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At least 1,153 records · Page 64Linked to original sources
PubMed2003

Granular entropy: explicit calculations for planar assemblies.

This paper proposes a new volume function for calculation of the entropy of planar granular assemblies. This function is extracted from the antisymmetric part of a new geometric tensor and is rigorously additive when summed over grains. It leads to the identification of a conveniently small phase space. The utility of the volume function is demonstrated on several case studies, for which we calculate explicitly the mean volume and the volume fluctuations.

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PubMed2003

Absence of magnetic order in Yb3Ga5O12: relation between phase transition and entropy in geometrically frustrated materials.

From muon spin relaxation spectroscopy experiments, we show that the sharp peak (lambda-type anomaly) detected by specific heat measurements at 54 mK for the ytterbium gallium garnet compound, Yb3Ga5O12, does not correspond to the onset of a magnetic phase transition, but to a pronounced building up of dynamical magnetic pair correlations. Beside the lambda anomaly, a broad hump is observed at higher temperature in the specific heat of this garnet and other geometrically frustrated compounds. Comparing with other frustrated magnetic systems we infer that a ground state with long-range order is reached only when at least 1/4-1/3 of the magnetic entropy is released at the lambda transition.

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PubMed2004

Boltzmann entropy for dense fluids not in local equilibrium.

Using computer simulations, we investigate the time evolution of the (Boltzmann) entropy of a dense fluid not in local equilibrium. The macrovariables M describing the system are the (empirical) particle density f=[f(x,v)] and the total energy E. We find that S(f(t),E) is a monotone increasing in time even when its kinetic part is decreasing. We argue that for isolated Hamiltonian systems monotonicity of S(M(t))=S(M(X(t))) should hold generally for "typical" (the overwhelming majority of) initial microstates (phase points) X0 belonging to the initial macrostate M0, satisfying M(X0)=M(0). This is a consequence of Liouville's theorem when M(t) evolves according to an autonomous deterministic law.

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PubMed2004

Climbing the entropy barrier: driving the single- towards the multichannel Kondo effect by a weak coulomb blockade of the leads.

We study a model proposed recently in which a small quantum dot is coupled symmetrically to several large quantum dots characterized by a charging energy E(c). Even if E(c) is much smaller than the Kondo temperature T(K), the long-ranged interactions destabilize the single-channel Kondo effect and induce a flow towards a multichannel Kondo fixed point associated with a rise of the impurity entropy with decreasing temperature. Such an "uphill flow" implies a negative impurity specific heat, in contrast with all systems with local interactions. An exact solution found for a large number of channels allows us to capture this physics and to predict transport properties.

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PubMed2004

Entropy production of Brownian macromolecules with inertia.

We investigate the nonequilibrium steady-state thermodynamics of single Brownian macromolecules with inertia under feedback control in an isothermal ambient fluid. With the control being represented by a velocity-dependent external force, we find such an open system can have a negative entropy production rate, and we develop a mesoscopic theory consistent with the second law. We propose an equilibrium condition and define a class of external force, which includes the transverse Lorentz force, leading to equilibrium.

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PubMed2004

Entanglement entropy of random quantum critical points in one dimension.

For quantum critical spin chains without disorder, it is known that the entanglement of a segment of N>>1 spins with the remainder is logarithmic in N with a prefactor fixed by the central charge of the associated conformal field theory. We show that for a class of strongly random quantum spin chains, the same logarithmic scaling holds for mean entanglement at criticality and defines a critical entropy equivalent to central charge in the pure case. This effective central charge is obtained for Heisenberg, XX, and quantum Ising chains using an analytic real-space renormalization-group approach believed to be asymptotically exact. For these random chains, the effective universal central charge is characteristic of a universality class and is consistent with a c-theorem.

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PubMed2005

Entropy, entanglement, and area: analytical results for harmonic lattice systems.

We revisit the question of the relation between entanglement, entropy, and area for harmonic lattice Hamiltonians corresponding to discrete versions of real free Klein-Gordon fields. For the ground state of the d-dimensional cubic harmonic lattice we establish a strict relationship between the surface area of a distinguished hypercube and the degree of entanglement between the hypercube and the rest of the lattice analytically, without resorting to numerical means. We outline extensions of these results to longer ranged interactions, finite temperatures, and for classical correlations in classical harmonic lattice systems. These findings further suggest that the tools of quantum information science may help in establishing results in quantum field theory that were previously less accessible.

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PubMed2005

Physical bounds to the entropy-depolarization relation in random light scattering.

We present a theoretical study of multimode scattering of light by optically random media, using the Mueller-Stokes formalism which permits us to encode all the polarization properties of the scattering medium in a real 4 x 4 matrix. From this matrix two relevant parameters can be extracted: the depolarizing power D(M) and the polarization entropy E(M) of the scattering medium. By studying the relation between E(M) and D(M), we find that all scattering media must satisfy some universal constraints. These constraints apply to both classical and quantum scattering processes. The results obtained here may be especially relevant for quantum communication applications, where depolarization is synonymous with decoherence.

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PubMed2005

Microscopic entropy of the black ring.

A surprising new seven-parameter supersymmetric black ring solution of five-dimensional supergravity has recently been discovered. In this paper, M theory is used to give an exact microscopic accounting of its entropy.

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PubMed2005

Shear-thickening and entropy-driven reentrance.

We discuss a generic mechanism for shear thickening analogous to entropy-driven phase reentrance. We implement it in the context of nonrelaxational mean-field glassy systems: although very simple, the microscopic models we study present a dynamical phase diagram with second- and first-order stirring-induced jamming transitions leading to intermittency, metastability, and phase coexistence as seen in some experiments. The jammed state is fragile with respect to change in the stirring direction. Our approach provides a direct derivation of a mode-coupling theory of shear thickening.

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PubMed2006

The alpha-gamma transition of cerium is entropy driven.

We emphasize, on the basis of experimental data and theoretical calculations, that the entropic stabilization of the gamma phase is the main driving force of the alpha-gamma transition of cerium in a wide temperature range below the critical point. Using a formulation of the total energy as a functional of the local density and of the f-orbital local Green's functions, we perform dynamical mean-field theory calculations within a new implementation based on the multiple linear muffin tin orbital (LMTO) method, which allows us to include semicore states. Our results are consistent with the experimental energy differences and with the qualitative picture of an entropy-driven transition, while also confirming the appearance of a stabilization energy of the alpha phase as the quasiparticle Kondo resonance develops.

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PubMed2006

Topological entanglement entropy.

We formulate a universal characterization of the many-particle quantum entanglement in the ground state of a topologically ordered two-dimensional medium with a mass gap. We consider a disk in the plane, with a smooth boundary of length L, large compared to the correlation length. In the ground state, by tracing out all degrees of freedom in the exterior of the disk, we obtain a marginal density operator rho for the degrees of freedom in the interior. The von Neumann entropy of rho, a measure of the entanglement of the interior and exterior variables, has the form S(rho) = alphaL - gamma + ..., where the ellipsis represents terms that vanish in the limit L --> infinity. We show that - gamma is a universal constant characterizing a global feature of the entanglement in the ground state. Using topological quantum field theory methods, we derive a formula for gamma in terms of properties of the superselection sectors of the medium.

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PubMed2006

Entropy and Galilean invariance of lattice Boltzmann theories.

A theory of lattice Boltzmann (LB) models for hydrodynamic simulation is developed upon a novel relation between entropy construction and roots of Hermite polynomials. A systematic procedure is described for constructing numerically stable and complete Galilean invariant LB models. The stability of the new LB models is illustrated with a shock tube simulation.

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PubMed2001

A fast Newton method for entropy maximization in statistical phase estimation.

A fast Newton method is presented for solving the entropy maximization problem in the Bayesian statistical approach to phase estimation. The method requires only O(n log n) instead of standard O(n3) floating point operations per iteration, while converging in the same rate as the standard Newton method. The method is described and related computational issues are discussed. Numerical results on simple test cases are also presented to demonstrate the behavior of the method.

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PubMed2002

Structure, odd lines and topological entropy of disorder of amorphous silicon.

A continuous random network model of amorphous silicon, subject to periodic boundary conditions, is partitioned into cells bounded by irreducible rings. An algorithm has been developed to find the cells and the rings that bound them. A thread can be imagined to pass through odd rings (rings containing an odd number of atoms) without passing through even rings. Such a thread is an algorithmic realization of an odd line, which is the only topological defect in glass or amorphous condensed matter. The topological entropy of disorder associated with these odd lines is found to be approximately 80% of the value for an ideal tetrahedrally bonded random network of atoms for which the rings that bound the cells are statistically independent.

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PubMed2002

The generalized F constraint in the maximum-entropy method--a study on simulated data.

One of the classical problems in the application of the maximum-entropy method (MEM) to electron-density reconstructions is the uneven distribution of the normalized residuals of the structure factors [|F(obs)(H)|-|F(calc)(H)|]/sigma(H) of the resulting electron density. This distribution does not correspond to the expected Gaussian distribution and it leads to erroneous features in the MEM reconstructions. It is shown that the classical chi(2) constraint is only one of many possible constraints, and that it is too weak to restrict the resulting distribution to the expected Gaussian shape. It is proposed that constraints should be used that are based on the higher-order central moments of the distribution of the structure-factor residuals. In this work, the influence of different constraints on the quality of the MEM reconstruction is investigated. It is proposed that the use of a combined constraint on more than one central moment simultaneously would lead to again improved results. Oxalic acid dihydrate was chosen as model structure, from which several data sets with different resolutions and different levels of noise were calculated and subsequently used in the MEM. The results clearly show that the use of different constraints leads to significantly improved results.

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PubMed2003

The maximum-entropy method in superspace.

One of the applications of the maximum-entropy method (MEM) in crystallography is the reconstruction of the electron density from phased structure factors. Here the application of the MEM to incommensurately modulated crystals and incommensurate composite crystals is considered. The MEM is computed directly in superspace, where the electron density in the (3+d)-dimensional unit cell (d > 0) is determined from the scattering data of aperiodic crystals. Periodic crystals (d = 0) are treated as a special case of the general formalism. The use of symmetry in the MEM is discussed and an efficient algorithm is proposed for handling crystal symmetry. The method has been implemented into a computer program BayMEM and applications are presented to the electron density of the periodic crystal NaV(2)O(5) and the electron density of the incommensurate composite crystal (LaS)(1.14)NbS(2). The MEM in superspace is shown to provide a model-independent estimate of the shapes of the modulation functions of incommensurate crystals. The discrete character of the electron density is found to be the major source of error, limiting the accuracy of the reconstructed modulation functions to approximately 10% of the sizes of the pixels. MaxEnt optimization using the Cambridge and Sakata-Sato algorithms are compared. The Cambridge algorithm is found to perform better than the Sakata-Sato algorithm, being faster, always reaching convergence, and leading to more reliable density maps. Nevertheless, the Sakata-Sato algorithm leads to similar density maps, even in cases where it does not reach complete convergence.

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PubMed2005

The prior-derived F constraints in the maximum-entropy method.

The method of the prior-derived F constraints (PDC) enhances the quality of reconstructions of electron densities from X-ray diffraction data by the maximum-entropy method (MEM). The method concentrates on artifacts arising due to inaccurate extrapolation of non-measured data by the MEM. While these artifacts are unavoidable, when a flat prior is used, they can be effectively suppressed, if the prior information about the structure is known in the form of a procrystal prior electron density. The missing, usually high-angle, structure factors can be effectively substituted by the structure factors derived from the procrystal prior. This approach eliminates the occurrence of spurious peaks in the difference electron densities in the vicinity of the atomic positions. The method is illustrated with a simple one-dimensional example. Its use is then demonstrated on simulated data of oxalic acid dihydrate and on experimental data of sodium nitrite.

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