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PubMed2005

Application of Maximum Entropy reconstruction to PISEMA spectra.

Maximum Entropy reconstruction is applied to two-dimensional PISEMA spectra of stationary samples of peptide crystals and proteins in magnetically aligned virus particles and membrane bilayers. Improvements in signal-to-noise ratios were observed with minimal distortion of the spectra when Maximum Entropy reconstruction was applied to non-linearly sampled data in the indirect dimension. Maximum Entropy reconstruction was also applied in the direct dimension by selecting sub-sets of data from the free induction decays. Because the noise is uncorrelated in the spectra obtained by Maximum Entropy reconstruction of data with different non-linear sampling schedules, it is possible to improve the signal-to-noise ratios by co-addition of multiple spectra derived from one experimental data set. The combined application of Maximum Entropy to data in the indirect and direct dimensions has the potential to lead to substantial reductions in the total amount of experimental time required for acquisition of data in multidimensional NMR experiments.

Bacteriophages↗

PubMed2000

Multiple attribute entropy classification of school-age injuries.

The data exploration task in epidemiology of school children injuries is aimed at defining specific risk groups that can be further analyzed for definition of prevention measures. These groups are selected by means of entropy classification of relevant data collected in the Koprivnica district, Croatia. The necessary pruning procedure for the entropy classification tree is proposed for: (a) entropy increase for uniformly populated classes, and (b) entropy decrease for the case of zeros in a class. The second reason for pruning is emphasized for multiple (> 3) attribute descriptions of injury events because the number of classes increases exponentially with the number of attributes. Four possible prevention groups have been found by entropy classification: (1) dislocation, sprain and strain injuries, mostly on legs of both age groups of boys (7-10 years, 11-14 years) in/around the house activities; (2) arm fractures of all boys in/around the house activities; (3) open wounds mostly of the head, in younger boys at school, and open wounds in younger boys in road traffic; and (4) contusions mostly on arms, of older girls at school and contusions in older boys in road traffic accidents. These groups comprise 57.2% of all considered cases.

Accidents↗

PubMed2005

Entropy-enthalpy compensations in solutions of dual character molecules with polymeric chromatographic liquid phases.

Careful gas chromatographic studies provide thermodynamic data for insights into solution processes in nonvolatile solvents. Using 24 solutes and five stationary phases, several entropy-enthalpy compensation effects in the thermodynamics of solution were identified. Despite solute structure differences, when excess enthalpy and entropy of solutions were examined, entropy-enthalpy compensation effects were found in solvents dominated by single types of interaction: squalane and, to some extent, methoxy poly(ethylene oxide) (PEO). The main reason for the absence of linearity in other solvents is pure solute state interactions in the reference state and the multicharacter nature of solvents. In this study, consideration of solute state interactions was removed through examination of the thermodynamics of transfer between solvent pairs. It was found that solute transfers from squalane to poly[methyl(trifluoropropyl)siloxane] (QF-1) and to poly(methylphenyl) (DC-550) also gave linear relationships. The former system contains a second correlation for ester type solutes. The transfer data for squalane to poly(methylsiloxane) (DC-200) had smaller ranges and were more scattered. The effects of derivatizing groups on the transfer enthalpy and entropy were treated as a summation of hydrocarbon cores with the derivative groups. The group properties of transfer then also show entropy-enthalpy compensation effects. Many solution effects could be explained on the basis of solvent composition and local interactions with solutes.

Journal Article↗

PubMed2005

Alkyl group as entropy reservoir in an MMX chain complex, Pt2(n-PenCS2)4I.

Heat capacity of halogen-bridged one-dimensional binuclear metal complex (so-called MMX chain) having four n-pentyl groups, Pt2(n-PenCS2)4I, was measured by adiabatic calorimetry. A first-order phase transition was observed at 207.4 K when measurement was made after cooling from room temperature. The enthalpy and entropy of transition were determined to be 10.19 kJ mol(-1) and 49.1 J K(-1) mol(-1), respectively. A monotropic phase transition was observed at 324 K on heating, and the entropy of transition was essentially null. The sample once heated above 324 K never returned to the initial phase at room temperature and underwent a higher-order phase transition at 173 K and a first-order phase transition at 220.5 K. The enthalpy and entropy of the first-order phase transition were estimated to be 11.6 kJ mol(-1) and 52.4 J K(-1) mol(-1), respectively. The magnitude of the entropy gain at the phase transition from the initial room-temperature phase to the high-temperature phase at 324 K shows that in Pt2(n-PenCS2)4I a large amount of entropy reserved in alkyl chain is transferred to dithiocarboxylato groups upon the phase transition, as in the cases of Pt2(n-PrCS2)4I and Pt2(n-BuCS2)4I.

Journal Article↗

PubMed2006

Molecular dynamics study of the thermal entropy in mixed zinc chalcogenides.

Molecular dynamics (MD) calculations were performed to determine the vibrational contribution to the entropy of mixing and its importance for the mixing of ZnO/ZnS and ZnS/Zn3P2. These systems were modeled by cyclic clusters Zn48O48, Zn32S32, and Zn48P32. The mixed cyclic clusters considered were Zn48O47S, Zn32S31O, Zn33S30P2, and Zn47S2P30. For each of the clusters, the entropy was calculated in the range of the experimental temperature of the mixing process. The convergence of the entropy with respect to the number of MD steps was studied. Finally, the thermal part of the entropy of mixing was determined, and its dependence on the number of MD steps was investigated. It was found that the thermal entropy is important for the Gibbs free energy of mixing near the miscibility gaps.

Journal Article↗

PubMed2006

Enthalpy-entropy compensation in the effects of urea on hydrophobic interactions.

By comparison of neopentane pair potentials of mean force (PMFs) in room temperature water and 6.9 molar aqueous urea, it was recently shown that urea molecules affect the PMF minima in an unexpected way (Lee, M.-E.; van der Vegt, N. F. A. J. Am. Chem. Soc. 2006, 128, 4948). While the first PMF minimum in urea solution has an identical shape and depth to those of the corresponding minimum in water, the second minimum in urea solution is broader, deeper, and shifted out to a slightly larger distance. Here, we present a study of the enthalpic and entropic contributions to these PMFs. Its significance for understanding the driving forces responsible for thermodynamically favorable neopentane contact and solvent-separated distances in urea solution is discussed. We propose that the solute-solvent entropy and solute-solvent enthalpy changes should be analyzed for obtaining an unambiguous molecular-scale picture. In urea solution, enthalpy-entropy compensation effects associated with structural solvent reorganization processes are large, causing changes of the system's enthalpy and entropy with hydrophobic pair separation to be very different from the solute-solvent enthalpy and entropy changes. The entropies are discussed in terms of the molecular-scale solvent reorganization processes.

Solvents↗

PubMed2004

Adolescent friendship as a dynamic system: entropy and deviance in the etiology and course of male antisocial behavior.

A dynamic systems framework was applied to understand the influence of friendship on antisocial behavior from childhood (age 9-10) through adulthood (age 24-25) for Oregon Youth Study males (N = 206). Boys were videotaped interacting with a friend at ages 14, 16, and 18, and deviant content and interpersonal processes were independently coded. Conditional dyadic interpersonal processes were studied as a communication system and summarized by an index of information entropy (F. Attneave, 1959). High entropy scores represent disorganized, unpredictable patterns of interaction, whereas low entropy scores reflect an organized dialogue. Conversations of early-onset antisocial boys and their best friends were less organized and included more deviant content than those of well-adjusted controls. Prediction analyses, however, revealed an interaction between entropy and deviant talk. Consistent with expectation, males with well-organized interactions (i.e., low entropy) but elevated levels of deviant content were most likely to continue antisocial behavior into adulthood. Findings suggest that individual risk for maladaptation may be amplified by early adolescent friendship dynamics organized around deviance.

Adolescent↗

PubMed2003

Spin entropy as the likely source of enhanced thermopower in Na(x)Co2O4.

In an electric field, the flow of electrons in a solid produces an entropy current in addition to the familiar charge current. This is the Peltier effect, and it underlies all thermoelectric refrigerators. The increased interest in thermoelectric cooling applications has led to a search for more efficient Peltier materials and to renewed theoretical investigation into how electron-electron interaction may enhance the thermopower of materials such as the transition-metal oxides. An important factor in this enhancement is the electronic spin entropy, which is predicted to dominate the entropy current. However, the crucial evidence for the spin-entropy term, namely its complete suppression in a longitudinal magnetic field, has not been reported until now. Here we report evidence for such suppression in the layered oxide Na(x)Co2O4, from thermopower and magnetization measurements in both longitudinal and transverse magnetic fields. The strong dependence of thermopower on magnetic field provides a rare, unambiguous example of how strong electron-electron interaction effects can qualitatively alter electronic behaviour in a solid. We discuss the implications of our finding--that spin-entropy dominates the enhancement of thermopower in transition-metal oxides--for the search for better Peltier materials.

Journal Article↗

PubMed2001

Thermodynamics of computing: Entropy of nonergodic systems.

Landauer discussed the minimum energy necessary for computation and stated that erasure of information is accompanied with kT ln 2/ bit of heat generation. We reconsider this problem on the basis of Clausius's equation defining the thermodynamic entropy. We show that the erasing process, involving a transition from a nonergodic to an ergodic state, is irreversible and accompanied with k ln 2/bit of entropy generation, while the heat generation occurs in a writing process. The inverse of the erasing process corresponds to spontaneous symmetry breaking from an ergodic to a nonergodic state, which induces a decrease(!) in thermodynamic entropy. Our theory is examined by a simulation of a binary device described by a Langevin equation. We argue that the so-called residual entropy of symmetry broken states, such as in ice, is not a thermodynamic quantity, even if it might be called "information entropy." (c) 2001 American Institute of Physics.

Journal Article↗

PubMed2003

Regularities unseen, randomness observed: levels of entropy convergence.

We study how the Shannon entropy of sequences produced by an information source converges to the source's entropy rate. We synthesize several phenomenological approaches to applying information theoretic measures of randomness and memory to stochastic and deterministic processes by using successive derivatives of the Shannon entropy growth curve. This leads, in turn, to natural measures of apparent memory stored in a source and the amounts of information that must be extracted from observations of a source in order for it to be optimally predicted and for an observer to synchronize to it. To measure the difficulty of synchronization, we define the transient information and prove that, for Markov processes, it is related to the total uncertainty experienced while synchronizing to a process. One consequence of ignoring a process's structural properties is that the missed regularities are converted to apparent randomness. We demonstrate that this problem arises particularly for settings where one has access only to short measurement sequences. Numerically and analytically, we determine the Shannon entropy growth curve, and related quantities, for a range of stochastic and deterministic processes. We conclude by looking at the relationships between a process's entropy convergence behavior and its underlying computational structure.

Markov Chains↗

PubMed2003

Estimation of entropies and dimensions by nonlinear symbolic time series analysis.

Symbolic nonlinear time series analysis methods have the potential for analyzing nonlinear data efficiently with low sensitivity to noise. In symbolic nonlinear time series analysis a time series for a fixed delay is partitioned into a small number (called the alphabet size) of cells labeled by symbols, creating a symbolic time series. Symbolic methods involve computing the statistics of words made from the symbolic time series. Specifically, the Shannon entropy of the distribution of possible words for a range of word lengths is computed. The rate of increase of the entropy with word length is the metric (Kolmogorov-Sinai) entropy. Methods of computing the metric entropy for flows as well as for maps are shown. A method of computing the information dimension appropriate to symbolic analysis is proposed. In terms of this formulation, the information dimension is determined by the scaling of entropy as alphabet size is modestly increased, using the information obtained from large word length. We discuss the role of sampling time and the issue of using these methods when there may be no generating partition.

Journal Article↗

PubMed1997

Entropy potential and Lyapunov exponents.

According to a previous conjecture, spatial and temporal Lyapunov exponents of chaotic extended systems can be obtained from derivatives of a suitable function, the entropy potential. The validity and the consequences of this hypothesis are explored in detail. The numerical investigation of a continuous-time model provides a further confirmation to the existence of the entropy potential. Furthermore, it is shown that the knowledge of the entropy potential allows determining also Lyapunov spectra in general reference frames where the time-like and space-like axes point along generic directions in the space-time plane. Finally, the existence of an entropy potential implies that the integrated density of positive exponents (Kolmogorov-Sinai entropy) is independent of the chosen reference frame. (c) 1997 American Institute of Physics.

Journal Article↗

PubMed1998

Entropy balance, time reversibility, and mass transport in dynamical systems.

We review recent results concerning entropy balance in low-dimensional dynamical systems modeling mass (or charge) transport. The key ingredient for understanding entropy balance is the coarse graining of the local phase-space density. It mimics the fact that ever refining phase-space structures caused by chaotic dynamics can only be detected up to a finite resolution. In addition, we derive a new relation for the rate of irreversible entropy production in steady states of dynamical systems: It is proportional to the average growth rate of the local phase-space density. Previous results for the entropy production in steady states of thermostated systems without density gradients and of Hamiltonian systems with density gradients are recovered. As an extension we derive the entropy balance of dissipative systems with density gradients valid at any instant of time, not only in stationary states. We also find a condition for consistency with thermodynamics. A generalized multi-Baker map is used as an illustrative example. (c) 1998 American Institute of Physics.

Journal Article↗

PubMed2006

Power-law scaling for macroscopic entropy and microscopic complexity: evidence from human movement and posture.

We investigated the relationship between macroscopic entropy and microscopic complexity of the dynamics of body rocking and sitting still across adults with stereotyped movement disorder and mental retardation (profound and severe) against controls matched for age, height, and weight. This analysis was performed through the examination of center of pressure (COP) motion on the mediolateral (side-to-side) and anteroposterior (fore-aft) dimensions and the entropy of the relative phase between the two dimensions of motion. Intentional body rocking and stereotypical body rocking possessed similar slopes for their respective frequency spectra, but differences were revealed during maintenance of sitting postures. The dynamics of sitting in the control group produced lower spectral slopes and higher complexity (approximate entropy). In the controls, the higher complexity found on each dimension of motion was related to a weaker coupling between dimensions. Information entropy of the relative phase between the two dimensions of COP motion and irregularity (complexity) of their respective motions fitted a power-law function, revealing a relationship between macroscopic entropy and microscopic complexity across both groups and behaviors. This power-law relation affords the postulation that the organization of movement and posture dynamics occurs as a fractal process.

Adult↗

PubMed1995

Enthalpy-entropy compensation in DNA melting thermodynamics.

We investigate enthalpy-entropy compensation for melting of nearest-neighbor doublets in DNA. Based on data for 10 normal doublets and for doublets containing a mispaired or analog base, the correlation of delta Szero with delta Hzero follows a rectangular hyperbola. Doublet melting temperature relates linearly to delta Hzero by Tm = T(o) + delta Hzero/a, where T(o) = 273 K and a = 80 cal/mol-K. Thus Tm is proportional to delta Hzero + aTo rather than to delta Hzero alone as previously thought by assuming delta Szero to be constant. The term aTo = 21.8 kcal/mol may reflect a constant enthalpy change in solvent accompanying the DNA enthalpy change for doublet melting and is roughly equivalent to breaking four H-bonds between water molecules for each melted doublet. The solvent entropy change (aTo/Tm) declines with increasing Tm, while the DNA entropy change (delta Hzero/Tm) rises, so the combined DNA + solvent entropy change stays constant at 80 cal/K/mol of doublet. If such constancy in DNA + solvent entropy changes also holds for enzyme clefts as "solvent," then free energy differences for competing correct and incorrect base pairs in polymerase clefts may be as large as enthalpy differences and possibly sufficient to account for DNA polymerase accuracy. The hyperbolic relationship between delta Szero and delta Hzero observed in 1 M salt can be used to evaluate delta Hzero and delta Szero from Tm at lower, physiologically relevant, salt concentrations.

Base Sequence↗

PubMed1999

Angle-angular-momentum entropic bounds and optimal entropies for quantum scattering of spinless particles.

In this paper the angle-angular-momentum entropic lower and upper bounds are proved by using Tsallis-like entropies, the Riesz theorem, and the Lagrange multiplier method for the quantum scattering of the spinless particles. A connection between optimal states and the most stringent entropic bounds on Tsallis-like entropies in the quantum scattering is established. The results of experimental tests of the state-independent angle-angular-momentum entropic bounds as well as of the stringent entropic optimal bounds in pion-nucleus scattering are obtained by calculations of the scattering entropies from the experimental available pion-nucleus phase shifts. Comparisons of these results with predictions of the principle of minimum distance in the space of states are presented. Then it is shown that experimental pion-nucleus entropies are well described by optimal entropies, and that the experimental data are consistent with the principle of minimum distance in the space of scattering states.

Journal Article↗

PubMed2000

Dynamical entropy for systems with stochastic perturbation

Dynamics of deterministic systems perturbed by random additive noise is characterized quantitatively. Since for such systems the Kolmogorov-Sinai (KS) entropy diverges if the diameter of the partition tends to zero, we analyze the difference between the total entropy of a noisy system and the entropy of the noise itself. We show that this quantity is finite and non-negative and we call it the dynamical entropy of the noisy system. In the weak noise limit this quantity is conjectured to tend to the KS entropy of the deterministic system. In particular, we consider one-dimensional systems with noise described by a finite-dimensional kernel for which the Frobenius-Perron operator can be represented by a finite matrix.

Journal Article↗

PubMed2003

Entropy crisis, ideal glass transition, and polymer melting: exact solution on a Husimi cactus.

We investigate an extension of the lattice model of melting of semiflexible polymers originally proposed by Flory. Along with a bending penalty epsilon, present in the original model and involving three sites of the lattice, we introduce an interaction energy epsilon (p), corresponding to the presence of a pair of parallel bonds and an interaction energy epsilon (h), associated with a hairpin turn. Both these new terms represent four-site interactions. The model is solved exactly on a Husimi cactus, which approximates a square lattice. We study the phase diagram of the system as a function of the energies. For a proper choice of the interaction energies, the model exhibits a first-order melting transition between a liquid and a crystalline phase at a temperature T(M). The continuation of the liquid phase below T(M) gives rise to a supercooled liquid, which turns continuously into a new low-temperature phase, called metastable liquid, at T(MC)<T(M). This liquid-liquid transition seems to have some features that are characteristic of the critical transition predicted by the mode-coupling theory. The exact calculation provides a thermodynamic justification for the entropy crisis (entropy becoming negative), generally known as the Kauzmann paradox, caused by the rapid drop of the entropy near the Kauzmann temperature. It occurs not in the supercooled liquid, but in the metastable liquid phase since its Helmholtz free energy equals the absolute zero equilibrium free energy at a positive temperature. A continuous ideal glass transition occurs to avoid the crisis when the metastable liquid entropy, and not the excess entropy, goes to zero. The melting transition in the original Flory model, corresponding to the vanishing of the four-site interactions, appears as a tricritical point of the model.

Journal Article↗