Canonical Ensemble Research Articles

Emergence of the Gibbs ensemble as a steady state in Lindbladian dynamics

Emergence of the Gibbs ensemble as a steady state in Lindbladian dynamics

Semi-empirical supported, Ab initio derived thermodynamic properties for ClO2 and its sub and extended species, applied in water treatment cycles

This paper describes a group of sixty (60) sub and extended chlorine oxide species with the general formulae of ClxOy (with x ≤ 2, y ≤ 8). Their role in water treatment cycles, behaving as key reactive species, is represented by a complex sequence of chemical inter-dependencies, exposed as a cohesive set of chemical reactions to demonstrate their cyclic role in aqueous media. An empirical/semi-empirical computational approach, supported by Ab Initio simulations, in accordance with open-shell character, has been followed to determine their optimum molecular geometries, to obtain their thermochemical properties. Besides a single molecular analysis, Grand Canonical Ensemble simulations, supported by a revised library of force field parameters, constituted a core component of the computational approach and proved to be invaluable in confirming thermochemical properties. This approach also offered finite estimates of optimum model sizes, a benefit with wider modelling application. Extended molecular species of ClO2 display a complex sequence of bonding character, with a variable charge dissipation (reported as partial charges), which complicates selection of basis sets in optimizing molecular geometries, during Ab Initio analyses.Optimum molecular geometries were obtained using Gaussian and MOPAC, which in turn resulted in reliable Heats of Formation. These correlated well with energies extracted from the open literature. Thermodynamic Analysis of the reaction of selected chlorine oxides with water using FactSage, predicted the production of known and two previously undetected chlorine species, [ClO4]- and [ClOH2]+.

Temperature and pressure effects on the decomposition mechanisms of 2,6-diamino-3,5-dinitropyrazine-1-oxide crystal: ab initio molecular dynamics study.

The decomposition process of 2,6-diamino-3,5-dinitropyrazine-1-oxide (LLM-105) crystal at high temperatures (2500 and 3390K) and detonation pressure of 33.4 GPa coupled with temperatures were studied by ab initio molecular dynamics simulations. The results show that the initial decomposition mechanism of LLM-105 is the same under different conditions. The product analysis indicates that high temperature is conducive to the formation of N2 and CO2, but inhibited the formation of H2O. It is found that the formation mechanism of H2O is the same under different conditions, which involves the reaction between OH radical and H radical. Although the detailed processes of the formation of N2 are different, they all involve the reaction between nitrogen-containing fragments, and its core is the formation of intermediates with R1-NN-R2 structure. The core of the formation of CO2 under different conditions is to form the intermediate R1-CO-R2 with carbonyl structure, and then generate the fragment with -OCO- structure, and finally generate CO2. This research may provide new insights into the initiation and subsequent decomposition mechanisms of energetic materials under extreme conditions. The LLM-105 supercell was constructed using the Materials Studio 7.0 package. AIMD simulations were performed in the CASTEP package. AIMD simulations adopted NVT and NPT ensemble, and the temperature was controlled by Nosé thermostat, while the pressure was controlled by Andersen barostat. Besides, DFT calculations were carried out at the B3LYP/6-311 + G(d,p) level using the Gaussian 09 package.

Statistical Thermodynamic Description of Self-Assembly of Large Inclusions in Biological Membranes.

Recent studies revealed anomalous underscreening in concentrated electrolytes, and we suggest that the underscreened electrostatic forces between membrane proteins play a significant role in the process of self-assembly. In this work, we assumed that the underscreened electrostatic forces compete with the thermodynamic Casimir forces induced by concentration fluctuations in the lipid bilayer, and developed a simplified model for a binary mixture of oppositely charged membrane proteins with different preference to liquid-ordered and liquid-disordered domains in the membrane. In the model, like macromolecules interact with short-range Casimir attraction and long-range electrostatic repulsion, and the cross-interaction is of the opposite sign. We determine energetically favored patterns in a system in equilibrium with a bulk reservoir of the macromolecules. Different patterns consisting of clusters and stripes of the two components and of vacancies are energetically favorable for different values of the chemical potentials. Effects of thermal flutuations at low temperature are studied using Monte Carlo simulations in grand canonical and canonical ensembles. For fixed numbers of the macromolecules, a single two-component cluster with a regular pattern coexists with dispersed small one-component clusters, and the number of small clusters depends on the ratio of the numbers of the molecules of the two components. Our results show that the pattern formation is controlled by the shape of the interactions, the density of the proteins, and the proportion of the components.

Ab initio molecular dynamics investigation on hydrogen diffusion behavior in liquid aluminum alloy melts

In this work, ab initio molecular dynamics (AIMD) simulations under both NVT and NPT ensembles were performed to study the influence of alloying elements of Mg, Fe, Si, Ti, Cu, Zn, F, and Cl on the H diffusion behavior in liquid aluminum melt. It is found that the diffusion coefficient of H simulated by AIMD under the NVT model is highly consistent with the reported experimental results. Specifically, the addition of Cu, Cl, Si, and Zn is inclined to increase the diffusion coefficient of H in the melt, whereas the opposite result is observed with the addition of F, Fe, and Ti. Moreover, it is proved that the H diffusion coefficients are positively correlated with the H-Al bond lengths and the coordination number of H in a constant volume system. The obtained results deepen the understanding of the diffusion of H atoms in Al melts and contribute to the optimization of existing melt purification technologies.

Discharging of Ramsdellite MnO2 Cathode in a Lithium-Ion Battery.

We report an application of our unbiased Monte Carlo approach to investigate thermodynamic and electrochemical properties of lithiated manganese oxide in the ramsdellite phase (R-MnO2) to uncover the mechanism of lithium intercalation and understand charging/discharging of R-MnO2 as a cathode material in lithium-ion batteries. The lithium intercalation reaction was computationally explored by modeling thermodynamically significant distributions of lithium and reduced manganese in the R-MnO2 framework for a realistic range of lithium molar fractions 0 < x < 1 in Li x MnO2. We employed interatomic potentials and analyzed the thermodynamics of the resultant grand canonical ensemble. We found ordered or semiordered phases at x = 0.5 and 1.0 in Li x MnO2, verified by configurational entropy changes and simulated X-ray diffraction patterns of partially lithiated R-MnO2. The radial distribution functions show the preference of lithium for homogeneous distributions across the one-dimensional 2 × 1 ramsdellite channels accompanied by alternating reduced/oxidized manganese ions. The occupation of the interstitial sites in the channels is correlated with the calculated voltage profile, showing a sharp voltage drop at x = 0.5, which is explained by the energy penalty of shifting lithium ions from stable tetrahedral to unstable octahedral sites. To facilitate this work, our in-house software, Knowledge Led Master Code (KLMC) was extended to support massive parallelism on high-performance computers.

Plasma-Plasma Third Order Phase Transition from Type IIB Supergravity.

We show that the planar, charged black hole in asymptotically anti-de Sitter spacetime, dual to the strongly coupled quark-gluon plasma thermal state of large N, SU(N), N=4 super Yang-Mills at finite chemical potential undergoes a third-order phase transition in the grand canonical ensemble to a hairy black hole of type IIB supergravity. The hairy phase is another strongly coupled fluid with a conformal equation of state and can be interpreted as another kind of quark-gluon plasma. This new quark-gluon plasma has less entropy and, therefore, seems to characterize some form of smooth hadronization. The locus of the transition in terms of the critical values of the "baryon" chemical potential μ_{c} and the temperature T_{c} is μ_{c}=2πT_{c}.

Phase Diagrams of a Relativistic Self-Interacting Boson System

Within the Canonical Ensemble, we investigate a system of interacting relativistic bosons at finite temperatures and finite isospin densities in a mean-field approach. The mean field contains both attractive and repulsive terms. Temperature and isospin density dependences of thermodynamic quantities are obtained. It is shown that, in the case of attraction between particles in a bosonic system, a liquid-gas phase transition develops against the background of the Bose–Einstein condensate. The corresponding phase diagrams are given. We explain the reasons for why the presence of a Bose condensate significantly increases the critical temperature of the liquid-gas phase transition compared to that obtained for the same system within the framework of Boltzmann statistics. Our results may have implications for the interpretation of experimental data, in particular, how sensitive the critical point of the mixed phase is to the presence of the Bose–Einstein condensate.

RASPA3: A Monte Carlo code for computing adsorption and diffusion in nanoporous materials and thermodynamics properties of fluids.

We present RASPA3, a molecular simulation code for computing adsorption and diffusion in nanoporous materials and thermodynamic and transport properties of fluids. It implements force field based classical Monte Carlo/molecular dynamics in various ensembles. In this article, we introduce the new additions and changes compared to RASPA2. RASPA3 is rewritten from the ground up in C++23 with speed and code readability in mind. Transition-matrix Monte Carlo is added to compute the density of states and free energies. The Monte Carlo code for rigid molecules is based on quaternions, and the atomic positions needed in the energy evaluation are recreated from the center of mass position and quaternion orientation. The expanded ensemble methodology for fractional molecules, with a scaling parameter λ between 0 and 1, now also keeps track of analytic expressions of dU/dλ, allowing independent verification of the chemical potential using thermodynamic integration. The source code is freely available under the MIT license on GitHub. Using this code, we compare four Monte Carlo (MC) insertion/deletion techniques: unbiased Metropolis MC, Configurational-Bias Monte Carlo (CBMC), Continuous Fractional Component MC (CFCMC), and CB/CFCMC. We compare particle distribution shapes, acceptance ratios, accuracy and speed of isotherm computation, enthalpies of adsorption, and chemical potentials, over a wide range of loadings and systems, for the grand canonical ensemble and for the Gibbs ensemble.

Generalized hydrodynamics for the volterra lattice: ballistic and non-ballistic behavior of correlation functions

Abstract In recent years, a lot of effort has been put in describing the hydrodynamic behavior of in- tegrable systems. In this paper, we describe such picture for the Volterra lattice. Specifically, we are able to explicitly compute the susceptibility matrix and the current-field correlation matrix in terms of the density of states of the Volterra lattice endowed with a Generalized Gibbs ensemble. Furthermore, we apply the theory of linear Generalized Hydrodynamics to describe the Euler scale behavior of the correlation functions. We anticipate that the solution to the Generalized Hydrodynamics equations develops shocks at ξ0=x/t ; so this linear approximation does not fully describe the behavior of correlation functions. Intrigued but this fact, we performed several numerical investigations which show that, exactly when the solution to the hydrodynamic equations develops shock, the correlation functions show an highly oscillatory behavior. In view of this empirical observation, we believe that at this point ξ0 the diffusive contribution are not sub-leading corrections to the ballistic transport, but they are of the same order.

A thermophysical mechanism exploration of the brain: Motor cortex modeling with canonical ensemble theory

The brain, recognized as one of the most intricate systems globally, has been a focal point for scientific exploration. Researchers have made efforts to construct models of the brain based on neural dynamics and complex networks to gain insights into its workings. It is crucial to investigate the brain's working principles from various perspectives. This study presents a novel thermophysical model of the motor cortex and examines its potential thermodynamic properties. Utilizing canonical ensemble theory, we constructed the thermophysical model using spike and local field potential (LFP) signals obtained from intracortical brain-machine-interfaces (iBMIs) in two monkeys. The parameters derived from this model—namely internal energy, free energy, and entropy—were employed to assess the thermodynamic properties and observe alterations in these properties during reaching and grasping movements. Furthermore, this proposed model was applied to movement pattern decoding, highlighting its potential in neural decoding tasks. In both LFP- and spike-based thermodynamic models, there was an increase in internal energy and free energy, coupled with a decrease in entropy when the motor cortex was activated across various movement tasks. This suggests that the neural system adheres to the principles of a thermophysical system. Notably, the thermodynamic features demonstrated superior performance in decoding movement intentions compared to traditional LFP and spike features. This study represents the first construction of a comprehensive thermodynamic model of the motor cortex based on LFP and spike signals. The model exhibits remarkable stationarity and holds promise for long-term and stable evaluations of motor cortex functions.

Molecular insights into methane hydrate dissociation: Role of methane nanobubble formation.

Understanding the underlying physics of natural gas hydrate dissociation is necessary for efficient CH4 extraction and in the exploration of potential additives in the chemical injection method. Silica being "sand" is already present inside the reservoir, making the silica nanoparticle a potential green additive. Here, molecular dynamics (MD) simulations have been performed to investigate the dissociation of the CH4 hydrate in the presence and absence of ∼1, ∼2, and ∼3nm diameter hydrophilic silica nanoparticles at 100bar and 310K. We find that the formation of a CH4 nanobubble has a strong influence on the dissociation rate. After the initial hydrate dissociation, the rate of dissociation slows down till the formation of a CH4 nanobubble. We find the critical concentration and size limit to form the CH4 nanobubble to be ∼0.04 molefraction of CH4 and ∼40 to 50 CH4 molecules, respectively. The solubility of CH4 and the chemical potential of H2O and CH4 are determined via Gibbs ensemble Monte Carlo simulations. The liquid phase chemical potential of both H2O and CH4 in the presence and absence of the nanoparticle is nearly the same, indicating that the effect of this additive will not be significant. While the formation of the hydration shell around the nanoparticle via hydrogen bonding confirms the strength of interactions between the water molecules and the nanoparticle in our MD simulations, the contact of the nanoparticle with the interface is infrequent, leading to no explicit effect of the nanoparticle on the dynamics of methane hydrate dissociation.

Non-defective degeneracy in non-Hermitian bipartite system

Starting from a Hermitian operator with two distinct eigenvalues, we construct a non-Hermitian bipartite system in Gaussian orthogonal ensemble according to random matrix theory, where we introduce the off-diagonal fluctuations through random eigenkets and realizing the bipartite configuration consisting of two D × D subsystems (with D being the Hilbert space dimension). As required by the global thermalization (chaos), one of the two subsystems is fully ranked, while the other is rank deficient. For the latter (rank-deficient) subsystem, there is a block with non-defective degeneracies that contains non-local symmetries, as well as the accumulation effect of the linear map in adjacent eigenvectors. The maximally mixed state formed by the eigenvectors of this special region does not exhibit thermal ensemble behavior (neither canonical or Gibbs), and displays similar characteristics to the corresponding reduced density, which can be verified through the Loschmidt echo and variance of the imaginary spectrum. This non-defective degeneracy region partially meets the Lemma in 10.1103/PhysRevLett.122.220603 and theorem in 10.1103/PhysRevLett.120.150603. The coexistence of strong entanglement and initial state fidelity in this region make it possible to achieve a maximally mixed density, which, however, does not correspond to a thermal canonical ensemble (with complete insensitivity to the environmental energy or temperature). Outside this region, the collection of eigenstates (reduced density) always exhibit restriction on the corresponding Hilbert space dimension (with, e.g., infinite number of bound states), and thus suppress the global thermalization. There are abundant physics for those densities in Hermitian and non-Hermitian bases, which we investigate separately in this work. For example, the disentangling effect originates from non-Hermitian skin effect where the coherence exists along the direction orthogonal to the entangled boundaries of the Loschmidt echo spectrum in the Hermitian basis, while it originates from the many-body localization with the coherence among echo boundaries in the non-Hermitian basis which is disorder-free.

Random Transitions of a Binary Star in the Canonical Ensemble.

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→+∞.

Exploring the UV and IR of a type-II holographic superconductor using a dyonic black hole

In this study, we investigate a type-II holographic superconductor with a perturbative scalar field over a (3 + 1)-dimensional electric and magnetically charged planar AdS black hole. We review the thermodynamical properties of the background relevant for the dual description of the Ginzburg–Landau density of superconducting states, showing that the adoption of a London gauge allows a consistent description of the Abrikosov vortex lattices, typical of type-II superconductors. We further derive a new expression for the upper critical magnetic field as a function of temperature in the grand canonical ensemble, supplementary to the one previously obtained in the canonical ensemble setup. These results confirm that our perturbative scalar field model consistently reproduces the well-known temperature behavior of the upper critical magnetic field according to the Ginzburg–Landau theory and other Abelian–Higgs holographic developments for type-II superconductors. We then continue with an original analysis of the scalar field equation in terms of a Schrödinger potential that led to the observation of bound states, a signal for the condensation of Cooper pairs. These results provide robust evidence for the existence of an IR order parameter near extremality. In view of this, we performed a closer inspection of the IR effective scalar equation in which the geometry adopts a Schwarzschild AdS2×R2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {AdS}_{2}\ imes {\\mathbb {R}}^{2}$$\\end{document} structure, finding novel condensed bound states in the IR regime.

Self-assembly of single species polygons with patchy models in 2D

The goal of this work is to produce single species of polygons in two dimensions using the self-assembly of a simple patchy molecular model. A molecule is defined as a central soft repulsive Weeks Chandler and Anderson (WCA) atom that is decorated with two or four patches, which describe the two models studied in this work. Model I has two Lennard–Jones (LJ) patches inside of its central atom separated by an angle θ that intends to define the number of polygon sides. The attractive potential of these patches, interacting as pairs, is used to bond molecules together to form polygons. Model II, having two additional soft repulsive WCA patches, tangent on the outside, produces single polygon species configurations. An example of Model I with an angle θ = 120 ∘ , forming a mixture of polygons, is included. Model II produces single polygon species with 3-8 sides, depending on the angle θ between the attractive patches. Molecular dynamics simulations in the canonical ensemble are used to calculate thermodynamic properties such as internal energy, percentage of polygons, pressure and contour plots for the percentage of polygons following isochoric processes. Different starting configurations are used to verify the consistency of the equilibrium results.

Sum rule for fluctuations of work.

We study the fluctuations of work caused by applying cyclic perturbations and obtain an exact sum rule satisfied by the moments of work for a broad class of quantum stationary ensembles. In the case of the canonical ensemble, the sum rule reproduces the Jarzynski equality. The sum rule can also be simplified into a linear relationship between the work average and the second moment of work, which we numerically confirm via an exact diagonalization of a spin model system.

Topology of charged AdS black hole in restricted phase space* *Supported by the National Natural Science Foundation of China (12075143, 12375050), and the Natural Science Foundation of Shanxi Province, China (202203021221209, 202303021211180)

The local topological properties of black hole systems can be expressed through winding numbers as defects. To date, AdS black hole thermodynamics are often depicted by the dual parameters of in the extended phase space, while there have been several studies on the black hole thermodynamics in the restricted phase space. In this paper, we analyze the topological properties of charged AdS black holes in the restricted phase space under the higher-dimension and higher-order curvature gravity frame. The results show that the topological number of the charged black hole in the same canonical ensembles is a constant and is independent of the concrete dual thermodynamical parameters. However, the topological number in the grand canonical ensemble is different from that in the canonical ensemble for the same black hole system. Furthermore, these results are independent of dimension d and highest order k of the Lanczos-Lovelock densities.

Topological equivalence and phase transition rate in holographic thermodynamics of regularized Maxwell theory

Utilizing the holographic dictionary from the proposal that treats Newton’s constant as a thermodynamic variable, we establish a thermodynamic topological equivalence between the AdS black holes in the bulk and the thermal states in the dual CFT. The findings further reveal that the thermodynamic topological characteristics of the RegMax AdS black holes are strongly influenced by the characteristic parameter of the regularized Maxwell theory. Additionally, we investigate the phase transition between low and high entropy thermal states within a canonical ensemble in the dual CFT. Our observations indicate that the phase transition behavior of the thermal states mirrors that of the black holes. By modeling the phase transition process as a stochastic process, we are able to calculate the rates of phase transition between the thermal states. This result enhances our understanding of the dominant processes involved in the phase transition of the thermal states in the dual CFT.

Hyperdensity Functional Theory of Soft Matter.

We present a scheme for investigating arbitrary thermal observables in spatially inhomogeneous equilibrium many-body systems. Extending the grand canonical ensemble yields any given observable as an explicit hyperdensity functional. Associated local fluctuation profiles follow from an exact hyper-Ornstein-Zernike equation. While the local compressibility and simple observables permit analytic treatment, complex order parameters are accessible via simulation-based supervised machine learning of neural hyperdirect correlation functionals. We exemplify efficient and accurate neural predictions for the cluster statistics of hard rods, square-well rods, and hard spheres. The theory allows one to treat complex observables, as is impossible in standard density functional theory.