Entropy Term Research Articles

Thermodynamic Description of Synergy in Solvent Extraction: II Thermodynamic Balance of Driving Forces Implied in Synergistic Extraction

In the second part of this study, we analyze the free energy of transfer in the case of synergistic solvent extraction. This free energy of the transfer of an ion in dynamic equilibrium between two coexisting phases is decomposed into four driving forces combining long-range interactions with the classical complexation free energy associated with the nearest neighbors. We demonstrate how the organometallic complexation is counterbalanced by the cost in free energy related to structural change on the colloidal scale in the solvent phase. These molecular forces of synergistic extraction are driven not only by the entropic term associated with the tight packing of electrolytes in the solvent and by the free energy cost of coextracting water toward the hydrophilic core of the reverse aggregates present but also by the entropic costs in the formation of the reverse aggregate and by the interfacial bending energy of the extractant molecules packed around the extracted species. Considering the sum of the terms, we can rationalize the synergy observed, which cannot be explained by classical extraction modeling. We show an industrial synergistic mixture combining an amide and a phosphate complexing site, where the most efficient/selective mixture is observed for a minimal bending energy and maximal complexation energy.

Thermodynamics of solution of L-valine in water

This paper focuses on the accurate thermodynamic study of solution of L-valine in water in a wide temperature range. Enthalpies of solution of L-valine in water have been calorimetrically determined between T=279K and T=323 К. Standard enthalpies and heat capacities of solution as well as standard partial molal heat capacities have been calculated and compared with available literature values. The free energy of solution and its enthalpic and entropic terms have been computed using the combination of solubility and calorimetric data via the Gibbs-Helmholtz equation from T=280K to T=360K. The temperature dependence of solubility of the amino acid has been also computed and compared with experimental quantities. The satisfactory agreement is found between experimental and predicted solubility values.

Brane bounce from logarithmic entropic corrections in the bulk

We calculate new corrections to the braneworld dynamics, lying in a 5D Schwarzschild–de Sitter black hole, generalizing the result of Nojiri, Odintsov and Ogushi (NOO). The NOO entropy effect is based on the logarithmic correction to the bulk entropy firstly calculated by Mukherji and Pal. We calculate higher order contributions to the brane worldsheet. The extra terms obtained lead to interesting implications in brane cosmology. In particular, new entropic terms rapidly disappear in the late Universe while exploding in the very early Universe. In particular, we show that they may trigger a cosmological bounce in the very early Universe. On the other hand, they contribute to the cosmological expansion in the late Universe. We also discuss a scenario in which the BLK anisotropies are washed out, toward a new ekpyrotic brane cosmology.

Maximum entropy formalism for the analytic continuation of matrix-valued Green's functions

We present a generalization of the maximum entropy method to the analytic continuation of matrix-valued Green's functions. To treat off-diagonal elements correctly based on Bayesian probability theory, the entropy term has to be extended for spectral functions that are possibly negative in some frequency ranges. In that way, all matrix elements of the Green's function matrix can be analytically continued; we introduce a computationally cheap element-wise method for this purpose. However, this method cannot ensure important constraints on the mathematical properties of the resulting spectral functions, namely positive semidefiniteness and Hermiticity. To improve on this, we present a full matrix formalism, where all matrix elements are treated simultaneously. We show the capabilities of these methods using insulating and metallic dynamical mean-field theory (DMFT) Green's functions as test cases. Finally, we apply the methods to realistic material calculations for LaTiO$_3$, where off-diagonal matrix elements in the Green's function appear due to the distorted crystal structure.

Giant direct and inverse magnetocaloric effect linked to the same forward martensitic transformation

Metamagnetic shape memory alloys have aroused considerable attraction as potential magnetic refrigerants due to the large inverse magnetocaloric effect associated to the magnetic-field-induction of a reverse martensitic transformation (martensite to austenite). In some of these alloys, the austenite phase can be retained on cooling under high magnetic fields, being the retained phase metastable after field removing. Here, we report a giant direct magnetocaloric effect linked to the anomalous forward martensitic transformation (austenite to martensite) that the retained austenite undergoes on heating. Under moderate fields of 10 kOe, an estimated adiabatic temperature change of 9 K has been obtained, which is (in absolute value) almost twice that obtained in the conventional transformation under higher applied fields. The observation of a different sign on the temperature change associated to the same austenite to martensite transformation depending on whether it occurs on heating (retained) or on cooling is attributed to the predominance of the magnetic or the vibrational entropy terms, respectively.

Wasserstein Blue Noise Sampling

In this article, we present a multi-class blue noise sampling algorithm by throwing samples as the constrained Wasserstein barycenter of multiple density distributions. Using an entropic regularization term, a constrained transport plan in the optimal transport problem is provided to break the partition required by the previous Capacity-Constrained Voronoi Tessellation method. The entropic regularization term cannot only control spatial regularity of blue noise sampling, but it also reduces conflicts between the desired centroids of Vornoi cells for multi-class sampling. Moreover, the adaptive blue noise property is guaranteed for each individual class, as well as their combined class. Our method can be easily extended to multi-class sampling on a point set surface. We also demonstrate applications in object distribution and color stippling.

Conformational Dynamics and Exchange Kinetics of N-Formyl and N-Acetyl Groups Substituting 3-Amino-3,6-dideoxy-α-d-galactopyranose, a Sugar Found in Bacterial O-Antigen Polysaccharides.

Three dimensional shape and conformation of carbohydrates are important factors in molecular recognition events and the N-acetyl group of a monosaccharide residue can function as a conformational gatekeeper whereby it influences the overall shape of the oligosaccharide. NMR spectroscopy and quantum mechanics (QM) calculations are used herein to investigate both the conformational preferences and the dynamic behavior of N-acetyl and N-formyl substituents of 3-amino-3,6-dideoxy-α-d-galactopyranose, a sugar and substitution pattern found in bacterial O-antigen polysaccharides. QM calculations suggest that the amide oxygen can be involved in hydrogen bonding with the axial OH4 group primarily but also with the equatorial OH2 group. However, an NMR J coupling analysis indicates that the θ1 torsion angle, adjacent to the sugar ring, prefers an ap conformation where conformations <180° also are accessible, but does not allow for intramolecular hydrogen bonding. In the formyl-substituted compound 4JHH coupling constants to the exo-cyclic group were detected and analyzed. A van't Hoff analysis revealed that the trans conformation at the amide bond is favored by ΔG° ≈ - 0.8 kcal·mol-1 in the formyl-containing compound and with ΔG° ≈ - 2.5 kcal·mol-1 when the N-acetyl group is the substituent. In both cases the enthalpic term dominates to the free energy, irrespective of water or DMSO as solvent, with only a small contribution from the entropic term. The cis-trans isomerization of the θ2 torsion angle, centered at the amide bond, was also investigated by employing 1H NMR line shape analysis and 13C NMR saturation transfer experiments. The extracted transition rate constants were utilized to calculate transition energy barriers that were found to be about 20 kcal·mol-1 in both DMSO-d6 and D2O. Enthalpy had a higher contribution to the energy barriers in DMSO-d6 compared to in D2O, where entropy compensated for the loss of enthalpy.

Optimal protocol for maximum work extraction in a feedback process with a time-varying potential

The nonequilibrium nature of information thermodynamics is characterized by the inequality or non-negativity of the total entropy change of the system, memory, and reservoir. Mutual information change plays a crucial role in the inequality, in particular if work is extracted and the paradox of Maxwell’s demon is raised. We consider the Brownian information engine where the protocol set of the harmonic potential is initially chosen by the measurement and varies in time. We confirm the inequality of the total entropy change by calculating, in detail, the entropic terms including the mutual information change. We rigorously find the optimal values of the time-dependent protocol for maximum extraction of work both for the finite-time and the quasi-static process.

Numerical study of two-dimensional cylindrical underwater explosion by a modified method of characteristics

A modified method of characteristics (mMOC) is introduced for solution of 2D axisymmetric supersonic flow, as well as its application to simulation of a cylindrical underwater explosion, which is a typical non-homentropic flow problem. The modifications include a family of compatibility equations which contains entropy term in streamline direction, an improved backward scheme with second-order accuracy, a modified forward scheme that uses adaptive technique, which in total make this mMOC be appropriate for a branch fluid dynamics with isentropic or non-isentropic flows. The numerical results show good agreement between the mMOC and experiments. It is established that this mMOC yields shock location, shock peak pressure, and gas-water interface location with an acceptable accuracy. Compared with an explicit dynamics program AUTODYN, which needs to select an appropriate artificial viscosity to handle shock discontinuity properly, the mMOC typically requires far less computer time with the same accuracy in the calculation of the underwater shock wave. Besides, the formation of a secondary shock is well revealed in the pressure nephogram, which suggests the mMOC is able to capture small variation in flow field. In addition, this mMOC can clearly display the domain of dependence in characteristic net, which makes it possible to quantitatively describe the connection between near field shock and detonation products expansion.

Wasserstein Blue Noise Sampling

In this article, we present a multi-class blue noise sampling algorithm by throwing samples as the constrained Wasserstein barycenter of multiple density distributions. Using an entropic regularization term, a constrained transport plan in the optimal transport problem is provided to break the partition required by the previous Capacity-Constrained Voronoi Tessellation method. The entropic regularization term cannot only control spatial regularity of blue noise sampling, but it also reduces conflicts between the desired centroids of Vornoi cells for multi-class sampling. Moreover, the adaptive blue noise property is guaranteed for each individual class, as well as their combined class. Our method can be easily extended to multi-class sampling on a point set surface. We also demonstrate applications in object distribution and color stippling.

Partition of methylpheophorbide a, dioxidine and their conjugate in the 1-octanol/phosphate saline buffer biphasic system

The 1-octanol/phosphate saline buffer partition coefficients (P) for the well-established antimicrobial drug “Dioxidine” and its conjugate with the chlorin e6 molecule have been determined between the temperatures 298.15K and 318.15K and compared with corresponding quantities for several chlorophyll-type photosensitizers (PSs). The lipid-like phase is found to be enriched by solute molecules for all cases and the effect strongly depends on the solute structure. The temperature changes of partition coefficient are very small for chlorin e6-type PSs but significant for methylpheophorbide a and its glycol derivative. Thermodynamic calculations indicate that all solutes are better solvated in OctOH than in phosphate saline buffer mainly due to the favorable enthalpic term. The entropic term contributes to the behavior of phorbin-type pigments in an opposite manner but favors solvation of two chlorin e6-type PSs in a lipid-like phase.

Quantifying the dynamics of electroencephalographic (EEG) signals to distinguish alcoholic and non-alcoholic subjects using an MSE based K-d tree algorithm.

In this paper, we have employed K-d tree algorithmic based multiscale entropy analysis (MSE) to distinguish alcoholic subjects from non-alcoholic ones. Traditional MSE techniques have been used in many applications to quantify the dynamics of physiological time series at multiple temporal scales. However, this algorithm requires O(N2), i.e. exponential time and space complexity which is inefficient for long-term correlations and online application purposes. In the current study, we have employed a recently developed K-d tree approach to compute the entropy at multiple temporal scales. The probability function in the entropy term was converted into an orthogonal range. This study aims to quantify the dynamics of the electroencephalogram (EEG) signals to distinguish the alcoholic subjects from control subjects, by inspecting various coarse grained sequences formed at different time scales, using traditional MSE and comparing the results with fast MSE (fMSE). The performance was also measured in terms of specificity, sensitivity, total accuracy and receiver operating characteristics (ROC). Our findings show that fMSE, with a K-d tree algorithmic approach, improves the reliability of the entropy estimation in comparison with the traditional MSE. Moreover, this new technique is more promising to characterize the physiological changes having an affect at multiple time scales.

Wasserstein blue noise sampling

In this article, we present a multi-class blue noise sampling algorithm by throwing samples as the constrained Wasserstein barycenter of multiple density distributions. Using an entropic regularization term, a constrained transport plan in the optimal transport problem is provided to break the partition required by the previous Capacity-Constrained Voronoi Tessellation method. The entropic regularization term cannot only control spatial regularity of blue noise sampling, but it also reduces conflicts between the desired centroids of Vornoi cells for multi-class sampling. Moreover, the adaptive blue noise property is guaranteed for each individual class, as well as their combined class. Our method can be easily extended to multi-class sampling on a point set surface. We also demonstrate applications in object distribution and color stippling.

Conductivity and dissociation behavior of l(+)-lactic acid in the aqueous solutions of (1-butyl-4-methylpyridinium halide, 1-butyl-3-methylimidazolium halide + polyethylene glycol) at different temperatures

In this paper, the effect of some ionic liquids on the conductivity behavior of l(+)–lactic acid was studied in polyethylene glycol aqueous solutions. The molar conductivities of l(+)–lactic acid in the aqueous solutions of polyethylene glycol, polyethylene glycol+1–butyl–3–methylimidazolium bromide, polyethylene glycol+1–butyl–3–methylimidazolium chloride, polyethylene glycol+1–butyl–4–methylpyridinium bromide, and polyethylene glycol+1–butyl–4–methylpyridinium chloride were measured at the temperature ranges of (288.15–318.15)K. The molar conductivity data were correlated using Quint–Viallard (QV) conductivity equation to calculate the limiting molar conductivities (Λ0) and dissociation constants (KD). The results show that limiting molar conductivity increase by increasing both of the anion size and acidic power of ILs cation. The KD values were also used to calculate the dissociation standard thermodynamic functions (ΔGD0, ΔSD0, and ΔHD0). The values of ΔGD0 are positive and become more positive at higher temperatures. This implies that the dissociation of the acid is controlled by entropy term.

Self-Assembly of Di-N-Heterocyclic Carbene-Gold-Adorned Corannulenes on C60.

The deprotonation of a corannulene-based bisazolium salt allowed the preparation of a corannulene-based NHC di-AuI complex. The prepared di-AuI -complex was tested in the recognition of fullerene-C60 , demonstrating good binding affinity in toluene solution, and producing a host-guest complex with 3:1 stoichiometry, as evidenced by a combination of NMR spectroscopy and ITC titrations. The experimental results are fully supported by DFT calculations. The binding of C60 with the di-AuI complex in toluene solution is enthalpically and entropically favoured. Remarkably, the entropic term is the dominant parameter in the binding process. The good complementarity that exists between the concave shape of the corannulene-di-gold complex and the convex surface of the fullerene, together with the presence of tBu groups and the AuCl fragment are key factors for the measured high affinity between host and guest. The obtained results indicate that fullerene may be acting as a template for the formation of a self-assembled aggregate involving up to three molecules of the di-AuI complex.

Thermodynamic cost of external control

Artificial molecular machines are often driven by the periodic variation of an external parameter. This external control exerts work on the system of which a part can be extracted as output if the system runs against an applied load. Usually, the thermodynamic cost of the process that generates the external control is ignored. Here, we derive a refined second law for such small machines that include this cost, which is, for example, generated by free energy consumption of a chemical reaction that modifies the energy landscape for such a machine. In the limit of irreversible control, this refined second law becomes the standard one. Beyond this ideal limiting case, our analysis shows that due to a new entropic term unexpected regimes can occur: the control work can be smaller than the extracted work and the work required to generate the control can be smaller than this control work. Our general inequalities are illustrated by a paradigmatic three-state system.

Large deviation principle for empirical fields of Log and Riesz gases

We study a system of N particles with logarithmic, Coulomb or Riesz pairwise interactions, confined by an external potential. We examine a microscopic quantity, the tagged empirical field, for which we prove a large deviation principle at speed N. The rate function is the sum of an entropy term, the specific relative entropy, and an energy term, the renormalized energy introduced in previous works, coupled by the temperature. We deduce a variational property of the sine-beta processes which arise in random matrix theory. We also give a next-to-leading order expansion of the free energy of the system, proving the existence of the thermodynamic limit.

Conformation and dynamics of single polymer chain studied by optical microscopy techniques beyond the diffraction limit.

The origin of the unique properties of a polymer material is the large entropic term of a single molecule, which has a chain-like structure with a large molecular weight. From the viewpoint of understanding the fundamental polymer physics, conformation of the single polymer chain is one of the most important matters; however, it has been difficult to examine the behavior of a single chain because of the limitation of conventional experimental methods. Recent developments in optical microscopy allow the fluorescence imaging beyond the diffraction limit of light, and the author's group showed that the conformation and the dynamics of a single polymer chain can be examined by the high-resolution fluorescence imaging. This review presents the application of optical microscopy with nanometric spatial resolution to study the polymer materials at the single-chain level.

Comprehensive Thermodynamic Profiling for the Binding of a G-Quadruplex Selective Indoloquinoline.

Binding of a positively charged indoloquinoline derivative to a G-quadruplex formed by the G-rich promoter element of the c-MYC oncogene was subjected to a rigorous isothermal calorimetric analysis. Binding of the indoloquinoline is primarily enthalpy-driven but is also promoted by a favorable entropy term. Both binding enthalpy ΔH° and binding entropy ΔS° exhibit a noticeable temperature dependence with almost complete enthalpy-entropy compensation as a result of a negative change in heat capacity ΔCp°. Salt-dependent polyelectrolyte effects only moderately contribute to the overall free energy of association. More details on the binding process are revealed in an attempt to dissect the total free energy into individual contributory terms. Accordingly, specific intermolecular interactions between the indoloquinoline ligand and G-quadruplex substantially contribute in addition to hydrophobic effects in promoting the association. Comparing thermodynamic profiles for various quadruplex ligands indicates different energetic patterns that may aid in the rational design of more efficient quadruplex binding ligands in the future.

Quantum Gravity Effects on Hawking Radiation of Schwarzschild-de Sitter Black Holes

The correction of Hawking temperature of Schwarzschild-de Sitter (SdS) black hole is investigated using the generalized Klein-Gordon equation and the generalized Dirac equation by taking the quantum gravity effects into account. We derive the corrected Hawking temperatures for scalar particles and fermions crossing the event horizon. The quantum gravity effects prevent the rise of temperature in the SdS black hole. Besides correction of Hawking temperature, the Hawking radiation of SdS black hole is also investigated using massive particles tunneling method. By considering self gravitation effect of the emitted particles and the space time background to be dynamical, it is also shown that the tunneling rate is related to the change of Bekenstein-Hawking entropy and small correction term (1 + 2β m 2). If the energy and the angular momentum are taken to be conserved, the derived emission spectrum deviates from the pure thermal spectrum. This result gives a correction to the Hawking radiation and is also in agreement with the result of Parikh and Wilczek.