An entropy meter based on the thermoelectric potential of a nonisothermal solid electrolyte cell

The theory, design, and performance of a solid electrolyte twin thermocell for the direct determination of the partial molar entropy of oxygen in a single-phase or multiphase mixture are described. The difference between the Seebeck coefficients of the concentric thermocells is directly related to the difference in the partial molar entropy of oxygen in the electrodes of each thermocell. The measured potentials are sensitive to small deviations from equilibrium at the electrodes. Small electric disturbances caused by simultaneous potential measurements or oxygen fluxes caused by large oxygen potential gradients between the electrodes also disturb the thermoelectric potential. An accuracy of ±0.5 calth K−1 mol−1 has been obtained by this method for the entropies of formation of NiO and NiAl2O4. This “entropy meter” may be used for the measurement of the entropies of formation of simple or complex oxides with significant residual contributions which cannot be detected by heat-capacity measurements.

The standard enthalpy and entropy of formation of Rh2O3 - A third-law optimization

The standard Gibbs energy of formation of Rh203 at high temperature has been determined recently with high precision. The new data are significantly different from those given in thermodynamic compilations.Accurate values for enthalpy and entropy of formation at 298.15 K could not be evaluated from the new data,because reliable values for heat capacity of Rh2O3 were not available. In this article, a new measurement of the high temperature heat capacity of Rh2O3 using differential scanning calorimetry (DSC) is presented.The new values for heat capacity also differ significantly from those given in compilations. The information on heat capacity is coupled with standard Gibbs energy of formation to evaluate values for standard enthalpy and entropy of formation at 289.15 K using a multivariate analysis. The results suggest a major revision in thermodynamic data for Rh2O3. For example, it is recommended that the standard entropy of Rh203 at 298.15 K be changed from 106.27 J mol-' K-'given in the compilations of Barin and Knacke et al. to 75.69 J mol-' K". The recommended revision in the standard enthalpy of formation is from -355.64 kJ mol-'to -405.53 kJ mol".

Magnetic Field Dependence of Entropy And Specific Heat of YBa2Cu3O7-delta Superconductors

The change in thermodynamic quantities (e. g., entropy, specific heat etc.) by the application of magnetic field in the case of the high-T-c superconductor YBCO system is examined phenomenological by the Ginzburg-Landau theory of anisotropic type-II superconductors. An expression for the change in the entropy (Delta S) and change in specific heat (Delta C) in a magnetic field for any general orientation of an applied magnetic field B-a with respect to the crystallographic c-axis is obtained. The observed large reduction of specific heat anomaly just below the superconducting transition and the observed variation of entropy with magnetic field are explained quantitatively.

Statistical properties of entropy-consuming fluctuations in jammed states of laponite suspensions: Fluctuation relations and generalized Gumbel distribution

We report a universal large deviation behavior of spatially averaged global injected power just before the rejuvenation of the jammed state formed by an aging suspension of laponite clay under an applied stress. The probability distribution function (PDF) of these entropy consuming strongly non-Gaussian fluctuations follow an universal large deviation functional form described by the generalized Gumbel (GG) distribution like many other equilibrium and nonequilibrium systems with high degree of correlations but do not obey the Gallavotti-Cohen steady-state fluctuation relation (SSFR). However, far from the unjamming transition (for smaller applied stresses) SSFR is satisfied for both Gaussian as well as non-Gaussian PDF. The observed slow variation of the mean shear rate with system size supports a recent theoretical prediction for observing GG distribution.

Transport in nanoporous zeolites: Relationships between sorbate size, entropy, and diffusivity

Molecular dynamics simulations have been performed on monatomic sorbates confined within zeolite NaY to obtain the dependence of entropy and self-diffusivity on the sorbate diameter. Previously, molecular dynamics simulations by Santikary and Yashonath J. Phys. Chem. 98, 6368 (1994)], theoretical analysis by Derouane J. Catal. 110, 58 (1988)] as well as experiments by Kemball Adv. Catal. 2, 233 (1950)] found that certain sorbates in certain adsorbents exhibit unusually high self-diffusivity. Experiments showed that the loss of entropy for certain sorbates in specific adsorbents was minimum. Kemball suggested that such sorbates will have high self-diffusivity in these adsorbents. Entropy of the adsorbed phase has been evaluated from the trajectory information by two alternative methods: two-phase and multiparticle expansion. The results show that anomalous maximum in entropy is also seen as a function of the sorbate diameter. Further, the experimental observation of Kemball that minimum loss of entropy is associated with maximum in self-diffusivity is found to be true for the system studied here. A suitably scaled dimensionless self-diffusivity shows an exponential dependence on the excess entropy of the adsorbed phase, analogous to excess entropy scaling rules seen in many bulk and confined fluids. The two trajectory-based estimators for the entropy show good semiquantitative agreement and provide some interesting microscopic insights into entropy changes associated with confinement.

On maximum entropy and minimum KL-divergence optimization by Grobner basis methods

In this paper we study constrained maximum entropy and minimum divergence optimization problems, in the cases where integer valued sufficient statistics exists, using tools from computational commutative algebra. We show that the estimation of parametric statistical models in this case can be transformed to solving a system of polynomial equations. We give an implicit description of maximum entropy models by embedding them in algebraic varieties for which we give a Grobner basis method to compute it. In the cases of minimum KL-divergence models we show that implicitization preserves specialization of prior distribution. This result leads us to a Grobner basis method to embed minimum KL-divergence models in algebraic varieties. (C) 2012 Elsevier Inc. All rights reserved.

Role of Specific Cations and Water Entropy on the Stability of Branched DNA Motif Structures

DNA three-way junctions (TWJs) are important intermediates in various cellular processes and are the simplest of a family of branched nucleic acids being considered as scaffolds for biomolecular nanotechnology. Branched nucleic acids are stabilized by divalent cations such as Mg2+, presumably due to condensation and neutralization of the negatively charged DNA backbone. However, electrostatic screening effects point to more complex solvation dynamics and a large role of interfacial waters in thermodynamic stability. Here, we report extensive computer simulations in explicit water and salt on a model TWJ and use free energy calculations to quantify the role of ionic character and strength on stability. We find that enthalpic stabilization of the first and second hydration shells by Mg2+ accounts for 1/3 and all of the free energy gain in 50% and pure MgCl2 solutions, respectively. The more distorted DNA molecule is actually destabilized in pure MgCl2 compared to pure NaCl. Notably, the first shell, interfacial waters have very low translational and rotational entropy (i.e., mobility) compared to the bulk, an entropic loss that is overcompensated by increased enthalpy from additional electrostatic interactions with Mg2+. In contrast, the second hydration shell has anomalously high entropy as it is trapped between an immobile and bulklike layer. The nonmonotonic entropic signature and long-range perturbations of the hydration shells to Mg2+ may have implications in the molecular recognition of these motifs. For example, we find that low salt stabilizes the parallel configuration of the three-way junction, whereas at normal salt we find antiparallel configurations deduced from the NMR. We use the 2PT analysis to follow the thermodynamics of this transition and find that the free energy barrier is dominated by entropic effects that result from the decreased surface area of the antiparallel form which has a smaller number of low entropy waters in the first monolayer.

Quantum phases of dimerized and frustrated Heisenberg spin chains with s=1/2, 1 and 3/2: an entanglement entropy and fidelity study

We study here different regions in phase diagrams of the spin-1/2, spin-1 and spin-3/2 one-dimensional antiferromagnetic Heisenberg systems with frustration (next-nearest-neighbor interaction J(2)) and dimerization (delta). In particular, we analyze the behaviors of the bipartite entanglement entropy and fidelity at the gapless to gapped phase transitions and across the lines separating different phases in the J(2)-delta plane. All the calculations in this work are based on numerical exact diagonalizations of finite systems.

Entanglement entropy in higher derivative holography

We consider holographic entanglement entropy in higher derivative gravity theories. Recently Lewkowycz and Maldacena 1] have provided a method to derive the equations for the entangling surface from first principles. We use this method to compute the entangling surface in four derivative gravity. Certain interesting differences compared to the two derivative case are pointed out. For Gauss-Bonnet gravity, we show that in the regime where this method is applicable, the resulting equations coincide with proposals in the literature as well as with what follows from considerations of the stress tensor on the entangling surface. Finally we demonstrate that the area functional in Gauss-Bonnet holography arises as a counterterm needed to make the Euclidean action free of power law divergences.

Information content of molecular graph and prediction of gas phase thermal entropy of organic compounds

Entropy is a fundamental thermodynamic property that has attracted a wide attention across domains, including chemistry. Inference of entropy of chemical compounds using various approaches has been a widely studied topic. However, many aspects of entropy in chemical compounds remain unexplained. In the present work, we propose two new information-theoretical molecular descriptors for the prediction of gas phase thermal entropy of organic compounds. The descriptors reflect the bulk and size of the compounds as well as the gross topological symmetry in their structures, all of which are believed to determine entropy. A high correlation () between the entropy values and our information-theoretical indices have been found and the predicted entropy values, obtained from the corresponding statistically significant regression model, have been found to be within acceptable approximation. We provide additional mathematical result in the form of a theorem and proof that might further help in assessing changes in gas phase thermal entropy values with the changes in molecular structures. The proposed information-theoretical molecular descriptors, regression model and the mathematical result are expected to augment predictions of gas phase thermal entropy for a large number of chemical compounds.

Entropy of quantum states: Ambiguities

The von Neumann entropy of a generic quantum state is not unique unless the state can be uniquely decomposed as a sum of extremal or pure states. As pointed out to us by Sorkin, this happens if the GNS representation (of the algebra of observables in some quantum state) is reducible, and some representations in the decomposition occur with non-trivial degeneracy. This non-unique entropy can occur at zero temperature. We will argue elsewhere in detail that the degeneracies in the GNS representation can be interpreted as an emergent broken gauge symmetry, and play an important role in the analysis of emergent entropy due to non-Abelian anomalies. Finally, we establish the analogue of an H-theorem for this entropy by showing that its evolution is Markovian, determined by a stochastic matrix.

Entanglement entropy from the holographic stress tensor

We consider entanglement entropy in the context of gauge/gravity duality for conformal field theories in even dimensions. The holographic prescription due to Ryu and Takayanagi (RT) leads to an equation describing how the entangling surface extends into the bulk geometry. We show that setting to zero, the timetime component of the Brown-York stress tensor evaluated on the co-dimension 1 entangling surface, leads to the same equation. By considering a spherical entangling surface as an example, we observe that the Euclidean actionmethods in AdS/CFT will lead to the RT area functional arising as a counterterm needed to regularize the stress tensor. We present arguments leading to a justification for the minimal area prescription.

ENTANGLEMENT ENTROPY FROM SURFACE TERMS IN GENERAL RELATIVITY

Entanglement entropy in local quantum field theories is typically ultraviolet divergent due to short distance effects in the neighborhood of the entangling region. In the context of gauge/gravity duality, we show that surface terms in general relativity are able to capture this entanglement entropy. In particular, we demonstrate that for 1+1-dimensional (1 + 1d) conformal field theories (CFTs) at finite temperature whose gravity dual is Banados-Teitelboim-Zanelli (BTZ) black hole, the Gibbons-Hawking-York term precisely reproduces the entanglement entropy which can be computed independently in the field theory.

On generalized gravitational entropy, squashed cones and holography

We consider generalized gravitational entropy in various higher derivative theories of gravity dual to four dimensional CFTs using the recently proposed regularization of squashed cones. We derive the universal terms in the entanglement entropy for spherical and cylindrical surfaces. This is achieved by constructing the Fefferman-Graham expansion for the leading order metrics for the bulk geometry and evaluating the generalized gravitational entropy. We further show that the Wald entropy evaluated in the bulk geometry constructed for the regularized squashed cones leads to the correct universal parts of the entanglement entropy for both spherical and cylindrical entangling surfaces. We comment on the relation with the Iyer-Wald formula for dynamical horizons relating entropy to a Noether charge. Finally we show how to derive the entangling surface equation in Gauss-Bonnet holography.

3D flat holography: entropy and logarithmic corrections

We compute the leading corrections to the Bekenstein-Hawking entropy of the Flat Space Cosmological (FSC) solutions in 3D flat spacetimes, which are the flat analogues of the BTZ black holes in AdS(3). The analysis is done by a computation of density of states in the dual 2D Galilean Conformal Field Theory and the answer obtained by this matches with the limiting value of the expected result for the BTZ inner horizon entropy as well as what is expected for a generic thermodynamic system. Along the way, we also develop other aspects of holography of 3D flat spacetimes.