, and maltitol). These curves represent the intensity of sweetness as a function of sugar concentration in water. A Sensory Measuring Unit for Recording Flux (SMURF) device is used to obtain intensity–time curves for each of the studied sweeteners. To model these curves we have established the expressions of some models using grand canonical ensemble formalism in statistical physics and applying some simplification approaches. The fitting of the psychophysical data with statistical models by numerical simulation demonstrates a good correlation between the models and the experimental curves. Some physicochemical parameters interfere in the expression of the established models. These parameters are classified in two categories: on one hand, the steric aspect, which is manifested by the density of taste receptor site, and the number of molecules per receptor site and on the other hand, an energetic aspect illustrated by the concentration at half saturation, which gives indirectly the sweet molecule-receptor site energy of interaction.

A novel atomistic Monte Carlo (MC) methodology is presented for the simulation of systems with a complex internal microstructure away from equilibrium, directly from first principles. The methodology is based on the general equation for the nonequilibrium reversible−irreversible coupling (GENERIC) and proposes MC, and not molecular dynamics (MD), simulations in a generalized canonical ensemble. The new approach, also termed GENERIC MC, is hierarchical and starts with the definition or selection of the set of state variables describing the system at a coarse-grained level. To each state variable, a field or conjugate variable is introduced as a proper Lagrange multiplier when projecting atomistic coordinates onto the macroscopic state variables. Each conjugate variable is formally defined as the partial derivative of the system thermodynamic potential (the entropy) with respect to the corresponding coarse-grained state variable, keeping the rest of the state variables constant. The set of conjugate variables defines the extended canonical ensemble of the atomistic GENERIC MC simulation. By analyzing the structure of the canonical GENERIC equation for spatially homogeneous, time-independent flows, a kinematic interpretation is attributed to the conjugate variables of the structural state variables connecting them to the velocity gradient tensor. This sets the framework for performing realistic atomistic MC simulations, guided by the thermodynamically admissible macroscopic models derived from GENERIC, to calculate the free energy of the nonequilibrium system, without going through the full dynamical problem. The formulation is outlined here for three different viscoelastic fluid models:  the single- and multiple-conformation tensor viscoelastic models for unentangled polymers and the pompon model for long-chain branched (LCB) molecules. Results are presented from detailed end-bridging, atomistic MC simulations with the new method for the elasticity of a linear C156 polyethylene (PE) melt, in a steady-state uniaxial elongational flow. In the simulations, a four-mode conformation tensor viscoelastic model was employed to project atomistic coordinates. The dependence of the melt free energy of elasticity on chain degree of deformation due to applied flow field is reported and compared against the predictions of simple analytic models, commonly used in polymer flow calculations, such as the Hookean dumbbell and the FENE-P. The latter, which accounts for the finite extensibility of the polymer, is seen to be more representative of the actual melt response than the former. It is also seen that, in the regime of small Deborah numbers studied, only the components of the first-mode conformation tensor deviate from their equilibrium values; higher-mode conformation tensors retain their equilibrium, spherical symmetry. This explains the success of the single conformation tensor FENE-P viscoelastic model in fitting rheological data.

A general density-functional formalism using an extended variable space is presented for classical fluids in the canonical ensemble (CE). An exact equation that plays the role of the Ornstein-Zernike (OZ) equation in the grand canonical ensemble (GCE) is derived in the CE. When applied to the ideal gas we obtain the exact result for the total correlation function hN. In the case of the homogeneous fluid with Nparticles, the new equation only differs from OZ by 1/Nand it allows us to obtain an approximate expression for hNin terms of its GCE counterpart that agrees with the expansion of hNin powers of 1/N.

Reformulation of existing Monte Carlo algorithms used in the study of grand canonical systems has yielded massive improvements in efficiency. Here we present an energy biasing scheme designed to address targeting issues encountered in particle swap moves using sophisticated algorithms such as the Aggregation-Volume-Bias and Unbonding-Bonding methods. Specifically, this energy biasing scheme allows a particle to be inserted to (or removed from) a region that is more acceptable. As a result, this new method showed a several-fold increase in insertion/removal efficiency in addition to an accelerated rate of convergence for the thermodynamic properties of the system.

We hereby introduce a research about a grand canonical ensemble for the extended two-site Hubbard model, that is, we consider the intersite interaction term in addition to those of the simple Hubbard model. To calculate the thermodynamical parameters, we utilize the nonextensive statistical mechanics; specifically, we perform the simulations of magnetic internal energy, specific heat, susceptibility, and thermal mean value of the particle number operator. We found out that the addition of the intersite interaction term provokes a shifting in all the simulated curves. Furthermore, for some values of the on-site Coulombian potential, we realize that, near absolute zero, the consideration of a chemical potential varying with temperature causes a nonzero entropy.

We present a canonical ensemble approach for weakly interacting composite boson systems, which is confined with a finite number of particles. Composite bosons, made of fermion pairs, correlate to each other through the Coulomb interaction associated with the fermion exchange, and are treated perturbatively. We study Bose--Einstein condensation of composite bosons according to the specific heat capacity, the composite-boson distribution function, and the condensate fraction up to the first-order perturbations. As an example, we investigate two-dimensional confined excitons. The study shows that the fermion exchange tends to assist the exciton condensation by raising the temperature. This stabilization of the exciton condensation owing to the fermion exchange is characterized by a small trough in the specific heat capacity profile. As the temperature becomes higher than the transition temperature, the effective Coulomb interaction reduces the thermal fluctuation of excitons, leading to a negative correction to the specific heat capacity in the normal phase. Weakly interacting excitons stay in a more stable thermodynamic state in comparison with ideal exciton gases.

We present automated methods for determining the value of Adams' Bparameter corresponding to a target solvent density in grand canonical ensemble Monte Carlo simulations. The method found to work best employs a proportional-integral control equation commonly used in industrial process control applications. We show here that simulations employing this method rapidly converge to the desired target density. We further show that this method is robust over a wide range of system sizes. This advance reduces the overall CPU time and user effort in determining the equilibrium excess chemical potential in these systems.

This paper argues that the weak cosmic censorship hypothesis implies that the Schwarzschild black hole has maximal entropy in all stationary black holes of fixing temperature, or equivalently, to store a same amount of information the Schwarzschild black hole has highest temperature. It then gives the independent mathematical proofs for 4-dimensional general static black holes and stationary-axisymmetric black holes which have "t -" reflection isometry. This result does not only provide a new universal bound between temperature and entropy of black holes but also offers us new evidence to support the weak cosmic censorship hypothesis. [ABSTRACT FROM AUTHOR]

The thermodynamic behavior of the Angelescu-Verbeure-Zagrebnov (AVZ) Hamiltonian [1], also called the superstable Bogoliubov model, is solved for any temperature and any chemical potential. It is found that its thermodynamics coincides with one for the Mean-Field Gas for small chemical potential or high temperature. However, for large chemical potential or low temperature, a non-conventional Bose condensation appears with, even at zero-temperature, a (non-zero) particle density outside the condensate. Following [2], the analysis in the present paper corresponds to the main technical step to deduce, in the canonical ensemble, a new microscopic theory of superfluidity at all temperatures explained in [3].

A new computational method is presented that efficiently describes open thermodynamic systems within the grand canonical ensemble formalism. The method is based on the j-walking algorithm, which circumvent sampling difficulties by coupling random walkers in different thermodynamic states. By imposing detailed balance, a new acceptance probability is derived and applied to the construction of adsorption isotherms for atomic monolayers. The method converges much faster than the standard grand canonical Monte Carlo method and permits the construction of accurate adsorption isotherms and the identification of phase transitions occurring in the adsorbed material.

In this paper, we investigate the thermodynamics of the global monopole anti-de-Sitter black hole in the grand canonical ensemble following the York's formalism. The black hole is enclosed in a cavity with a finite radius where the temperature and potential are fixed. We have studied some thermodynamical properties, i.e. the reduced action, thermal energy and entropy. By investigating the stability of the solutions, we find stable solutions and instantons.

We investigate the thermodynamics of the slowly rotating Kerr-Newman (K-N) black hole in the grand canonical ensemble with York's formalism. Some thermodynamical properties, such as the thermodynamical action, entropy, thermodynamical energy and heat capacity are studied and solutions of the slowly rotating K-N black hole with different boundary conditions are analysed. We found stable solutions and instantons under certain boundary conditions.

We compute the shift of the critical temperature Tcwith respect to the ideal case for a weakly interacting uniform Bose gas. We work in the framework of the canonical ensemble, extending the criterion of condensation provided by the canonical particle counting statistics for the zero-momentum state of the uniform ideal gas. The perturbative solution of the crossover equation to lowest order in powers of the scattering length yields (Tc-Tc0)/Tc0= -0.93a?1/3, where Tc0is the transition temperature of the corresponding ideal Bose gas, ais the scattering length, and ? is the particle number density. This result is at variance with the standard grand canonical prediction of a null shift of the critical temperature in the lowest perturbative order. The non-equivalence of statistical ensembles for the ideal Bose gas is thus confirmed (at the lowest perturbative level) also in the presence of interactions.

A quantum statistical model of nuclear multifragmentation is proposed. The recurrence equation method used within the canonical ensemble makes the model solvable and transparent to physical assumptions and allows to get results without involving the Monte Carlo technique. The model exhibits the first-order phase transition. Quantum statistics effects are clearly seen on the microscopic level of occupation numbers but are almost washed out for global thermodynamic variables and the averaged observables studied. In the latter case, the recurrence relations for multiplicity distributions of both intermediate-mass and all fragments are derived and the specific changes in the shape of multiplicity distributions in the narrow region of the transition temperature is stressed. The temperature domain favorable to search for the HBT effect is noted.

The present study aims primarily at refining a structure model for interlayer cations and H2O molecules in tri-hydrated (3W) smectite (d001= 18-19 Å). The <2 mm fraction of the SWy-2 source clay (low-charge montmorillonite) was saturated by Mg2+, Ca2+, Ba2+, or Na+cations, before collection of X-ray diffraction (XRD) patterns at 98% relative humidity. Experimental d001values derived for the essentially homogeneous 3W hydrates provided volume constraints for Grand Canonical Monte Carlo (GCMC) simulations. Computed atomic density distribution of interlayer species were used in turn to calculate XRD intensities of 00l reflections. The agreement between calculated and experimental 00l intensities allowed validating the GCMC results of both interlayer H2O content and distribution of interlayer species (cations and H2O molecules). Computed atomic density profiles do not correspond to the usual model of three discrete planes of H2O molecules but rather exhibit two sharp planes of H2O molecules wetting the clay surfaces (at ~2.7 Å from the clay layer surface). Additional H2O molecules belong to cation hydration shells or define a poorly organized ensemble filling internal voids. This alternative model suggests that the stability of the 3W hydrate results from the dual interaction of some H2O molecules with interlayer cation, through their second hydration shell, and with the 2:1 clay surface. Computed atomic density profiles were approximated to propose an interlayer structure model for 3W smectite. This simplified model includes two sets of two planes (symmetrical relative to the interlayer mid-plane) for H2O molecules and one set for interlayer cations. This model allows reproducing experimental XRD patterns for the different samples investigated and thus represents a valid set of parameters for routine quantitative analysis of XRD profiles in an effort to determine smectite reactivity close to water-saturated conditions. Implications of such studies are crucial to provide experimental constraints on the behavior of the main vector of element transfer under conditions common in surficial environments and prevailing in waste repositories. In addition, the present study provides an experimental validation of structure models derived from the widely used ClayFF model, and thus allows its use to predict the fate of water in clayey systems close to water-saturated conditions.

We have previously (M. N. Kobrak, J. Phys. Cond. Matt., 25, 095006 (2013)) developed a novel thermodynamic theory describing the behavior of ions in a mesoscale pore with a charged interface. In the limit where the Debye length of the electrolyte is smaller than the pore, there exists an electroneutral "bulk liquid" domain sufficiently far from the interface that the surface charge is screened. Under such conditions, charging the interface can reduce the ionic strength of the electrolyte in the bulk liquid domain. Here, we improve on the model using a lattice gas treatment of the interface. The results confirm that the effect of interest is significant for concentrated electrolytes at moderate voltages in pores as large as 0.5 microns.

Functional derivative relations are developed for a finite non-uniform molecular fluid in the canonical ensemble. The total correlation function h(12) satisfies a normalization condition that renders the corresponding response kernel singular. Thus the inverse response kernel does not exist, and the direct correlation function cannot be defined in terms of h(12) by the Ornstein-Zernike equation. This difficulty is circumvented by subtracting the finite volume correction term from h(12) to obtain a modified total correlation function h(12). A simple derivation of the form of this correction term is given; the result confirms and generalizes an earlier result of Lebowitz and Percus. The Ornstein-Zernike equation defines the direct correlation function in terms of h(12). The functional derivative relations then assume the familiar forms appropriate to an infinite system or in the grand canonical ensemble, but with h(12) replaced by h(12) and with the external potential φ(1) replaced by φ(1) - μ, where μ is the chemical potential. The relation of this development to the use of the grand canonical ensemble is briefly discussed.

The existing Monte Carlo simulation models for the grand canonical ensemble proposed by many researchers to date use sequential state-generating schemes which require large amounts of computational time. In this study, a new Monte Carlo simulation model based on the stochastic Markov process theory for computer simulation of the grand canonical ensemble is developed. Essentially, in this new model the states in the grand canonical ensemble are grouped into macro states of the canonical ensembles, and a macro state Markov chain is established by a Monte Carlo sampling technique. This macro state Markov chain is then solved for a stationary solution. A prominent advantage of this new macro state Markov chain model is that it is suitable for massively parallel implementation, and hence the computational time required for the computer experiments can be reduced greatly. A massively parallel scheme for gas adsorption in zeolite 5A based on this model has been implemented on the Connection Machine CM2. A preliminary study shows that results are in good agreement with the experimental data available in the literature, and the simulation time is dramatically reduced in comparison with conventional sequential schemes.

In this article the Taylor-expansion method is introduced by which Monte Carlo (MC) simulations in the canonical ensemble can be speeded up significantly. Substantial gains in computational speed of 20-40% over conventional implementations of the MC technique are obtained over a wide range of densities in homogeneous bulk phases. The basic philosophy behind the Taylor-expansion method is a division of the neighborhood of each atom (or molecule) into three different spatial zones. Interactions between atoms belonging to each zone a re treated at different levels of computational sophistication. For example, only interactions between atoms belonging to the primary zone immediately surrounding an atom are treated explicitly before and after displacement. The change in the configurational energy contribution from secondary-zone interactions is obtained from the first-order term of a Taylor expansion of the configurational energy in terms of the displacement vector d. Interactions with atoms in the tertiary zone adjacent to the secondary zone are neglected throughout. The Taylor-expansion method is not restricted to the canonical ensemble but may be employed to enhance computational efficiency of MC simulations in other ensembles as well. This is demonstrated for grand canonical ensemble MC simulations of an inhomogeneous fluid which can be performed essentially on a modern personal computer.

The grand canonical ensemble has been used to study electrochemical potentials in confined ionic systems. Grand canonical ensemble Monte Carlo calculations for the primitive model of electrolyte solutions are presented for spherical systems, and the evaluation of single ion activity coefficients by such calculations is discussed. It is also shown that the introduction of finite, confined systems resolves a well-known problem associated with the application of the Kirkwood-Buff theory to ionic systems.

We present an algorithm for implementing molecular dynamics simulations in the grand canonical ensemble that takes advantage of parallelism. The algorithm is an extension of the one presented recently for performing Monte Carlo simulations in the same ensemble. In contrast to most commonly used algorithms for open systems, instead of physically adding or deleting molecules to generate concentration fluctuations, parallel sets of trajectories are generated using molecular dynamics simulations in the canonical ensemble, corresponding to various compositions. Appropriate combinations of chains of configurations are selected according to the prescription of the grand canonical probability distribution. The method is illustrated for a test case of the isotopic Lennard-Jones mixture. We compare the thermodynamic properties obtained with this parallel method to those obtained from the Adams algorithm for performing Monte Carlo simulations in the same ensemble, observing a faster convergence to equilibrium and smaller errors with our method. Comparisons with the parallel Monte Carlo algorithm are also made.

AbstractIt is shown by consideration of the fundamental theory that when dealing with potentials having hard cores the Grand Canonical Ensemble Monte Carlo (GCEMC) method should not introduce large errors of the type previously found in the use of the Shing-Gubbins (SG) method for estimation of the chemical potential. This is confirmed by making simulation runs using the GCEMC and the Canonical Ensemble Monte Carlo (CEMC) methods on similar systems having the hard-core Lennard-Jones intermolecular potential. Only when the hardcore parameter (α) (where the hard-core diameter is α[sgrave], [sgrave] being the Lennard-Jones length parameter) is increased from 0.9 to 0.95 are appreciable changes in density and reduced potential energy (for a given μ) found. Corresponding, though much larger, changes in the fluctuations quantities fNN(= < N2> - < N> 2) and fNU(= < NUN> - < N> < UN>), though not in fNU/fNN, also occur.

As in the grand canonical treatment of Reissner–Nordström black holes in anti-de Sitter spacetime, the canonical ensemble formulation also shows that non-extremal black holes tend to have lower action than extremal ones. However, some small non-extremal black holes have higher action, leading to the possibility of transitions between non-extremal and extremal black holes.

A study of the action of electrostatic forces leads to an electrostatic model for simulating the interaction energy between an ion and the point charges which constitute its atmosphere. The electrostatic model employs a geometrical configuration of the charges of an ion atmosphere in which the charges are considered to move about the ion in a plane polarized motion under the control of the electrostatic forces, leading to an effective reduction in the ionization potential. Thus, a new physical model is presented which can serve as a basis for analyzing the long range electrostatic effects encountered in the multiple ionization thermally of a gaseous mixture and for incorporating these effects in the evaluation of the canonical ensemble partition function of the thermodynamic system.

The canonical ensemble molecular dynamics method proposed by Nosé (1984, Molec. Phys., 52, 255 and 1984, J. chem. Phys., 81, 511) is extended to include more than one temperature control variable. This extension makes it possible to control temperatures of different degrees of freedom (e.g. translation and molecular rotation) separately.

A hybrid Monte Carlo method with adaptive temperature choice is presented that exactly generates the distribution of a mixed‐canonical ensemble composed of two canonical ensembles at low and high temperature. The analysis of resulting Markov chains with the reweighting technique shows an efficient sampling of the canonical distribution at low temperature whereas the high temperature component facilitates conformational transitions, which allows shorter simulation times. The algorithm is tested by comparing analytical and numerical results for the small n‐butane molecule before simulations are performed for a triribonucleotide. Sampling the complex multiminima energy landscape of this small RNA segment, we observe enforced crossing of energy barriers. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1689–1697, 1998

A study is made of the grand canonical ensemble of single-component systems of particles in a region ?. A new representation of the Ursell functions is given. In it an Ursell function is represented as a sum of products of Mayer and Boltzmann functions over the subset of connected graphs labeled by trees. Such a representation greatly reduces the complexity of the structure of these functions. A new definition of all-round tending of the region ? to infinity is given. The relationship between this definition and the well-known definition of tending of the set ? to infinity in the sense of Fisher is demonstrated in examples. It is shown that in the case of all-round tending of the set ? to infinity a term-by-term passage to the limit can be made in the series in Ruelle's representation of the correlation functions as a finite sum of finite products of convergent series. The domain of convergence of the obtained expansions is discussed. As examples, the expansions of the single-particle and binary correlation functions are obtained.

The grand canonical ensemble of single-component systems of particles in a region ? is considered. It is shown that if the distribution density of one particle tends to a finite limit as the diameter of ? tends to infinity then under fairly general conditions this limit is represented by the function that, as is shown in an earlier paper of the author, is, under certain conditions, the analytic continuation of the Mayer expansion representing the density as a function of the activity.

A representation is found for the coefficients of the expansion of the one-point correlation function (the one-particle distribution density) in a series in powers of the activity that makes it possible to calculate, at least approximately, the first few coefficients of the expansion. The results can also be used to investigate problems of the thermodynamic limit in the grand canonical ensemble.

AbstractFive methods are described for the distribution over a 3D Transputer array of the calculation of the pair interaction component of particle energy. The most efficient method, expressed in terms of the time to complete a simulation, depends on the size of the simulation and the Transputer array. This dependence is quantified, with emphasis on Grand Canonical Ensemble Monte Carlo simulation, and yields criteria for the optimum strategy for parallel implementation of GCEMC algorithms. The equations derived are generally applicable, and have implications for the programming of Molecular Dynamics simulations.

An extended system Hamiltonian for the grand canonical ensemble that includes the number dependence of the ideal chemical potential is investigated. Use of the ideal contribution explicitly in the equations of motion provides simpler and more stable equations of motion than previous grand molecular dynamics methods. We find the equations of motion remain quite stable even in gaseous conditions where mean field treatments of the ideal contribution provide a trivial result. The equations of motion are solved in real variable space as opposed to using virtual variables. Application of this simulation method with a Lennard-Jones fluid in the gas, fluid and solid phases is demonstrated.

The heat batch coupling of Andersen leading to canonical ensemble molecular dynamics (MD) simulations is extended to fully or partially rigid molecules within a description using cartesian coordinates for the atoms. In particular, we propose a new method to sample cartesian velocities of the individual atoms in which the use of generalized coordinates is completely avoided. We also give a straightforward implementation of this method when it is combined with a usual MD program integrating the cartesian equations of motion. For systems consisting of partially rigid molecules, this method is particularly appropriate for establishing, in an efficient way, the thermal equilibrium among all the inter-intramolecular modes explicitly considered.

We apply a technique to simulate the canonical ensemble, mixing molecular dynamics and Monte Carlo techniques, in which particles suffer virtual hard shocks. In the limit of infinite time the system approaches a Boltzmann distribution. A good approximation to the Boltzmann distribution is achieved in computationally accessible time for some model systems including the one-dimensional jellium.

We present a new technique to simulate the contact of a molecular dynamics system with a thermal wall. A canonical ensemble is obtained, and its statistical and thermodynamic fluctuations are studied. The values of the specific heat found by simulation agree with the experimental data. By means of thermal walls at different temperatures, thermal gradients are obtained. The values of the thermal conductivity are consistent with the experimental data.

Thermal equilibrium between (quantum) systems is taken to mean stability for the combined system. Necessary and sufficient conditions for such stability are found and used to show that any system in equilibrium with suitably complex second system (“heat bath”) will be characterized by a canonical ensemble. Thus the notion of temperature is derived directly from that of equilibrium, without, for example, recourse to microcanonical ensembles or information theory. Discussed briefly are the generalization of these results to grand canonical ensembles and their application to the equilibrium between a black hole and the surrounding radiation field.