Excess Entropy Research Articles

Understanding dynamics in coarse-grained models. II. Coarse-grained diffusion modeled using hard sphere theory.

The first paper of this series [J. Chem. Phys. 158, 034103 (2023)] demonstrated that excess entropy scaling holds for both fine-grained and corresponding coarse-grained (CG) systems. Despite its universality, a more exact determination of the scaling relationship was not possible due to the semi-empirical nature. In this second paper, an analytical excess entropy scaling relation is derived for bottom-up CG systems. At the single-site CG resolution, effective hard sphere systems are constructed that yield near-identical dynamical properties as the target CG systems by taking advantage of how hard sphere dynamics and excess entropy can be analytically expressed in terms of the liquid packing fraction. Inspired by classical equilibrium perturbation theories and recent advances in constructing hard sphere models for predicting activated dynamics of supercooled liquids, we propose a new approach for understanding the diffusion of molecular liquids in the normal regime using hard sphere reference fluids. The proposed "fluctuation matching" is designed to have the same amplitude of long wavelength density fluctuations (dimensionless compressibility) as the CG system. Utilizing the Enskog theory to derive an expression for hard sphere diffusion coefficients, a bridge between the CG dynamics and excess entropy is then established. The CG diffusion coefficient can be roughly estimated using various equations of the state, and an accurate prediction of accelerated CG dynamics at different temperatures is also possible in advance of running any CG simulation. By introducing another layer of coarsening, these findings provide a more rigorous method to assess excess entropy scaling and understand the accelerated CG dynamics of molecular fluids.

Understanding dynamics in coarse-grained models. I. Universal excess entropy scaling relationship.

Coarse-grained (CG) models facilitate an efficient exploration of complex systems by reducing the unnecessary degrees of freedom of the fine-grained (FG) system while recapitulating major structural correlations. Unlike structural properties, assessing dynamic properties in CG modeling is often unfeasible due to the accelerated dynamics of the CG models, which allows for more efficient structural sampling. Therefore, the ultimate goal of the present series of articles is to establish a better correspondence between the FG and CG dynamics. To assess and compare dynamical properties in the FG and the corresponding CG models, we utilize the excess entropy scaling relationship. For Paper I of this series, we provide evidence that the FG and the corresponding CG counterpart follow the same universal scaling relationship. By carefully reviewing and examining the literature, we develop a new theory to calculate excess entropies for the FG and CG systems while accounting for entropy representability. We demonstrate that the excess entropy scaling idea can be readily applied to liquid water and methanol systems at both the FG and CG resolutions. For both liquids, we reveal that the scaling exponents remain unchanged from the coarse-graining process, indicating that the scaling behavior is universal for the same underlying molecular systems. Combining this finding with the concept of mapping entropy in CG models, we show that the missing entropy plays an important role in accelerating the CG dynamics.

Housekeeping and excess entropy production for general nonlinear dynamics

We propose a housekeeping/excess decomposition of entropy production for general nonlinear dynamics in a discrete space, including chemical reaction networks and discrete stochastic systems. We exploit the geometric structure of thermodynamic forces to define the decomposition; this does not rely on the notion of a steady state, and it even applies to systems that exhibit multistability, limit cycles, and chaos. In the decomposition, distinct aspects of the dynamics contribute separately to entropy production: the housekeeping part stems from a cyclic mode that arises from external driving, generalizing Schnakenberg's cyclic decomposition to nonsteady states, while the excess part stems from an instantaneous relaxation mode that arises from conservative forces. Our decomposition refines previously known thermodynamic uncertainty relations and speed limits. In particular, it not only improves an optimal-transport-theoretic speed limit, but it also extends the optimal transport theory of discrete systems to nonlinear and nonconservative settings.

Influence of dispersive long-range interactions on transport and excess properties of simple mixtures

The influence of dispersive long-range interactions on liquid bulk phase transport and excess properties of six binary Lennard–Jones (LJ) mixtures was studied by molecular dynamics simulation and equation of state modelling. For the transport properties, the self-diffusion coefficients, mutual diffusion coefficients, shear viscosity, and thermal conductivity were considered. For the excess properties, the excess energy, volume, Gibbs energy, and entropy were studied. Moreover, the thermodynamic factor was studied. The two components had the same size parameter in all cases, but different dispersion energies and different cross-interaction parameters. Thereby, the six resulting mixtures show three types of phase behaviour: ideal, high- and low-boiling azeotrope. For studying the influence of the dispersive long-range interactions, the results of the full LJ potential were compared to the LJ truncated and shifted (LJTS) potential applying the corresponding states principle. The dispersive long-range interactions have a significant influence on the self-diffusion and the mutual diffusion coefficients, whereas the shear viscosity and the thermal conductivity are hardly affected. For all investigated properties, the dispersive long-range interactions have practically no influence on the composition dependency.

Mass spectrometric study and modeling of the thermodynamic properties of SrO-Al2 O3 melts at high temperatures.

The SrO-Al2 O3 system holds promise as a base for a wide spectrum of advanced materials, which may be synthesized or applied at high temperatures. Therefore, studying vaporization and high-temperature thermodynamic properties of this system is of great practical importance. Samples of the SrO-Al2 O3 system were obtained by solid-state synthesis and identified by X-ray fluorescence analysis, X-ray phase analysis, scanning electron microscopy, electron probe microanalysis, simultaneous thermal analysis, and thermogravimetric analysis. The thermodynamic properties of the SrO-Al2 O3 system were studied by the Knudsen effusion mass spectrometric (KEMS) method and were fitted by the Redlich-Kister and Wilson polynomials. The thermodynamic values obtained were also optimized within the generalized lattice theory of associated solutions (GLTAS). The vapor composition, temperature, and concentration dependences of the partial vapor pressures over the samples under study as well as the SrO activities in melts of the SrO-Al2 O3 system were determined by the KEMS method. Usage of the Redlich-Kister and Wilson polynomials allowed calculation of the excess Gibbs energies, enthalpies of mixing, and excess entropies in the concentration range 0-33 mol% of SrO at temperatures of 2450 and 2550 K. Significant negative deviations from the ideality were observed in the melts of the SrO-Al2 O3 system at 2450, 2550, and 2650 K. The Wilson polynomial was found to be the optimal approach to describe the thermodynamic properties in the system studied. Optimization of the experimental data using the GLTAS approach allowed the characteristic features of the thermodynamic description of the SrO-Al2 O3 system to be elucidated and explained.

Normal spectral emissivity and heat capacity of Pd–Fe melts measured at constant pressure under electromagnetic levitation with a static magnetic field

The normal spectral emissivity at 807 and 940 nm and heat capacity at constant pressure of Pd–Fe melts were measured under electromagnetic levitation with a static magnetic field. The samples were made of Fe of mass purity 99.9985%. The present emissivity of Fe melts was relatively low compared with previously reported data using Fe with purity lower than 99.95% mass purity. The spectral emission of the Fe melts was analyzed using their normal spectral emissivity obtained from the Drude model. The excess heat capacity of Pd–Fe melts was evaluated from the measured heat capacity of Pd–Fe melts. Applying the Lupis–Elliot rule, we concluded from the obtained excess heat capacity that the enthalpy of mixing and excess entropy of the Pd–Fe melts should be negative. The composition dependence of the enthalpy of mixing, excess entropy, and excess Gibbs energy of Pd–Fe melts were evaluated using data obtained in this study and the literature.

A new molecular thermodynamic model of liquid-liquid interfacial tension

• A new molecular thermodynamic model of interfacial tension is derived. • This model yields satisfactory prediction results for interfacial tension. • It doesn't require mutual solubility data for interfacial tension predictions. • This model is simple in implementation and reliable in application. Interfacial tension between water and organic liquids plays an important role in the design and optimization of various processes, such as enhanced oil recovery, the entrapment and migration of non-aqueous phase liquid (NAPL), chemical separation technology (liquid-liquid extraction) relevant to ex-situ hazardous waste remediation and chemical processing. A new molecular thermodynamic approach of monolayer interface model was developed in this work, in which the total interfacial energy includes contributions from the excess interface cohesive energy and excess interface entropy (entropy from partially mixing and entropy from free volume change). The accuracy of this model in the prediction of interfacial tension for water-organic liquid and mercury-nonmetallic liquid systems has been examined with satisfactory results. The investigation results indicates that for water-organic liquid systems, the excess interface entropy term makes considerable contribution (9.5%∼46.6%) to the total interfacial energy, which may result in the interaction parameter of Girifalco and Good model being greater than unity (1.04≤ Φ ≤1.15) for water-alcohols; while for mercury-nonmetallic liquid systems, the contribution to the total interfacial energy from interfacial entropy is negligible (1.2%∼2.7%), the difference in cohesive energy of molecules between the bulk phase and interfacial phase dominates the wetting process. This method doesn't require measured mutual solubility data for interfacial tension predictions, which is simple in implementation and reliable in application.

Vibrational Model of Heat Transfer in Strongly Coupled Yukawa Fluids (Dusty Plasma Liquids)

A concise overview of the vibrational model of heat transfer in simple fluids with soft pairwise interactions is presented. The model is applied to evaluate the thermal conductivity coefficient of the strongly coupled Yukawa fluid, which often serves as a simplest model of a real liquid-like dusty (complex) plasma. A reasonable agreement with the available data from molecular dynamics numerical simulations is observed. Universality of the properly reduced thermal conductivity coefficient with respect to the effective coupling parameter is examined. Relations between the vibrational model and the excess entropy scaling of the thermal conductivity coefficient are discussed.

Interfacial tension of carbon dioxide - water under conditions of CO2 geological storage and enhanced geothermal systems: A molecular dynamics study on the effect of temperature

In recent years, CO2 injection into geological formations under a wide range of temperature conditions, including super-hot geothermal reservoirs, has attracted much attention (i.e., higher than 500 K). Despite the importance, however, no study has been reported on the interfacial tension (IFT) of CO2 - water systems at temperatures higher than 478 K. In this study, we performed molecular dynamics (MD) simulations to estimate the CO2 - water IFT from 278 to 573 K at 8 to 50 MPa. Our results show the IFT at 10 MPa and 573 K is approximately 80% lower than that at a typical reservoir condition for CO2 geological storage. This indicates that the effect of the capillary pressure on the flow of CO2 and water in the geological formation is expected to be significantly reduced in such a super-hot geothermal reservoir.We discuss a possible mechanism for the IFT variation against temperature, including the maxima around 373 K at 8 to 12 MPa, which is reproduced and tackled by MD simulations for the first time. On the basis of the Gibbs-Duhem relation, the temperature dependence is directly related to the interfacial excess molar entropy. Our analyses show (1) the IFT increase is attributed to the substantial variation of the entropy and density of the bulk CO2 phase near the critical point, and (2) this variation is characterized by the distinct behavior of the molecular ordering and the mobility of CO2 at the interface, consistent with the close relationship between the disorder in molecular arrangement and configurational entropy.

Measurements and correlation of activity coefficients at infinite dilution for organic solutes in 1-heptyl-3-methylimidazolium chloride

This work is a continuation of our studies on the determination of activity coefficients at infinite dilution (γi∞) for organic solutes (i) in ionic liquids (ILs) and their use in separation processes. The values of γi∞ for 31 organic solutes including alkanes, cycloalkanes, 1,4-dioxane, aromatic hydrocarbons, cyclohexene, chloromethanes, acetonitrile, acetone, tetrahydrofuran, ethyl acetate and alcohols in the IL 1-heptyl-3-methylimidazolium chloride ([C7MIm]Cl) at six temperatures in range of (313.15–363.15) K were determined by gas-liquid chromatography (GLC). The density of [C7MIm]Cl as a function of temperature at pressure p= 101.33 kPa was measured and the values of gas-liquid partition coefficients (KL) were obtained. The linear relationship between lnγi∞ and 1/T was fitted by the Gibbs-Helmholtz equation. The molar excess thermodynamic functions including the infinite dilution partial molar excess Gibbs free energies (G¯iE,∞), partial molar excess enthalpies (H¯iE,∞) and entropies (TrefS¯iE,∞) at Tref = 298.15 K were calculated. In addition, the solubility parameters (δi) of [C7MIm]Cl were obtained from the regular solution theory combined with Flory “combinatorial” equation. The interaction between the solute and the IL was quantified based on the linear free energy relationship (LFER) model. The infinite dilution selectivity coefficients (Sij∞) of n-hexane (i)/benzene (j) and cyclohexane (i)/benzene (j) were calculated at T = 323.15 K from γi∞ and compared to literature values for [Cl]-based ILs for the same separation problems.

Analysis of entropy production in finitely slow processes between nonequilibrium steady states.

We investigate entropy production in finitely slow transitions between nonequilibrium steady states in Markov jump processes using the improved adiabatic approximation method, which has a close relationship with the slow driving perturbation. This method provides systematic improvement of the adiabatic approximation on infinitely slow transitions from which we obtain nonadiabatic corrections. We analyze two types of excess entropy production and confirm that the leading adiabatic contribution reproduces known results, and then obtain nonadiabatic corrections written in terms of thermodynamic metrics defined in protocol parameter spaces. We also numerically study the resulting excess entropy production in a two-state system.

Investigation of structure and properties of polymerizable deep eutectic solvent based on choline chloride and acrylic acid

Deep eutectic solvents (DESs) are multi-component solvents appearing in a broad range of applications. The next necessary step for the development of new DESs is understanding the molecular mechanisms of DES formation and the interactions that determine its structure and properties. In this work, we use multiscale simulations supported by experiments to investigate the detailed structure and properties of polymerizable DESs based on choline chloride and acrylic acid as a basis for creating inks for 3D printing. Thermodynamic and structural analyses show the physical mechanisms of DES formation in these materials: due to the significant size difference between the acrylic acid and choline ions, and favorable interactions between acrylic acid and the Cl- ions, the acrylic acid molecules are able to incorporate into the free spaces of the first coordination shells of the Cl- ions. As a consequence, the mixture has less volume than its individual components and this excess volume determines the negative value of the enthalpy of mixing. Structurally, the mixture is a network with the Cl- ions as nodes connecting the other DES components. This was confirmed by both the FTIR experiments and the atomistic MD simulations. The calculations show the necessity of correct accounting of excess enthalpy and entropy for determining DESs structures and other properties.

Correlation between structures and atomic transport properties of compound forming liquid Cu-In alloys

The Lebowitz solution of the Percus-Yevick hard-sphere mixture is invoked with the square-well potential function to determine Ashcroft-Langreth type three partial correlation functions in binary Cu-In liquid alloys. These computed partial correlation functions have been employed to generate Bhatia-Thornton fluctuations in the considered melts. Using these structural parameters we investigate the temperature and composition-dependent diffusion coefficients of considered melts. The computed values of concentration-concentration fluctuations, in the long-wavelength limit, and the Warren-Cowley short-range order parameter, show the formation of chemical compounds between unlike atoms in the In-rich region of Cu-In melts. We find a very good agreement between theoretically formulated and computed data of with the corresponding experimental values. Computed results of and suggest that hetero coordination is favorable over homo coordination in the investigated melts. The validity of the Stokes-Einstein relation was observed over a wide range of temperatures and compositions in the investigated melts. Further, a new correlation between two body pair excess entropy and the Stoke-Einstein relation has been formulated for square-well binary liquid alloys. Surface tension and compressibility as a function of In composition have been computed through microscopic structural functions of the alloys. Computed surface tension and ratio of mutual to intrinsic diffusion (D m /D id ) are found comparable to available simulated data. The computed values of shear viscosity are in good agreement with the experimental data. Calculated results suggest that the combination of hard sphere potential with square-well tail under mean spherical model approximation is one of the good method for determining the structures and transport coefficients of compound forming binary liquid alloys.

First-Principles Calculations of Elastic and Thermodynamic Properties for Multi-component Co-based Superalloys

First-principles calculations were performed to investigate the elastic and thermodynamic properties for multi-component Co-based superalloy systems and explored the effect of alloying on stabilizing the γ′ phase. First, the comparisons were carried out for the γ′ phase in Co3(Al,TM) (TM being transition metals) and Ni3Al systems between the present computational results using the EMTO-CPA method and other available DFT calculations as well as experimental data. The lattice parameters, elastic constants, and Debye temperatures are consistent with experimental results and other calculations. The predicted thermodynamic properties, e.g., the Gibbs free energy, excess entropy, and linear thermal expansion coefficient, agree well with CALPHAD results, experimental results, and other available first-principles calculations. A combination of EMTO-CPA method and Debye–Grüneisen model is utilized in this work to ensure that the alloying effect on the stability of the γ′ phase in a multi-component Co-based system is captured efficiently. This could open the path for designing novel multi-component Co-based alloys based on first-principles calculation. To demonstrate this, predictions for the properties of multicomponent systems were undertaken. Our results show that Ni aids in the stabilization of the (CoNi)3(Al, Mo, Nb) phase.Graphical

Mesoscopic perspectives on dynamic van der Waals theory for liquid–vapor phase transition

We present a macroscopic dynamic van der Waals theory for liquid–vapor phase transition from mesoscopic perspectives offered by the kinetic model for multiphase fluids. We show that the excess effects stem from the unbalanced long-range molecular interaction in the inhomogeneous region, and, thus, only the excess internal (potential) energy but not the excess entropy is introduced. The excess internal energy is given as −12κρ∇·∇ρ rather than the canonical 12κ∇ρ·∇ρ, which leads to the same equilibrium state but different thermohydrodynamics. The present dynamic equations are identical to the macroscopic equations recovered by the kinetic model.

Unified theory of thermodynamics and stochastic thermodynamics for nonlinear Langevin systems driven by non-conservative forces

We construct a unified theory of thermodynamics and stochastic thermodynamics for classical nonequilibrium systems driven by non-conservative forces, using the recently developed covariant Ito-Langevin theory. The thermodynamic forces are split into a conservative part and a non-conservative part. Thermodynamic functions are defined using the reference conservative system. Work and heat are partitioned into excess parts and house-keeping parts, which are due to, respectively, conservative forces and non-conservative forces. Excess entropy production (EP) and house-keeping EP are analogously defined. The splitting of thermodynamic forces is subjected to an arbitrariness resembling a gauge symmetry, with each gauge defining a reference conservative Langevin system. In the special Gibbs gauge, the nonequilibrium steady state (NESS) is characterized by Gibbs canonical distribution, the excess heat agrees with that defined by Hatano and Sasa, and the excess EP agrees with that of Glansdorff and Prigogine, i.e., it is the time rate of the second-order variation of system entropy near the NESS. Adopting the Gibbs gauge, and focusing on the excess parts of thermodynamic quantities, a complete analogy between thermodynamics of non-conservative systems and that of conservative systems is established. One important consequence of this analogy is that both the free energy and excess EP are minimized at NESS. Our theory therefore constitutes a statistical foundation both for the steady-state thermodynamics theory due to Sasa and Tasaki and for the stability theory of NESS due to Glansdorff and Prigogine. These results are valid even if the system is far from equilibrium. By studying detailed fluctuation theorem, we find striking differences between systems with symmetric kinetic matrices and those with asymmetric kinetic matrices. For systems with asymmetric kinetic matrices, the total EP is the sum of house-keeping EP, excess EP, and pumped entropy. Entropy pumping is an exchange of entropy between the system and environment without necessarily involving dissipation. In the presence of entropy pumping, the system may behave as either a demon or an antidemon. Fluctuation theorems and work relations are derived both for total work and for excess work. For systems with symmetric kinetic matrices, there is no entropy pumping, yet in the Gibbs gauge, the excess work and house-keeping work each satisfies a separate fluctuation theorem. We illustrate our theory using many concrete examples.

Pair entropy and universal viscosity scaling for molecular systems via molecular dynamics simulations

The scaling between the excess entropy and transport coefficients of liquids is an interesting property found by Rosenfeld in atomistic simulations. Later, Dzugutov proposed to estimate the excess entropy on the basis of the pair entropy. That approach has been shown to work well for atomic liquids and rigid molecules, but there is a problem of pair entropy definition for molecular substances in general. In this work, we propose a new method of estimation of the pair contribution to the excess entropy for hydrocarbon liquids. We present the results on viscosity-pair entropy Rosenfeld scaling for linear alkanes and an aromatic compound in two different force fields, and compare the results with the available experimental and correlation data. We show that our method accounts for 75–90% of excess entropy changes in molecular liquid, comparable to the pair entropy contribution in atomic liquids. The universal nearly-univariate dependence of the scaled viscosity and pair entropy is observed for each compound at different temperatures, and the scaling is shown to be transferable between the force fields models.

Information-geometric structure for chemical thermodynamics: An explicit construction of dual affine coordinates.

We construct an information-geometric structure for chemical thermodynamics, applicable to a wide range of chemical reaction systems including nonideal and open systems. For this purpose, we explicitly construct dual affine coordinate systems, which completely designate an information-geometric structure, using the extent of reactions and the affinities of reactions as coordinates on a linearly constrained space of amounts of substances. The resulting structure induces a metric and a divergence (a function of two distributions of amounts), both expressed with chemical potentials. These quantities have been partially known for ideal-dilute solutions, but their extensions for nonideal solutions and the complete underlying structure are novel. The constructed geometry is a generalization of dual affine coordinates for stochastic thermodynamics. For example, the metric and the divergence are generalizations of the Fisher information and the Kullback-Leibler divergence. As an application, we identify the chemical-thermodynamic analog of the Hatano-Sasa excess entropy production using our divergence.

Entropic quantifier of spin–boson nonclassicality

Spin systems interacting with boson environments are ubiquitous in nature. To what extent quantum states in such systems depart from classicality is becoming an increasingly important issue. Here, we study nonclassicality in systems involving the interaction between a spin and a boson mode. We introduce a simple and effective method for quantifying spin–boson nonclassicality in terms of the entropy excess between the classical and the quantum Tsallis entropy. The method can be naturally extended to more general systems. Fundamental properties of the nonclassicality quantifier are revealed, which render it reasonable for spin–boson states. Basic features are illustrated by a variety of typical spin–boson states. As applications, we further investigate spin–boson nonclassicality in the Dicke model, which sheds light on the normal-superradiant phase transition and quantum metrology.

Vapor-liquid equilibrium experiment and prediction of excess property of new working pair CO2-[BMP][Tf2N] in absorption refrigeration system: Expérience d'équilibre vapeur-liquide et prédiction de la propriété excédentaire de la nouvelle paire de travail CO2-[BMP][Tf2N] dans un système de réfrigération à absorption

Solubility of CO2 in ionic liquids (ILs) is of great importance in absorption refrigeration system as new working pairs. Vapor-liquid equilibrium (VLE) of CO2 in [BMP][Tf2N] (1-butyl-1-methyl-pyrrolidine bis(trifluoromethylsulfonyl)imide) is carried out experimentally using the experiment system at temperature range 303.15 K-363.15 K. The experimental results show that the solubility of CO2 in [BMP][Tf2N] can reach up to 0.1235–0.5324 (molar fraction) within temperature range 283.15∼363.15 K and pressure range of 0.2∼5 MPa. The solubility of CO2 in [BMP][Tf2N] increases with increase of temperature and pressure. The VLE data of CO2-[BMP][Tf2N] binary system is correlated with two models (SRK equation of state +WS mixing rule +UNIFAC activity coefficient model and PR equation of state +WS mixing rule +UNIFAC activity coefficient model). The excess Gibbs free energy (GE), excess enthalpy (HE) and excess entropy (SE) of the system are obtained and the interaction parameters kij is regressed based on the VLE of CO2-[BMP][Tf2N] binary system. The variation trend of GE, HE and SE are obtained with temperature, pressure and molar fraction of CO2. The calculation results show that the accuracy of SRK equation of state is slightly higher than that of PR equation of state in CO2-[BMP][Tf2N] binary system. The accuracy of SRK equation of state and PR equation of state decreases with increase of temperature and pressure.