Excess Entropy Research Articles

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.

Effect of Thermodynamic Stability Parameters on Tracer Diffusion Kinetics in High Entropy Alloys

The high entropy effect and sluggish diffusion effect postulate that the alloys with higher thermodynamic stability exhibit anomalously slow diffusion kinetics. This postulation assumed that the enthalpy of mixing and excess entropy in random single-phase solid solution based high entropy alloys (HEAs) are negligible and configurational entropy is the dominant contributor towards the overall thermodynamic stability. The highly stable HEAs were assumed to exhibit very rugged potential energy landscape characterized by larger potential energy fluctuations, which slows down the diffusion kinetics. These assumptions, however, were challenged by several investigations. Therefore, this work investigates the dependence of tracer diffusion kinetics on thermodynamic stability parameters by systematically investigating the underlying assumptions of high entropy and sluggish diffusion effects. The effect of enthalpy of mixing and excess entropy on the overall thermodynamic stability of several FCC HEAs was also examined. Findings suggest that: (1) FCC HEAs exhibit non-ideal solid solution behavior because enthalpy of mixing and excess entropy contributes significantly towards the overall thermodynamic stability; (2) contrary to sluggish diffusion effect, higher entropy do not always result in higher potential energy fluctuations; and (3) tracer diffusion in FCC alloys is composition dependent and exhibit no direct correlation with the thermodynamic stability parameters.

Discovering Noncritical Organization: Statistical Mechanical, Information Theoretic, and Computational Views of Patterns in One-Dimensional Spin Systems.

We compare and contrast three different, but complementary views of “structure” and “pattern” in spatial processes. For definiteness and analytical clarity, we apply all three approaches to the simplest class of spatial processes: one-dimensional Ising spin systems with finite-range interactions. These noncritical systems are well-suited for this study since the change in structure as a function of system parameters is more subtle than that found in critical systems where, at a phase transition, many observables diverge, thereby making the detection of change in structure obvious. This survey demonstrates that the measures of pattern from information theory and computational mechanics differ from known thermodynamic and statistical mechanical functions. Moreover, they capture important structural features that are otherwise missed. In particular, a type of mutual information called the excess entropy—an information theoretic measure of memory—serves to detect ordered, low entropy density patterns. It is superior in several respects to other functions used to probe structure, such as magnetization and structure factors. -Machines—the main objects of computational mechanics—are seen to be the most direct approach to revealing the (group and semigroup) symmetries possessed by the spatial patterns and to estimating the minimum amount of memory required to reproduce the configuration ensemble, a quantity known as the statistical complexity. Finally, we argue that the information theoretic and computational mechanical analyses of spatial patterns capture the intrinsic computational capabilities embedded in spin systems—how they store, transmit, and manipulate configurational information to produce spatial structure.

Geometric decomposition of entropy production into excess, housekeeping, and coupling parts.

For a generic overdamped Langevin dynamics driven out of equilibrium by both time-dependent and nonconservative forces, the entropy production rate can be decomposed into two positive terms, termed excess and housekeeping entropy. However, this decomposition is not unique: There are two distinct decompositions, one due to Hatano and Sasa, the other one due to Maes and Netočný. Here we establish the connection between these two decompositions and provide a simple, geometric interpretation. We show that this leads to a decomposition of the entropy production rate into three positive terms, which we call the excess, housekeeping, and coupling part, respectively. The coupling part characterizes the interplay between the time-dependent and nonconservative forces. We also derive thermodynamic uncertainty relations for the excess and housekeeping entropy in both the Hatano-Sasa and Maes-Netočný decomposition and show that all quantities obey integral fluctuation theorems. We illustrate the decomposition into three terms using a solvable example of a dragged particle in a nonconservative force field.

Thermodynamic and kinetic analysis of ternary intermetallics formation in Al–Cu–La alloy

The thermodynamic and kinetic analysis of rare earth (RE) intermetallics formation in Al–Cu–La alloy was carried out in this study. The formation enthalpy, excess entropy, excess Gibbs free-energy and activity of each component of Al–Cu–La ternary alloy were calculated combining Miedema model with Toop model. The calculated results show that the formation enthalpy, excess entropy and excess Gibbs free-energy of Al–Cu–La ternary alloy are all negative in the whole alloy composition range. The activities of Al, Cu and La are all tiny in the central zone of composition triangle of Al–Cu–La ternary alloy, indicating that Al, Cu and La components are easy to form ternary intermetallics. Moreover, the parabolic growth kinetics equation of RE intermetallics was derived integrating the Fick's second law with the mass balance law. According to the parabolic growth rate, the thickness of the RE intermetallics increases in proportion to the square root of the diffusion time.

Vibrational Model of Heat Conduction in a Fluid of Hard Spheres

Application of a vibrational model of heat transfer to a fluid made of hard spheres is discussed. The model was originally proposed to describe heat conduction in fluids with soft pairwise interactionsHere, it is shown that only minor modifications are required to apply the model in the opposite limit of hard sphere interactions. Good agreement with recent results from molecular dynamics simulation is documented in the moderately dense regime. Near the freezing point, however, the model overestimates the thermal conductivity coefficient (by ≃50%). The new approach is compared with other simple models for the thermal conductivity coefficients such as Bridgman’s expression and the Enskog formula. The value of the coefficient in the Bridgman’s expression, appropriate for the hard sphere fluid, is determined. A new expression for the dependence of the reduced thermal conductivity coefficient on the reduced excess entropy is proposed. The obtained results can be useful for rough estimates of the thermal conductivity coefficient of simple fluids with steep interactions when more accurate experimental results are not available.

Thermodynamics of trimethyltetradecylammonium bromide – Sodium deoxycholate binary mixed micelle formation in aqueous solution: Regular solution theory with mutual compensation of excess configurational and excess conformational entropy

A binary mixture of trimethyl(tetradecyl)ammonium bromide = TB-SD = sodium deoxycholate surfactants forms non-ideal binary mixed micelles that have molar excess Gibbs free energy described with the Margules function of the first order. Strong synergistic interactions exist between TB and SD particles (interaction coefficient with a magnitude of 10). Based on the temperature dependence of interaction coefficient and temperature dependence of TB and SD micellar molar fractions product logarithm, it follows that the molar excess entropy is zero. Therefore, although the surfactants TB and SD are structurally very different, their binary mixed micelles can still be described with regular solution theory (random mixing of TB and SD). However, the 2D ROESY spectrum indicates that the binary micellar pseudophase is not random in terms of the spatial distribution of TB and SD particles. Namely, intermolecular interactions between deoxycholic acid anions are missing in the binary mixed micelle. This results in the appearance of excess configuration entropy. However, a zero value of the total molar excess entropy and the existence of the first order Margules function for the molar excess Gibbs free energy means that the molar excess configurational entropy is compensated with the molar excess conformational entropy and that there are correlation effects between the excess configurational enthalpy and entropy as well as between the excess conformational enthalpy and entropy.

Correct use of excess configurational entropies to study the ideal glass transition in hard-sphere systems with continuous polydispersity

We systematically apply the resolution to the configurational entropy paradox from our previous paper [V. Baranau and U. Tallarek, J. Chem. Phys. 147, 224503 (2017)] to study configurational entropies and the glass transition in polydisperse hard-sphere systems with log-normal particle radius distributions (r) over a wide range of polydispersities δ=⟨Δr2⟩/⟨r⟩=0.1−0.3. The resolution implies the careful use of excess quantities for vibrational and configurational entropies. We obtain the fluid entropy from the fluid equation of state and the vibrational entropy from the glass equation of state; thereby, the configurational entropy becomes their difference. We discovered that the Adam–Gibbs relation is able to fit the asymptotic alpha-relaxation times τα of the hard-sphere systems under study at high volume fractions φ when our excess configurational entropies are supplied. For polydispersity δ = 0.1, the Adam–Gibbs relation is able to fit the data over the entire range of φ studied. Ideal glass transition densities φg obtained in this way are below predictions from the Vogel–Fulcher–Tammann fits. Our results indicate by extrapolation that the glass close packing limit φGCP for monodisperse systems is ∼0.65, consistent with granular matter studies. Our configurational entropies extrapolated to the monodisperse case are found to match Edwards entropies from granular matter studies very well.

New insights and updated correlations for density, viscosity, refractive index, and associated properties of aqueous 4-diethyl-amino-2-butanol solution

In this study, volumetric, viscometric, and refraction properties of binary 4-diethylamino-2-butanol (DEAB) and water mixture were comprehensively investigated over an entire range of amine concentration and a temperature range of 298.15-343.15 K. In addition to typical density, viscosity, refractive index, and their excess properties, the associated properties (including partial molar volume, apparent partial molar volume, partial molar volume and apparent partial molar volume at infinite dilution, thermal expansion coefficient, excess thermal expansion coefficient, Gibbs free energy, enthalpy, entropy, excess Gibbs free energy, and excess entropy for activation of viscous flow, molar polarizability, and molar free volume) were comprehensively considered. The obtained excess properties revealed that there was a strong contraction of liquid mixture through intermolecular interaction and/or preference molecular packing. Also, Gibbs free energy for activation of viscous flow was a key parameter affecting liquid viscosity. It was suggested that refractive index should be considered with density for a molar polarizability and a free molar volume for CO2 physical solubility. Additionally, the Redlich-Kister equation was very effective for correlating the studied excess physical properties.

A new thermodynamic method to estimate surface tension of liquids

A new thermodynamic model equation of Vapor-Liquid surface tension γ is derived, γAm=Φ(V)(E(L)−E(V))−TΔS; where Am is the molar surface area, E(L) and E(V) are the molar cohesive energy of liquid phase and vapor phase correspondingly, Φ(V) the mean volume fraction exposed to vapor phase of a surface molecule, ΔS the excess surface entropy. Φ(V) is a function of (E(L)− E(V))/nsRT, ns denotes the segment number in a chain molecule, Φ(V) increases slowly with elevating temperature T. This model has been verified for surface tension estimation of simple liquids, organic liquids (non-polar, polar and hydrogen-bonding) and metallic liquids at various temperatures with successful results.

Freezing density scaling of fluid transport properties: Application to liquefied noble gases.

A freezing density scaling of transport properties of the Lennard-Jones fluid is rationalized in terms of Rosenfeld's excess entropy scaling and isomorph theory of Roskilde-simple systems. Then, it is demonstrated that the freezing density scaling operates reasonably well for viscosity and thermal conductivity coefficients of liquid argon, krypton, and xenon. Quasi-universality of the reduced transport coefficients at their minima and at freezing conditions is discussed. The magnitude of the thermal conductivity coefficient at the freezing point is shown to agree remarkably well with the prediction of the vibrational model of heat transfer in dense fluids.

Friction in Myocardial Anoxia Leads to Negative Excess Entropy Production, Self-Organization, and Dissipative Structures.

Contraction of the heart is caused by actin filaments sliding along myosin filaments. This generates a frictional force inducing wear of the contractile apparatus. We postulated that this process could be exacerbated when the heart was submitted to severe anoxia. Anoxia induced dramatic abnormalities in the molecular properties of actin-myosin crossbridges. We applied the formalism of far-from-equilibrium thermodynamics to the left ventricular papillary muscles (LVPMs) of mammalian rat hearts which had been subjected to a prolonged anoxia (3 h). We showed that when subjected to prolonged anoxia, the heart operated far-from-equilibrium as evidenced by the non-linearity between thermodynamic force (F/T: Frictional force/Kelvin temperature) and thermodynamic flow (v0: myofilament sliding velocity). The rate of entropy production (EPR) was the product of (F/T) and v0. The excess entropy production (EEP) was equal to = vo; (S: entropy). The tribological system remained stable when EEP was positive and became unstable when EEP became negative, thus characterizing instability of the system and reflecting the occurrence of self-organization and possibly dissipative structures. After 3 h anoxia, re-oxygenation induced significant reversibility. About 20% of the myosin heads did not recover despite re-oxygenation. These results may be of importance in the context of heart transplantation where the delay between the time of sampling from the donor and the time of the graft installation in the recipient should be as short as possible.

Understanding of glass-forming ability of Zr–Cu alloys from the perspective of vibrational entropy of crystalline phases

Glass formation is of fundamental importance for understanding the origin of glass transition and the design of new bulk metallic glasses. However, its nature has been extremely elusive and intangible over the past few decades. By combining experimental techniques and molecular dynamics simulations, we explored the mystery of glass-forming ability from the perspective of vibrational entropy in the prototypic Zr–Cu alloys. Our results suggest that the excess vibrational entropy of crystalline states and the low-frequency vibration modes can disclose the underlying physics behind good glass formers. The former works as an excellent indicator of glass formability to guide the more efficient composition design of novel glasses.

Interaction between Triton X100 and Brij 58 in their binary mixed micelles: Micellization in aqueous solution and aqueous solution of Poloxamer 188 at the range of temperature T = (273.15–323.15) K

The micellization of the binary mixture of surfactants Triton X100 – Brij 58 in an aqueous solution (with and without Poloxamer 188) was investigated using a spectrofluorimetric method with pyrene as a probe molecule. There are synergistic interactions between the micellar building units in the binary mixed micelles Triton X100 – Brij 58, which increase with increasing temperature. The analyzed binary mixed micelles possess molar excess entropy. The molar excess Gibbs free energy is a first-order Margules function from the surfactant (Triton X100 or Brij 58) molar fraction in the binary mixed micelles Triton X100 – Brij 58. Poloxamer 188, in the temperature range T = (273.15–323.15) K, does not form micelles. Poloxamer 188 in an aqueous surfactant solution (0.01 w/w) reduces the thermodynamic stabilization of the binary mixed micelle Triton X100 – Brij 58 concerning the state of the same binary mixed micelle when this polymer is not present in an aqueous solution. In the presence of Poloxamer 188, the thermodynamic destabilization of the binary mixed micelle Triton X100 – Brij 58 increases with increasing temperature.

Reaction Entropies in Solution from Analytical Three-Dimensional Reference Interaction Site Model Derivatives with Application to Redox and Spin-Crossover Processes.

An analytical approach to compute the excess entropy of solvation at constant pressure in three-dimensional reference interaction site model (3D-RISM) calculations is presented. It includes the changes in the macroscopic dielectric constant of the solvent upon variation of temperature and density. The approach is exact within the framework of force-field descriptions of the solute and gives reasonable results for self-consistently determined electrostatics as used in the 3D-RISM-self-consistent field approach, particularly for entropy differences. The new method is applied to simple examples of reaction entropies of iron complexes in aqueous solution, for which simple gas-phase calculations and many other approaches give unreliable estimates. For both redox half-reactions and spin-crossover processes, (semi)quantitative agreement with experimental reaction entropies can be achieved out of the box.

Thermodynamics of BPS and near-BPS AdS6 black holes

We develop the thermodynamics of BPS and near-BPS AdS6 black holes. We study the phase diagram of BPS black holes in the grand canonical ensemble. We highlight two distinct deformations orthogonal to the BPS surface: (i) increasing the temperature while keeping the charges fixed, (ii) changing the charges while maintaining extremality such that the BPS constraint is no longer satisfied. For both these deformations, we show that the considerations of the BPS entropy function can be extended to describe the near-BPS regime. The excess entropy together with changes in all potentials are perfectly accounted for via the extremization principle.

Positional information as a universal predictor of freezing

Variation of positional information, measured by the two-body excess entropy , is studied across the liquid-solid equilibrium transition in a simple two-dimensional system. Analysis reveals a master relation between and the freezing temperature T 1, from which a scaling law is extracted, . Theoretical and practical implications of the observed universality are discussed.

Excess Entropy Scaling in Active-Matter Systems.

Active-matter systems feature discrete particles that can convert stored or ambient free energy into motion. To realize the engineering potential of active matter, there is a strong need for predictive and theoretically grounded techniques for describing transport in these systems. In this work, we perform molecular-dynamics (MD) simulations of a model active-matter system, in which we vary the total fraction of active particles (0.01 ≤ ϕ ≤ 0.5) as well as the degree of activity of the active particles. These simulations reveal a fascinating array of transport phenomena, including activity-enhanced diffusion coefficients. By adapting an existing result for binary (inactive) fluids, we demonstrate the existence of an excess entropy scaling relation in an active system. This relationship is well supported by our MD results and establishes a new connection between transport (dynamics) and structure (statics) in active matter, a promising step for predictive and generalizable models of other transport phenomena in such systems.

Thermophysical Properties of Alkanone + Aromatic Amine Mixtures at Varying Temperatures.

In the present investigation, an attempt has been made to evaluate internal pressure , energy , and enthalpy of vaporization along with excess entropy and excess isothermal compressibility for binary solutions of alkanones (2-propanone, 2-butanone, and 2-heptanone) and aromatic amines (aniline, N-methylaniline, and pyridine) at 293.15, 298.15, and 303.15 K, respectively. The cohesive energy density (CED) and solubility parameter are studied to understand the strength of molecular interactions. The coefficient of thermal expansion and isothermal compressibility have also been investigated using empirical equations and have been employed to understand the molecular interactions. All the evaluated properties have been used to understand the nature and extent of intermolecular interactions taking place. The observed trends in the properties and their variations have been discussed in terms of varying chain lengths of the alkyl group and the hydrogen bonding capability of the components. The findings show that the extent of interactions follows an order: aniline > NMA > pyridine, keeping the alkanone constant at all the temperatures under study.