SEARCH · PubMed Health

Results for “Entropy”

Explore indexed PubMed citations for clinical trials, systematic reviews and public health research. Read source abstracts and follow each citation to its original PubMed record.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 325 records · Page 18Linked to original sources

PubMed1995

Application of the maximum entropy method for evaluating phosphorus-31-magnetic resonance spectra in patients with liver metastases.

RATIONALE AND OBJECTIVES: The clinical feasibility and application of the maximum entropy method for data analysis from in vivo phosphorus-31-magnetic resonance (P-31-MR) spectra of the liver were determined. METHODS: Image-guided localized P-31-MR spectroscopy was performed in 24 patients with liver metastases and in 20 healthy volunteers. The spectra were obtained with a whole body scanner operating at 1.5 T using a surface coil. Phosphomonoester/beta-adenosine triphosphate (ATP), phosphodiester/beta-ATP, and inorganic phosphate/beta-ATP were calculated from the maximum entropy method-spectra and from spectra evaluated with standard data processing (Fourier transformation spectra). RESULTS: Phosphomonoester/beta-ATP and phosphodiester/beta-ATP were increased significantly with both methods in patients' spectra. Maximum entropy method spectra showed a distinct pattern with low noise. It was easier to determine peak borders and to attach resonances to the different metabolites using this method. CONCLUSIONS: Maximum entropy method is an alternative method for evaluation and quantification of P-31-MR spectra data and is preferred to standard data processing with Fourier transformation in cases of reduced signal-to-noise ratio of spectra.

Aged↗

PubMed1999

Effects of entropy inhomogeneity on density-temperature correlation in solar wind.

Compressive fluctuations in solar wind slow speed streams are studied by means of a magnetohydrodynamics (MHD) model, which represents the plasma in the vicinity of the heliospheric current sheet. The model contains a current sheet, as well as density and temperature variations, corresponding to a large scale modulation of the specific entropy. Alfvénic fluctuations are initially superimposed on the background equilibrium and compressive fluctuations are consequently generated during the time evolution. The resulting correlation between density and temperature fluctuations at various spatial scales is interpreted in terms of both generation of magnetosonic fluctuations and of an "entropy cascade." The latter phenomenon arises as a consequence of the interaction between the MHD turbulence and the underlying large scale entropy structure. In particular, it is responsible for anticorrelated density and temperature fluctuations detected at various scales. The results of the model are compared with the proton density-temperature correlation calculated during several crossings of solar wind slow speed streams by the Helios spacecraft. The model reproduces to a good extent the main observed features, in particular the dependence of the correlation coefficient on location (close to or far from the current sheet) and on the fluctuation scale. The results show that large scale inhomogeneities, in particular, that of specific entropy, are important ingredients in the dynamics of the MHD turbulence in slow speed streams.

Journal Article↗

PubMed1999

Dynamic entropy as a measure of caging and persistent particle motion in supercooled liquids.

The length-scale dependence of the dynamic entropy is studied in a molecular dynamics simulation of a binary Lennard-Jones liquid above the mode-coupling critical temperature T(c). A number of methods exist for estimating the entropy of dynamical systems, and we utilize an approximation based on calculating the mean first-passage time (MFPT) for particle displacement because of its tractability and its accessibility in real and simulation measurements. The MFPT dynamic entropy S(epsilon) is defined as equal to the inverse of the average first-passage time for a particle to exit a sphere of radius epsilon. This measure of the degree of chaotic motion allows us to identify characteristic time and space scales and to quantify the increasingly correlated particle motion and intermittency occurring in supercooled liquids. In particular, we identify a "cage" size defining the scale at which the particles are transiently localized, and we observe persistent particle motion at intermediate length scales beyond the scale where caging occurs. Furthermore, we find that the dynamic entropy at the scale of one interparticle spacing extrapolates to zero as the mode-coupling temperature T(c) is approached.

Journal Article↗

PubMed2000

Correlation between the kolmogorov-sinai entropy and the self-diffusion coefficient in simple liquids

Molecular dynamics simulations were performed for soft- and hard-sphere systems, for number densities ranging from 0.5 to 1.0, and the Kolmogorov-Sinai entropy (KS entropy) and self-diffusion coefficients were calculated. It is found that the KS entropy, when expressed in terms of average collision frequency, is uniquely related to the self-diffusion coefficient by a simple scaling law. The dependence of the KS entropy on average collision frequency and number density was also explored. Numerical results show that the scaling laws proposed by Dzugutov, and by Beijeren, Dorfman, Posch, and Dellago, can be applied to both soft- and hard-sphere systems by changing to more generalized forms.

Journal Article↗

PubMed2000

Density fluctuations and entropy

A functional for the entropy that is asymptotically correct both in the high- and low-density limits is proposed. The new form is S=S((id))+S((ln))+S((r))+S((c)), where the term S((c)) depends on the p-body density fluctuations alpha(p) and has the form S((c))/k= ln 2-1+ summation operator(infinity)(p=2) (ln 2)(p)/p! alpha(p)-[exp(alpha(2)-1)-alpha(2)]+Sinsertion mark. Sinsertion mark renormalizes the ring approximation S((r)). This result is obtained by analyzing the functional dependence of the most general expression of the entropy. Two main results for S((c)) are proved: (i) In the thermodynamic limit it is only a functional of the one-body distribution function and (ii) by summing to infinite order the leading contributions in the density a numerical expression for the entropy [Eq. (33)] with a renormalized ring approximation is obtained. The relation of these results to the incompressible approximation for the entropy is discussed and preliminary numerical results on hard spheres are presented.

Journal Article↗

PubMed2002

Dynamics and configurational entropy in the Lewis-Wahnström model for supercooled orthoterphenyl.

We study thermodynamic and dynamic properties of a rigid model of the fragile glass-forming liquid orthoterphenyl. This model, introduced by Lewis and Wahnström in 1993, collapses each phenyl ring to a single interaction site; the intermolecular site-site interactions are described by the Lennard-Jones potential whose parameters have been selected to reproduce some bulk properties of the orthoterphenyl molecule. A system of N=343 molecules is considered in a wide range of densities and temperatures, reaching simulation times up to 1 micros. Such long trajectories allow us to equilibrate the system at temperatures below the mode coupling temperature T(c) at which the diffusion constant reaches values of order 10(-10) cm(2)/s and thereby to sample in a significant way the potential energy landscape in the entire temperature range. Working within the inherent structures thermodynamic formalism, we present results for the temperature and density dependence of the number, depth and shape of the basins of the potential energy surface. We evaluate the total entropy of the system by thermodynamic integration from the ideal-noninteracting-gas state and the vibrational entropy approximating the basin free energy with the free energy of 6N-3 harmonic oscillators. We evaluate the configurational part of the entropy as a difference between these two contributions. We study the connection between thermodynamical and dynamical properties of the system. We confirm that the temperature dependence of the configurational entropy and of the diffusion constant, as well as the inverse of the characteristic structural relaxation time, are strongly connected in supercooled states; we demonstrate that this connection is well represented by the Adam-Gibbs relation, stating a linear relation between logD and the quantity 1/TS(c). This relation is found to hold both above and below the critical temperature T(c)-as previously found in the case of silica-supporting the hypothesis that a connection exists between the number of basins and the connectivity properties of the potential energy surface.

Journal Article↗

PubMed2002

Single-particle entropy in (1+2)-body random matrix ensembles.

Random matrix ensembles defined by a mean-field one-body plus a chaos generating random two-body interaction (called embedded Gaussian orthogonal ensembles of (1+2)-body interactions[EGOE(1+2)]) predict for the entropy defined by the occupation numbers of single-particle states, in the chaotic domain, an essentially one parameter Gaussian form for their energy dependence. Numerical embedded ensemble calculations are compared with the theory. In addition, it is shown that the single-particle entropy, thermodynamic entropy defined by the state density and information entropy defined by wave functions in the mean-field basis for EGOE(1+2) describe the results known for interacting Fermi systems such as those obtained from nuclear shell model.

Journal Article↗

PubMed2003

Family of additive entropy functions out of thermodynamic limit.

We derive a one-parametric family of entropy functions that respect the additivity condition, and which describe effects of finiteness of statistical systems, in particular, distribution functions with long tails. This one-parametric family is different from the Tsallis entropies, and is a convex combination of the Boltzmann-Gibbs-Shannon entropy and the entropy function proposed by Burg. An example of how longer tails are described within the present approach is worked out for the canonical ensemble. We also discuss a possible origin of a hidden statistical dependence, and give explicit recipes on how to construct corresponding generalizations of the master equation.

Journal Article↗

PubMed2003

Direct excess entropy calculation for a Lennard-Jones fluid by the integral equation method.

The present work is devoted to the calculation of excess entropy by means of correlation functions, in the framework of integral equation theory. The tangent linear method is set up to get exact thermodynamic derivatives of the pair-correlation function, essential for the calculation of the physical quantities, as well as to carry out an optimization process for the achievement of thermodynamic consistency. The two-body entropy of the Lennard-Jones fluid is in very good agreement with the available molecular dynamics results, attesting the high degree of accuracy of the integral equation scheme. It is shown that an accurate prediction of the excess entropy and the resulting residual multiparticle entropy relies on the correct evaluation of the excess chemical potential, especially at high density. Two independent routes to calculate the latter are compared, and the consequences are discussed.

Journal Article↗

PubMed2004

Entropy in the natural time domain.

A surrogate data analysis is presented, which is based on the fluctuations of the "entropy" S defined in the natural time domain [Phys. Rev. E 68, 031106 (2003)]]. This entropy is not a static one such as, for example, the Shannon entropy. The analysis is applied to three types of time series, i.e., seismic electric signals, "artificial" noises, and electrocardiograms, and it "recognizes" the non-Markovianity in all these signals. Furthermore, it differentiates the electrocardiograms of healthy humans from those of the sudden cardiac death ones. If deltaS and deltaSshuf denote the standard deviation when calculating the entropy by means of a time window sweeping through the original data and the "shuffled" (randomized) data, respectively, it seems that the ratio deltaSshuf /deltaS plays a key role. The physical meaning of deltaSshuf is investigated.

Journal Article↗

PubMed2005

Thermodynamic equilibrium and its stability for microcanonical systems described by the Sharma-Taneja-Mittal entropy.

It is generally assumed that the thermodynamic stability of equilibrium states is reflected by the concavity of entropy. We inquire, in the microcanonical picture, about the validity of this statement for systems described by the two-parametric entropy S(kappa,r) of Sharma, Taneja, and Mittal. We analyze the "composability" rule for two statistically independent systems A and B, described by the entropy S(kappa,r) with the same set of the deformation parameters. It is shown that, in spite of the concavity of the entropy, the "composability" rule modifies the thermodynamic stability conditions of the equilibrium state. Depending on the values assumed by the deformation parameters, when the relation S(kappa,r)(A union B) > S(kappa,r)(A) + S(kappa,r)(B) holds (superadditive systems), the concavity condition does imply thermodynamics stability. Otherwise, when the relation S(kappa,r)(A union B) < S(kappa,r)(A) + S(kappa,r)(B) holds (subadditive systems), the concavity condition does not imply thermodynamical stability of the equilibrium state.

Journal Article↗

PubMed2005

Nonlocal impedances and the Casimir entropy at low temperatures.

The problem with the temperature dependence of the Casimir force is investigated. Specifically, the entropy behavior in the low temperature limit, which caused debates in the literature, is analyzed. It is stressed that the behavior of the relaxation frequency in the T-->0 limit does not play a physical role since the anomalous skin effect dominates in this range. In contrast with the previous works, where the approximate Leontovich impedance was used for analysis of nonlocal effects, we give description of the problem in terms of exact nonlocal impedances. It is found that the Casimir entropy is going to zero at T-->0 only in the case when s polarization does not contribute to the classical part of the Casimir force. However, the entropy approaching zero from the negative side that, in our opinion, cannot be considered as thermodynamically satisfactory. The resolution of the negative entropy problem proposed in the literature is analyzed and it is shown that it cannot be considered as complete. The crisis with the thermal Casimir effect is stressed.

Journal Article↗

PubMed2005

Detecting nonlinearity in structural systems using the transfer entropy.

The transfer entropy was recently proposed as a means of exploring coupling in dynamical systems. Transfer entropy is an information theoretic that quantifies the degree to which one dynamical process affects the transition probabilities (dynamics) of another. Here we demonstrate how this metric may be utilized to detect the presence of nonlinearity in a system. Using the method of surrogate data, the transfer entropy computed at various lag times are compared to values computed from linearized surrogates. The transfer entropy is shown to be a more sensitive indicator of nonlinearity than is the mutual information for both simulated and experimental data. This technique is particularly applicable to the field of structural health monitoring, where damage is often equated with the presence of a nonlinearity in an otherwise linear system.

Journal Article↗

PubMed2006

Nonlinear model dynamics for closed-system, constrained, maximal-entropy-generation relaxation by energy redistribution.

We discuss a nonlinear model for relaxation by energy redistribution within an isolated, closed system composed of noninteracting identical particles with energy levels with . The time-dependent occupation probabilities are assumed to obey the nonlinear rate equations where and are functionals of the 's that maintain invariant the mean energy and the normalization condition . The entropy is a nondecreasing function of time until the initially nonzero occupation probabilities reach a Boltzmann-like canonical distribution over the occupied energy eigenstates. Initially zero occupation probabilities, instead, remain zero at all times. The solutions of the rate equations are unique and well defined for arbitrary initial conditions and for all times. The existence and uniqueness both forward and backward in time allows the reconstruction of the ancestral or primordial lowest entropy state. By casting the rate equations in terms not of the 's but of their positive square roots , they unfold from the assumption that time evolution is at all times along the local direction of steepest entropy ascent or, equivalently, of maximal entropy generation. These rate equations have the same mathematical structure and basic features as the nonlinear dynamical equation proposed in a series of papers ending with G. P. Beretta, Found. Phys. 17, 365 (1987) and recently rediscovered by S. Gheorghiu-Svirschevski [Phys. Rev. A 63, 022105 (2001);63, 054102 (2001)]. Numerical results illustrate the features of the dynamics and the differences from the rate equations recently considered for the same problem by M. Lemanska and Z. Jaeger [Physica D 170, 72 (2002)]. We also interpret the functionals and as nonequilibrium generalizations of the thermodynamic-equilibrium Massieu characteristic function and inverse temperature, respectively.

Journal Article↗

PubMed2006

Nonconcave entropies from generalized canonical ensembles.

It is well known that the entropy of the microcanonical ensemble cannot be calculated as the Legendre transform of the canonical free energy when the entropy is nonconcave. To circumvent this problem, a generalization of the canonical ensemble that allows for the calculation of nonconcave entropies was recently proposed. Here, we study the mean-field Curie-Weiss-Potts spin model and show, by direct calculations, that the nonconcave entropy of this model can be obtained by using a specific instance of the generalized canonical ensemble known as the Gaussian ensemble.

Journal Article↗

PubMed2000

Entropy production, fractals, and relaxation to equilibrium

The theory of entropy production in nonequilibrium, Hamiltonian systems, previously described for steady states using partitions of phase space, is here extended to time dependent systems relaxing to equilibrium. We illustrate the main ideas by using a simple multibaker model, with some nonequilibrium initial state, and we study its progress toward equilibrium. The central results are (i) the entropy production is governed by an underlying, exponentially decaying fractal structure in phase space, (ii) the rate of entropy production is largely independent of the scale of resolution used in the partitions, and (iii) the rate of entropy production is in agreement with the predictions of nonequilibrium thermodynamics.

Journal Article↗

PubMed2002

Configurational entropy of network-forming materials.

We present a computationally efficient method to calculate the configurational entropy of network-forming materials. The method requires only the atomic coordinates and bonds of a single well-relaxed configuration. This is in contrast to the multiple simulations that are required for other methods to determine entropy, such as thermodynamic integration. We use our method to obtain the configurational entropy of well-relaxed networks of amorphous silicon and vitreous silica. For these materials we find configurational entropies of 0.93k(B) and 0.88k(B) per silicon atom, respectively.

Journal Article↗

PubMed2003

Holographic entropy bound and local quantum field theory.

I show how the holographic entropy bound can be derived from elementary flat-spacetime quantum field theory when the total energy of Fock states is constrained gravitationally. This energy constraint makes the Fock space dimension (whose logarithm is the maximum entropy) finite for both bosons and fermions. Despite the elementary nature of my analysis, it results in an upper limit on entropy in remarkable agreement with the holographic bound, and also provides a microscopic deviation of a more general entropy bound recently introduced by Gour.

Journal Article↗