Search

Determining fluid pressure in Monte Carlo simulations can be a challenging task due to the reduced arsenal of computational tools available to perform such measurements. In addition, none of these tools is general enough to calculate the equilibrium pressure for a wide variety of models. The Gibbs–Duhem method, for example, is a very useful option, but only for pure (one component) systems. To enrich this arsenal, we propose here a direct method to calculate pressure in the canonical ensemble, which could easily be extended to mixtures at low densities. In analogy with the Widom method, our approach is based on the free energy variation with volume, described in terms of the removal of an empty or particle-occupied lattice column. We tested our approach for the lattice gas model and compared the results with exact Onsager solutions. Furthermore, the appearance of thermodynamic instabilities (loops) in the pressure isotherms during the phase transition and their relationship with interface effects are discussed. Finally, a phase diagram is obtained from these isotherms using the Hill construction. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we study the reentrant Hawking–Page transition in the grand canonical ensemble of Gauss–Bonnet AdS spacetime. We find that the four-dimensional Gauss–Bonnet hyperbolic AdS black hole always has a reentrant Hawking–Page transition in the range of electric potential $$0\Phi _{tr}$$ Φ > Φ tr , the Hawking–Page transition disappears. In the spacetime of five and higher dimensional Gauss–Bonnet hyperbolic AdS black hole, the reentrant Hawking–Page transition is solely observed to occur when the electric potential $$\Phi $$ Φ lies between two specific thresholds ( $$\Phi _{c}\Phi _{tr}$$ Φ > Φ tr ). We give the coexistence line, the triple point and critical point of the Hawking–Page transition in the phase diagram of the Gauss–Bonnet hyperbolic AdS black hole. The observed reentrant Hawking–Page transitions and triple points in the context of Gauss–Bonnet hyperbolic AdS black holes may correspond to the phase transitions and triple points in QCD phase diagrams, following the spirit of the AdS/CFT correspondence. To be a complete research, the Hawking–Page transition of d-dimensional charged spherical Gauss–Bonnet-AdS black hole in the grand canonical ensemble is also study in the Appendix, for which there exists a standard Hawking–Page transition with the transition temperature depending on the Gauss–Bonnet constant $$\alpha $$ α .

Employing the formalism of the joint density functional theory (JDFT) in the grand canonical ensemble, this paper studies the electronic structure and relative reactivity of an hydroxyl radical adsorbed on the surface of three different metal oxides that share the rutile-type structure and the (110) crystal plane; these materials are electrodes used in electrochemical advanced oxidation processes which consist in the generation of hydroxyl radicals, highly reactive species, that are able to oxidize organic compounds to CO 2 , making these anodes efficient for wastewater treatment. By analyzing the changes in the average number of electrons as a function of the applied chemical potential at fixed external potential, we studied two reactivity indices from conceptual density functional theory: global and local softness, to help us understand the differences between these materials, additionally we propose a new scheme to approximate the redox properties of clean surfaces or surfaces in contact with different adsorbed molecules so that these values can be arranged in a relative potential scale which would allow direct comparison with experimental results. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

After reviewing the peculiar thermodynamics and statistical mechanics of self-gravitating systems, we consider the case of a "binary star" consisting of two particles of size a in gravitational interaction in a box of radius R. The caloric curve of this system displays a region of negative specific heat in the microcanonical ensemble, which is replaced by a first-order phase transition in the canonical ensemble. The free energy viewed as a thermodynamic potential exhibits two local minima that correspond to two metastable states separated by an unstable maximum forming a barrier of potential. By introducing a Langevin equation to model the interaction of the particles with the thermal bath, we study the random transitions of the system between a "dilute" state, where the particles are well separated, and a "condensed" state, where the particles are bound together. We show that the evolution of the system is given by a Fokker–Planck equation in energy space and that the lifetime of a metastable state is given by the Kramers formula involving the barrier of free energy. This is a particular case of the theory developed in a previous paper (Chavanis, 2005) for N Brownian particles in gravitational interaction associated with the canonical ensemble. In the case of a binary star ( N = 2 ), all the quantities can be calculated exactly analytically. We compare these results with those obtained in the mean field limit N → + ∞ . [ABSTRACT FROM AUTHOR]

The surface of a material often undergoes dramatic structure evolution under a chemical environment, which, in turn, helps determine the different properties of the material. Here, we develop a general-purpose method for the automated search of optimal surface phases (ASOPs) in the grand canonical ensemble, which is facilitated by the stochastic surface walking (SSW) global optimization based on global neural network (G-NN) potential. The ASOP simulation starts by enumerating a series of composition grids, then utilizes SSW-NN to explore the configuration and composition spaces of surface phases, and relies on the Monte Carlo scheme to focus on energetically favorable compositions. The method is applied to silver surface oxide formation under the catalytic ethene epoxidation conditions. The known phases of surface oxides on Ag(111) are reproduced, and new phases on Ag(100) are revealed, which exhibit novel structure features that could be critical for understanding ethene epoxidation. Our results demonstrate that the ASOP method provides an automated and efficient way for probing complex surface structures that are beneficial for designing new functional materials under working conditions. [ABSTRACT FROM AUTHOR]

Progress in electrochemical technologies, such as automotive batteries, supercapacitors, and fuel cells, depends greatly on developing improved charged interfaces between electrodes and electrolytes. The rational development of such interfaces can benefit from the atomistic understanding of the materials involved by first-principles quantum mechanical simulations with Density Functional Theory (DFT). However, such simulations are typically performed on the electrode surface in the absence of its electrolyte environment and at constant charge. We have developed a new hybrid computational method combining DFT and the Poisson–Boltzmann equation (P–BE) capable of simulating experimental electrochemistry under potential control in the presence of a solvent and an electrolyte. The charged electrode is represented quantum-mechanically via linear-scaling DFT, which can model nanoscale systems with thousands of atoms and is neutralized by a counter electrolyte charge via the solution of a modified P–BE. Our approach works with the total free energy of the combined multiscale system in a grand canonical ensemble of electrons subject to a constant electrochemical potential. It is calibrated with respect to the reduction potential of common reference electrodes, such as the standard hydrogen electrode and the Li metal electrode, which is used as a reference electrode in Li-ion batteries. Our new method can be used to predict electrochemical properties under constant potential, and we demonstrate this in exemplar simulations of the differential capacitance of few-layer graphene electrodes and the charging of a graphene electrode coupled to a Li metal electrode at different voltages. [ABSTRACT FROM AUTHOR]

Finite temperature auxiliary field-based quantum Monte Carlo methods, including determinant quantum Monte Carlo and Auxiliary Field Quantum Monte Carlo (AFQMC), have historically assumed pivotal roles in the investigation of the finite temperature phase diagrams of a wide variety of multidimensional lattice models and materials. Despite their utility, however, these techniques are typically formulated in the grand canonical ensemble, which makes them difficult to apply to condensates such as superfluids and difficult to benchmark against alternative methods that are formulated in the canonical ensemble. Working in the grand canonical ensemble is furthermore accompanied by the increased overhead associated with having to determine the chemical potentials that produce desired fillings. Given this backdrop, in this work, we present a new recursive approach for performing AFQMC simulations in the canonical ensemble that does not require knowledge of chemical potentials. To derive this approach, we exploit the convenient fact that AFQMC solves the many-body problem by decoupling many-body propagators into integrals over one-body problems to which non-interacting theories can be applied. We benchmark the accuracy of our technique on illustrative Bose and Fermi--Hubbard models and demonstrate that it can converge more quickly to the ground state than grand canonical AFQMC simulations. We believe that our novel use of HS-transformed operators to implement algorithms originally derived for non-interacting systems will motivate the development of a variety of other methods and anticipate that our technique will enable direct performance comparisons against other many-body approaches formulated in the canonical ensemble. [ABSTRACT FROM AUTHOR]

The thermodynamics of the Bardeen black hole in asymptotically flat space is investigated with the corrected first law of thermodynamics via Rényi statistics. The nonextensive parameter λ gives the possibility to the thermal stability of Bardeen black hole, and there is a Hawking–Page phase transition in the grand canonical ensemble (fixed the potential), which is similar to the cases of Bardeen black hole and corrected Bardeen black hole in asymptotically anti-de Sitter (AdS) space via standard Gibbs–Boltzmann (GB) statistics. By introducing the general Smarr formula via Rényi statistics, the thermodynamic pressure P is defined with the parameter λ and its conjugate quantity V is the thermodynamic volume (not a geometric spherical volume with horizon radius r h ). The thermodynamics of the asymptotically flat Bardeen black hole via Rényi statistics in the canonical ensemble (fixed the charge q) behaves like the van der Waals system, which is also same as the asymptotically Bardeen-AdS black hole via GB statistics. The analogy between the thermodynamics of the asymptotically flat Bardeen black hole from Rényi statistics and the Bardeen-AdS black hole from GB statistics makes us to consider what is the relation between the nonextensive parameter λ and the cosmological constant Λ . [ABSTRACT FROM AUTHOR]

We present a wave function representation for the canonical ensemble thermal density matrix by projecting the thermofield double state against the desired number of particles. The resulting canonical thermal state obeys an imaginary-time evolution equation. Starting with the mean-field approximation, where the canonical thermal state becomes an antisymmetrized geminal power (AGP) wave function, we explore two different schemes to add correlation: by number-projecting a correlated grand-canonical thermal state and by adding correlation to the number-projected mean-field state. As benchmark examples, we use number-projected configuration interaction and an AGP-based perturbation theory to study the hydrogen molecule in a minimal basis and the six-site Hubbard model. [ABSTRACT FROM AUTHOR]

After reviewing the peculiar thermodynamics and statistical mechanics of self-gravitating systems, we consider the case of a “binary star” consisting of two particles of size a in gravitational interaction in a box of radius R. The caloric curve of this system displays a region of negative specific heat in the microcanonical ensemble, which is replaced by a first-order phase transition in the canonical ensemble. The free energy viewed as a thermodynamic potential exhibits two local minima that correspond to two metastable states separated by an unstable maximum forming a barrier of potential. By introducing a Langevin equation to model the interaction of the particles with the thermal bath, we study the random transitions of the system between a “dilute” state, where the particles are well separated, and a “condensed” state, where the particles are bound together. We show that the evolution of the system is given by a Fokker–Planck equation in energy space and that the lifetime of a metastable state is given by the Kramers formula involving the barrier of free energy. This is a particular case of the theory developed in a previous paper (Chavanis, 2005) for N Brownian particles in gravitational interaction associated with the canonical ensemble. In the case of a binary star (N=2), all the quantities can be calculated exactly analytically. We compare these results with those obtained in the mean field limit N→+∞.

Abstract The thermodynamics of the Bardeen black hole in asymptotically flat space is investigated with the corrected first law of thermodynamics via Rényi statistics. The nonextensive parameter $$\lambda $$ λ gives the possibility to the thermal stability of Bardeen black hole, and there is a Hawking–Page phase transition in the grand canonical ensemble (fixed the potential), which is similar to the cases of Bardeen black hole and corrected Bardeen black hole in asymptotically anti-de Sitter (AdS) space via standard Gibbs–Boltzmann (GB) statistics. By introducing the general Smarr formula via Rényi statistics, the thermodynamic pressure P is defined with the parameter $$\lambda $$ λ and its conjugate quantity V is the thermodynamic volume (not a geometric spherical volume with horizon radius $$r_{h}$$ r h ). The thermodynamics of the asymptotically flat Bardeen black hole via Rényi statistics in the canonical ensemble (fixed the charge q) behaves like the van der Waals system, which is also same as the asymptotically Bardeen-AdS black hole via GB statistics. The analogy between the thermodynamics of the asymptotically flat Bardeen black hole from Rényi statistics and the Bardeen-AdS black hole from GB statistics makes us to consider what is the relation between the nonextensive parameter $$\lambda $$ λ and the cosmological constant $$\Lambda $$ Λ .

Abstract We study the generalized free energy of the dyonic AdS black hole in an ensemble with varying electric charge q E and fixed magnetic charge q M . When we adjust the temperature T and the electric potential Φ E of the ensemble, the Ricci scalar curvature R and electromagnetic potential A u usually diverge at the horizon. We regularize them and incorporate the off-shell corrections into the Einstein-Hilbert action. Alternatively, we find that the off-shell corrections can also be obtained by adding a boundary near the horizon to exclude the singularities. Ultimately, we derive the generalized free energy which is consistent with the definition of the thermodynamic relations. Based on the generalized free energy landscape, we can describe the dynamics of state transition as a stochastic process quantified by the Langevin equation. The path integral framework can be formulated to derive the time-dependent trajectory of the order parameter and the time evolution of the transition probability. By comparing the probability with the result of the classical master equation, we attribute the contribution to the probability of one pseudomolecule or antipseudomolecule (the instanton and anti-instanton pairs) to the rate of state transition. These results are consistent with the qualitative analysis of the free energy landscape.

A finite-temperature many-body perturbation theory is presented, which expands in power series the electronic grand potential, chemical potential, internal energy, and entropy on an equal footing. Sum-over-states and sum-over-orbitals analytical formulas for the second-order perturbation corrections to these thermodynamic properties are obtained in a time-independent, nondiagrammatic, algebraic derivation, relying on the sum rules of the Hirschfelder–Certain degenerate perturbation energies in a degenerate subspace as well as nine algebraic identities for the zeroth-order thermal averages of one- through four-indexed quantities and products thereof. They reproduce numerically exactly the benchmark data obtained as the numerical derivatives of the thermal-full-configuration-interaction results for a wide range of temperatures. [ABSTRACT FROM AUTHOR]

We introduce a method to construct the interface potential from a series of molecular dynamics simulations conducted within the canonical ensemble. The interface potential provides the surface excess free energy associated with the growth of a fluid film from a surface. We collect the force that the fluid exerts on the surface (disjoining pressure) at a series of film thicknesses. These force data are then integrated to obtain the interface potential. "Spreading" and "drying" versions of the general approach are considered. The spreading approach focuses on the growth of a thin liquid film from a solid substrate in a mother vapor. The drying approach focuses on the growth of a thin vapor film on a solid substrate in a mother liquid. The methods provide a means to compute the contact angle of a fluid droplet in contact with the surface. The general method is applied to two model systems: (1) a monatomic Lennard-Jones fluid in contact with atomistically detailed face centered cubic (FCC) substrate and (2) TIP4P/2005 water in contact with a rigid silica surface. For the Lennard-Jones model system, we generate results with both the drying and spreading methods at various temperatures and substrate strengths. These results are compared to those from previous simulation studies. For the water system, the drying method is used to obtain wetting properties over a range of temperatures. The water system also highlights challenges associated with application of the spreading method within the framework pursued here. [ABSTRACT FROM AUTHOR]

Abstract A strategy is presented for the machine-learning emulation of electronic structure calculations carried out in the electronically grand-canonical ensemble. The approach relies upon a dual-learning scheme, where both the system charge and the system energy are predicted for each image. The scheme is shown to be capable of emulating basic electrochemical reactions at a range of potentials, and coupling it with a bootstrap-ensemble approach gives reasonable estimates of the prediction uncertainty. The method is also demonstrated to accelerate saddle-point searches, and to extrapolate to systems with one to five water layers. We anticipate that this method will allow for larger length- and time-scale simulations necessary for electrochemical simulations.

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.

We calculate the susceptibility of a canonical ensemble of quantum oscillators to the singular random metric. If the covariance of the metric is | x - x ′ | - 4 α ( 0 < α < 1 2 )then the expansion of the partition function in powers of the temperature involves non-integer indices. [ABSTRACT FROM AUTHOR]

Non-standard thermostatistical formalisms derived from generalizations of the Boltzmann–Gibbs entropy have attracted considerable attention recently. Among the various proposals, the one that has been most intensively studied, and most successfully applied to concrete problems in physics and other areas, is the one associated with the Sq non-additive entropies. The Sq-based thermostatistics exhibits a number of peculiar features that distinguish it from other generalizations of the Boltzmann–Gibbs theory. In particular, there is a close connection between the Sq-canonical distributions and the micro-canonical ensemble. The connection, first pointed out in 1994, has been subsequently explored by several researchers, who elaborated this facet of the Sq-thermo-statistics in a number of interesting directions. In the present work, we provide a brief review of some highlights within this line of inquiry, focusing on micro-canonical scenarios leading to Sq-canonical distributions. We consider works on the micro-canonical ensemble, including historical ones, where the Sq-canonical distributions, although present, were not identified as such, and also more resent works by researchers who explicitly investigated the Sq-micro-canonical connection.

In this paper, we will systematically present the method of collective variables with a reference system for a classical many-particle interacting system in the grand canonical ensemble. The emphasis will be placed on the details of calculations. In particular, the usage of total correlation functions defined for the grand canonical ensemble allows us to investigate very accurately the cumulants of the grand partition function for the reference system. It is shown that any cumulant Mn can be expressed as a product of three components: the average particle number within the reference system. Kronecker's symbol for n wave vectors, and the n-particle structure factor. The functional expression for the grand partition function is derived, with all coefficients explicitly defined. The coordinates of the critical point are computed in the mean field approximation. [ABSTRACT FROM AUTHOR]

Infrared spectroscopy is widely used for detailed insights into the three-dimensional molecular structure of biomolecules, however, the accurate description of experimental data by theoretical approaches remains challenging due to the dynamic processes that occur in biomolecules. Here, the authors report the accurate interpretation and reproduction of experimental infrared spectra of a model peptide in the gas phase using a combination of replica-exchange molecular dynamics simulations, machine learning and ab initio calculations based on representative structural conformers.

FEASST is an open-source Monte Carlo software package for particle-based simulations. This software, which was released in 2017, has been used to study phase equilibrium, self-assembly, aggregation or gelation in biological materials, colloids, polymers, ionic liquids, and adsorption in porous networks. We highlight some of the unique features available in FEASST, such as flat-histogram grand canonical ensemble, Gibbs ensemble, and Mayer-sampling simulations with support for anisotropic models and parallelization with flat-histogram and prefetching. We also discuss how the challenges of supporting a variety of Monte Carlo algorithms were overcome by an object-oriented design. This also allows others to extend classes, which improves software interoperability, as inspired by LAMMPS classes and user packages. This article describes version 0.25.1 with benchmarks, compilation instructions, and introductory tutorials for running, restarting, and testing simulations, user guidelines, software design strategies, alternative interfaces, and the test-driven development strategy. [ABSTRACT FROM AUTHOR]

Conventional molecular dynamics (MD) simulations struggle when simulating particles with steeply varying interaction potentials due to the need to use a very short time step. Here, we demonstrate that an event-driven Monte Carlo (EDMC) approach was first introduced by Peters and de With [Phys. Rev. E 85, 026703 (2012)] and represents an excellent substitute for MD in the canonical ensemble. In addition to correctly reproducing the static thermodynamic properties of the system, the EDMC method closely mimics the dynamics of systems of particles interacting via the steeply repulsive Weeks–Chandler–Andersen (WCA) potential. In comparison to time-driven MD simulations, EDMC runs faster by over an order of magnitude at sufficiently low temperatures. Moreover, the lack of a finite time step in EDMC circumvents the need to trade accuracy against the simulation speed associated with the choice of time step in MD. We showcase the usefulness of this model to explore the phase behavior of the WCA model at extremely low temperatures and to demonstrate that spontaneous nucleation and growth of the Laves phases are possible at temperatures significantly lower than previously reported. [ABSTRACT FROM AUTHOR]

We present a simulation method that allows us to calculate the titration curves for systems undergoing protonation/deprotonation reactions—such as charged colloidal suspensions with acidic/basic surface groups, polyelectrolytes, polyampholytes, and proteins. The new approach allows us to simultaneously obtain titration curves both for systems in contact with salt and acid reservoir (semi-grand canonical ensemble) and for isolated suspensions (canonical ensemble). To treat the electrostatic interactions, we present a new method based on Ewald summation—which accounts for the existence of both Bethe and Donnan potentials within the simulation cell. We show that the Donnan potential dramatically affects the pH of a suspension. Counterintuitively, we find that in suspensions with a large volume fraction of nanoparticles and low ionic strength, the number of deprotonated groups can be 100% larger in an isolated system, compared to a system connected to a reservoir by a semi-permeable membrane—both systems being at exactly the same pH. [ABSTRACT FROM AUTHOR]