Entropy Space Research Articles

Emission of Energy from Schwarzschild Black Holes

Induced energy is obtained in the exterior Schwarzschild space-time through one loop quantum correction to scalar field. It is discussed that energy tunnels quantum mechanically through the event horizon contrary to results of classical mechanics that black-holes cannot emit anything. Three decades ago, Hawking had obtained this type of result through the process of creation of scalar particles. Evaporation of energy from black-hole results into loss of mass. It is found that a primordial black-hole of mass 1015 gm might have evaporated by now. Moreover, luminosity of hole also increases gradually. It is suggested that decreasing area of the event horizon due to loss of mass causes increase in entropy in the outer space of the hole. It is speculated that black-holes in the extreme past might be glowing bright now and will leave behind dark naked next singularities.

Nonlinear Phase Mixing and Phase-Space Cascade of Entropy in Gyrokinetic Plasma Turbulence

Electrostatic turbulence in weakly collisional, magnetized plasma can be interpreted as a cascade of entropy in phase space, which is proposed as a universal mechanism for dissipation of energy in magnetized plasma turbulence. When the nonlinear decorrelation time at the scale of the thermal Larmor radius is shorter than the collision time, a broad spectrum of fluctuations at sub-Larmor scales is numerically found in velocity and position space, with theoretically predicted scalings. The results are important because they identify what is probably a universal Kolmogorov-like regime for kinetic turbulence; and because any physical process that produces fluctuations of the gyrophase-independent part of the distribution function may, via the entropy cascade, result in turbulent heating at a rate that increases with the fluctuation amplitude, but is independent of the collision frequency.

Emission of Energy from Schwarzschild Black Holes

Induced energy is obtained in the exterior Schwarzschild space-time through one loop quantum correction to scalar field. It is discussed that energy tunnels quantum mechanically through the event horizon contrary to results of classical mechanics that black-holes cannot emit anything. Three decades ago, Hawking had obtained this type of result through the process of creation of scalar particles. Evaporation of energy from black-hole results into loss of mass. It is found that a primordial black-hole of mass 1015 gm might have evaporated by now. Moreover, luminosity of hole also increases gradually. It is suggested that decreasing area of the event horizon due to loss of mass causes increase in entropy in the outer space of the hole. It is speculated that black-holes in the extreme past might be glowing bright now and will leave behind dark naked next singularities.

A Green–Naghdi approach to finite anisotropic rate-independent and rate-dependent thermo-plasticity in logarithmic Lagrangean strain–entropy space

The paper presents a phenomenological model of rate-independent and rate-dependent thermo-plasticity in the logarithmic Lagrangean strain–entropy space at finite strains. The formulation and computational implementation are based on an additive decomposition of the strain measure into an elastic and plastic part as proposed by Green and Naghdi. A rate-independent and rate-dependent constitutive model in the logarithmic Lagrangean strain–entropy space is developed for the modelling of isotropic elastic and anisotropic plastic material behaviour. Furthermore, the notion of a plastic metric as proposed by Miehe, an isotropic hardening variable and the notion of a plastic entropy as proposed by Simo and Miehe dominate the internal variable description. The model keeps the classical general return-mapping scheme in the implicit integration algorithm of the internal variables of associative thermo-plasticity. The resulting coupled thermo-mechanical problem is solved staggeredly via an isentropic phase for the deformation and an iso-geometrical phase for the thermal field. Representative numerical simulations demonstrate the performance of the proposed model.

Application of the scale entropy diffusion model to describe a liquid atomization process

Whatever the situation, liquid atomization processes show a continuous evolution of the liquid system shape. However, such a system is a multiscale object, i.e., its shape cannot be fully described by a single geometrical parameter. The present work makes use of the scale entropy function to describe this multiscale object. This function is found similar to the scale distribution previously introduced to take into account the droplet shape in liquid spray characterization. Time-averaged scale entropy is locally measured on images of atomizing liquid flows issuing from a low injection pressure single-hole triple-disk nozzle. The advantage in using this nozzle is that the atomization process and the spray are inscribed in a plane and can be fully described by 2-D visualizations. The measurements are performed from the nozzle exit down to the spray region. The operating conditions consider varying injection pressure and liquid physical properties. The temporal evolution of the scale entropy is described by the scale entropy diffusion model. Initially developed in turbulence, this model introduces new parameters such as the scale diffusivity and the local scale entropy flux sink, which characterize the diffusion dynamic of the scale entropy in the scale space. For the first time, these parameters are measured and strong correlations between them and the working conditions are evidenced. Furthermore, new parameters are introduced such as a scale viscosity and the total scale entropy flux lose. These results demonstrate the relevance of the scale entropy diffusion model to describe a liquid atomization process. This application is the first of its kind.

Theoretic-information entropies analysis of nanostructures: ab initio study of PAMAM precursors and dendrimers G0 to G3

Information theory in conjugated and in Hilbert spaces is employed to analyse the growing behaviour of nanostructures. Shannon entropies in position and momentum spaces require costly and time-consuming computations as the size of the molecules increases in contrast with information entropies in Hilbert space, which are shown to be highly advantageous for analysing large molecules. In this work, ab initio electronic structure calculations at the Hartree–Fock (HF), MP2 and B3LYP levels of theory were performed to analyse the initial steps towards growing nanostructured molecules of polyamidoamine (PAMAM) dendrimers, starting from the monomers, dimers, trimers and tetramers up to generations G0 (with 84 atoms), G1 (228 atoms), G2 (516 atoms) and G3 (1092 atoms). This was achieved by using selected physical descriptors such as the radius of gyration, the asphericity factor, the moments of inertia, the dipole moments, the total energies and chemical reactivity indices such as the hardness, softness and the electrophilicity index at the HF/3-21G* level of theory. For the chemical indices, higher level calculations at the B3LYP/6-311++ G** and MP2/6-311+ G* levels were also performed in order to account for the effects of electron correlation. Information-theoretic measures of the Shannon type in conjugated space were employed to characterise the G0–PAMAM precursors and G0. Hilbert space entropies of the Shannon and Kullback type were employed to provide theoretic-information evidence of the validity of the dense-core model of PAMAM precursors and dendrimers G0 to G3.

Higher dimensional black hole radiation and a generalized uncertainty principle

Based on the generalized uncertainty relation, the corrected Beckenstein–Hawking black hole entropy in the higher dimensional space–times is calculated. Using the corrected entropy, the black hole radiation is obtained in the tunneling formalism.

Phase space localization of antisymmetric functions

Upper and lower bounds are written down for the minimum information entropy in phase space of an antisymmetric wave function in any number of dimensions. Similar bounds are given when the wave function is restricted to belong to any of the proper subspaces of the Fourier transform operator.

Optical properties of PuO2 and α-Pu2O3 studied by empirical potentials simulation

The BMH empirical potentials of Pu-O bond in α-Pu2O3 are fitted by GULP program. The structure and optical properties of PuO2 and α-Pu2O3 crystal are calculated by molecular statics and molecular dynamics using BMH and shell potentials. The result shows that their simulated space groups, cell parameters, densities and entropies are approximately the samc as the data in published papers, with relative error less than 1.2%. Furthermore, their static （high frequency） dielectric constant tensor, IR dielectric function spectra and crystal lattice vibration peaks are all calculated. Part of the results are validated by experiment of spectroscopic ellipsometry, and the indirect energy bandgap of PuO2 is found to be 2.1 eV.

Generalized Poisson-Fermi formalism for investigating size correlation effects with multiple ions

We establish a generalized Poisson-Fermi formalism to compute the electrostatic potential next to charged surfaces in the presence of multiple ion species with different sizes. A generalized Fermi-like ion distribution is deduced from the excess free energy, after expansion of the functional entropy of free space in which the ions have all the same size. The ion distribution is expressed in terms of the bulk volume fractions of each ion species rather than their bulk concentrations so as to account for the excluded volumes. We present size correlations effects such as underscreening and ion stratification, which have not been investigated before with such a simple theory. The change of dielectric properties across the space, arising from the finite spatial occupancy of ions, can be solved self-consistently through the Bruggeman model. The generalized Poisson-Fermi formalism is anticipated to be useful for interpreting electrophoretic mobility measurements and for computing the electrostatic potential over the surface of biomolecules in ionic solutions.

Quantum Phase Transition in a Far-from-Equilibrium Steady State of anXYSpin Chain

Using quantization in the Fock space of operators, we compute the nonequilibrium steady state in an open Heisenberg XY spin 1/2 chain of a finite but large size coupled to Markovian baths at its ends. Numerical and theoretical evidence is given for a far-from-equilibrium quantum phase transition with the spontaneous emergence of long-range order in spin-spin correlation functions, characterized by a transition from saturation to linear growth with the size of the entanglement entropy in operator space.

A Novel Method for Prediction of Protein Domain Using Distance-Based Maximal Entropy

Detecting the boundaries of protein domains is an important and challenging task in both experimental and computational structural biology. In this paper, a promising method for detecting the domain structure of a protein from sequence information alone is presented. The method is based on analyzing multiple sequence alignments derived from a database search. Multiple measures are defined to quantify the domain information content of each position along the sequence. Then they are combined into a single predictor using support vector machine. What is more important, the domain detection is first taken as an imbalanced data learning problem. A novel undersampling method is proposed on distance-based maximal entropy in the feature space of Support Vector Machine (SVM). The overall precision is about 80%. Simulation results demonstrate that the method can help not only in predicting the complete 3D structure of a protein but also in the machine learning system on general imbalanced datasets.

Metastable black Saturns

Black Saturns have multiple horizons and so offer a testing ground for the ideas of black hole thermodynamics. In this note, we numerically scan for phases that are in equilibrium by extremizing total entropy in the 2-dimensional moduli space of stationary, singly rotating black Saturns with fixed total mass and angular momentum. On top of the known T_H=T_R, Omega_H=Omega_R configurations, we find phases that do not balance the temperature and angular velocity of the ring and the hole. But these (and most of the balanced Saturns) go away when we demand that the system is metastable, by imposing that the Hessian of the entropy is negative definite. Metastablity occurs when the dimensionless total angular momentum lies in a narrow window 0.92457<j<0.92463 of the thin ring branch. This is consistent with the expected range of classical stability of black Saturns and therefore may imply that thermal stability is tied to classical stability, in analogy with Gubser-Mitra in the translationally-invariant case. We also comment on the possibility of constructing plasma configurations that are dual to black Saturns in AdS.

Complexity of thermal states in quantum spin chains

We study the quantum correlations and complexity of simulation, characterized by quantum mutual information and entanglement entropy in operator space, respectively, for thermal states in critical, noncritical, and quantum chaotic spin chains. A simple general relation between the two quantities is proposed. We show that in all cases mutual information and entanglement entropy saturate with system size, whereas as a function of the inverse temperature, we find logarithmic divergences for critical cases and uniform bounds in noncritical cases. A simple efficient quasiexact method for computation of arbitrary entropy-related quantities in thermalized $XY$ spin chains is proposed.

Entropy function and higher derivative corrections to entropies in (anti-)de Sitter space

We first briefly discuss the relation between black hole thermodynamics and the entropy function formalism. We find that an equation which governs the relationship between Sen's entropy function and black hole entropy, can quickly give higher order corrections to entropy of pure (anti-) de Sitter space without knowing the corrected metric. We also show that near horizon geometry and the entropy function extremization is no longer required for pure (anti-)de Sitter space. The entropy of (anti-)de Sitter space and Schwarzschild-(anti-) de Sitter black holes together with Gauss-Bonnet terms, $R^2$ terms and $R^4$ terms are calculated as concrete examples.

Quantum and Ecosystem Entropies

Ecosystems and quantum gases share a number of superficial similarities including enormous numbers of interacting elements and the fundamental role of energy in such interactions. A theory for the synthesis of data and prediction of new phenomena is well established in quantum statistical mechanics. The premise of this paper is that the reason a comparable unifying theory has not emerged in ecology is that a proper role for entropy has yet to be assigned. To this end, a phase space entropy model of ecosystems is developed. Specification of an ecosystem phase space cell size based on microbial mass, length, and time scales gives an ecosystem uncertainty parameter only about three orders of magnitude larger than Planck’s constant. Ecosystem equilibria is specified by conservation of biomass and total metabolic energy, along with the principle of maximum entropy at equilibria. Both Bose - Einstein and Fermi - Dirac equilibrium conditions arise in ecosystems applications. The paper concludes with a discussion of some broader aspects of an ecosystem phase space.

Entanglement entropy, conformal invariance and extrinsic geometry

We use the conformal invariance and the holographic correspondence to fully specify the dependence of entanglement entropy on the extrinsic geometry of the 2d surface Σ that separates two subsystems of quantum strongly coupled N=4SU(N) superconformal gauge theory. We extend this result and calculate entanglement entropy of a generic 4d conformal field theory. As a byproduct, we obtain a closed-form expression for the entanglement entropy in flat space–time when Σ is sphere S2 and when Σ is two-dimensional cylinder. The contribution of the type A conformal anomaly to entanglement entropy is always determined by topology of surface Σ while the dependence of the entropy on the extrinsic geometry of Σ is due to the type B conformal anomaly.

Dynamic entropy-compressed sequences and full-text indexes

We give new solutions to the Searchable Partial Sums with Indels problem. Given a sequence of n k -bit numbers, we present a structure taking kn + o ( kn ) bits of space, able of performing operations sum , search , insert , and delete , all in O (log n ) worst-case time, for any k = O (log n ). This extends previous results by Hon et al. [2003c] achieving the same space and O (log n /log log n ) time complexities for the queries, yet offering complexities for insert and delete that are amortized and worse than ours, and supported only for k = O (1). Our result matches an existing lower bound for large values of k . We also give new solutions to the Dynamic Sequence problem. Given a sequence of n symbols in the range [1,σ] with binary zero-order entropy H 0 , we present a dynamic data structure that requires nH 0 + o ( n log σ) bits of space, which is able of performing rank and select , as well as inserting and deleting symbols at arbitrary positions, in O (log n log σ) time. Our result is the first entropy-bound dynamic data structure for rank and select over general sequences. In the case σ = 2, where both previous problems coincide, we improve the dynamic solution of Hon et al. [2003c] in that we compress the sequence. The only previous result with entropy-bound space for dynamic binary sequences is by Blandford and Blelloch [2004], which has the same complexities as our structure, but does not achieve constant 1 multiplying the entropy term in the space complexity. Finally, we present a new dynamic compressed full-text self-index, for a collection of texts over an alphabet of size σ, of overall length n and h th order empirical entropy H h . The index requires nH h + o ( n log σ) bits of space, for any h ≤ α log sigma n and constant 0 &lt; α &lt; 1. It can count the number of occurrences of a pattern of length m in time O ( m log n log σ). Each such occurrence can be reported in O (log 2 n log log n ) time, and displaying a context of length ℓ from a text takes time O (log n (ℓ log σ + log n log log n )). Insertion/deletion of a text to/from the collection takes O (log n log σ) time per symbol. This significantly improves the space of a previous result by Chan et al. [2004] in exchange for a slight time complexity penalty. We achieve at the same time the first dynamic index requiring essentially nH h bits of space, and the first construction of a compressed full-text self-index within that working space. Previous results achieve at best O ( nH h space with constants larger than 1 [Ferragina and Manzini 2000; Arroyuelo and Navarro 2005] and higher time complexities. An important result we prove in this paper is that the wavelet tree of the Burrows-Wheeler transform of a text, if compressed with a technique that achieves zero-order compression locally (e.g., Raman et al. [2002]), automatically achieves h th order entropy space for any h . This unforeseen relation is essential for the results of the previous paragraph, but it also derives into significant simplifications on many existing static compressed full-text self-indexes that build on wavelet trees.

Phantom and non-phantom dark energy: The cosmological relevance of non-locally corrected gravity

In this Letter we have investigated the cosmological dynamics of non-locally corrected gravity involving a function of the inverse d'Alembertian of the Ricci scalar, f(□−1R). Casting the dynamical equations into local form, we derive the fixed points of the dynamics and demonstrate the existence and stability of a one parameter family of dark energy solutions for a simple choice, f(□−1R)∼exp(α□−1R). The effective EoS parameter is given by, weff=(α−1)/(3α−1) and the stability of the solutions is guaranteed provided that 1/3<α<2/3. For 1/3<α<1/2 and 1/2<α<2/3, the underlying system exhibits phantom and non-phantom behavior respectively; the de Sitter solution corresponds to α=1/2. For a wide range of initial conditions, the system mimics dust like behavior before reaching the stable fixed point. The late time phantom phase is achieved without involving negative kinetic energy fields. A brief discussion on the entropy of de Sitter space in non-local model is included.

Phase space and black-hole entropy of higher genus horizons in loop quantum gravity

In the context of loop quantum gravity, we construct the phase space of isolated horizons with genus greater than 0. Within the loop quantum gravity framework, these horizons are described by genus g surfaces with N punctures and the dimension of the corresponding phase space is calculated including the genus cycles as degrees of freedom. From this, the black-hole entropy can be calculated by counting the microstates which correspond to a black hole of fixed area. We find that the leading term agrees with the A/4 law and that the sub-leading contribution is modified by the genus cycles.