Order Entropy Research Articles

Interfacial Entropy Profile in the One-loop Approximation

The near-critical interfacial entropy profile is calculated in the one-loop approximation of renormalized field theory. The shape of the profile is broadened by fluctuations and goes beyond the mean-field coupling between the entropy and the order parameter. The excess interfacial entropy and heat capacity are calculated by using the entropy profile. The interface creates corrections to the heat capacity and entropy of order χ/L, where $\xi$ is the correlation length, and L is a characteristic length of the system. These results are discussed in relation to finite-size scaling, surface critical phenomena, and the results of experiments and simulations.

Second sound resonances in superfluid 3He–4He mixtures

The resonances occurring during oscillations of quartz tuning forks in superfluid helium and its mixtures are studied. Quartz tuning forks are used to study various properties of helium, and also as a precision temperature sensor. Experimental observations of resonance phenomena were carried out in a wide range of temperatures and pressures, but the results of observations have not yet been exhaustively described theoretically. In this work we consider the pressure, entropy, and velocities oscillations in order to determine the conditions under which oscillations of a solid wall excite the first and second sound in superfluid helium and sound in supercritical helium, and to calculate the contributions of these processes to the formation of resonances during oscillations of closed tuning forks. In particular, the experimentally observed excitation of standing waves of pressure and entropy oscillations by an oscillating closed tuning fork, the appearance and properties of resonances depending on the temperature and pressure of helium are considered.

Structure-induced order – disorder transformation in Cd – Na liquid alloys

Abstract The origins of the S-shaped entropy of mixing and order – disorder transformation in Cd –Na liquid alloys have been investigated within a first-principle approach of a pseudo-potential perturbation scheme with the Gibbs–Bogoliubov variation technique.We find that the deepening of the structure part of the entropy around the stoichiometric composition (c Na ≈ 0.33) is responsible for the S-shaped entropy and suggests the existence of short-range order in the liquid state. The role of the local-field correction function, G(q), of conduction electrons on the entropy of mixing is examined. The impact of G(q) on partial structure factors is more visible towards low q (q → 0) than at higher q.

High order entropy stable and positivity-preserving discontinuous Galerkin method for the nonlocal electron heat transport model

The nonlocal electron heat transport model in laser heated plasmas plays a crucial role in inertial confinement fusion (ICF), and it is important to solve it numerically in an accurate and robust way. In this paper, we first develop an one-dimensional high-order entropy stable discontinuous Galerkin method for the nonlocal electron heat transport model. We further design our DG scheme to have the positivity-preserving property by using the scaling positivity-preserving limiter, which is shown, by a computer-aided proof, to have no extra time step constraint than that required by L2 stability. Next, we extend our one-dimensional scheme to two-dimensions on rectangular meshes and tensor product polynomial spaces. Numerical examples are given to verify the high-order accuracy and positivity-preserving properties of our scheme. By comparing the local and nonlocal electron heat transport models, we also observe more physical phenomena such as the flux reduction and the preheat effect from the nonlocal model.

Explicit solvation thermodynamics in ionic solution: extending grid inhomogeneous solvation theory to solvation free energy of salt\u2013water mixtures

Hydration thermodynamics play a fundamental role in fields ranging from the pharmaceutical industry to environmental research. Numerous methods exist to predict solvation thermodynamics of compounds ranging from small molecules to large biomolecules. Arguably the most precise methods are those based on molecular dynamics (MD) simulations in explicit solvent. One theory that has seen increased use is inhomogeneous solvation theory (IST). However, while many applications require accurate description of salt–water mixtures, no implementation of IST is currently able to estimate solvation properties involving more than one solvent species. Here, we present an extension to grid inhomogeneous solvation theory (GIST) that can take salt contributions into account. At the example of carbazole in 1 M NaCl solution, we compute the solvation energy as well as first and second order entropies. While the effect of the first order ion entropy is small, both the water–water and water–ion entropies contribute strongly. We show that the water–ion entropies are efficiently approximated using the Kirkwood superposition approximation. However, this approach cannot be applied to the water–water entropy. Furthermore, we test the quantitative validity of our method by computing salting-out coefficients and comparing them to experimental data. We find a good correlation to experimental salting-out constants, while the absolute values are overpredicted due to the approximate second order entropy. Since ions are frequently used in MD, either to neutralize the system or as a part of the investigated process, our method greatly extends the applicability of GIST. The use-cases range from biopharmaceuticals, where many assays require high salt concentrations, to environmental research, where solubility in sea water is important to model the fate of organic substances.

Annealing metallic glasses above Tg in order to accelerate the relaxation process in molecular dynamics simulations

To bridge the gap between nano- and micro-seconds molecular dynamics simulations and milliseconds timescale phenomena in metallic glasses remains an area of active research. Through systematic control of the annealing parameters, we have been able to simulate metallic glasses resembling structures usually obtained by quenching at cooling rates used in the melt spinning process. Density, local order, and local entropy calculations predict metallic glasses with structures prepared at cooling rates orders of magnitude lower than those typically realized in atomistic modeling. Hence, annealing above Tg is an alternative to melt quenching simulations and offers the prospect of modeling well relaxed glassy structures that were not achievable before in molecular dynamics simulations.

Entropic order parameters in weakly coupled gauge theories

The entropic order parameters measure in a universal geometric way the statistics of non-local operators responsible for generalized symmetries. In this article, we compute entropic order parameters in weakly coupled gauge theories. To perform this computation, the natural route of evaluating expectation values of physical (smeared) non-local operators is prevented by known difficulties in constructing suitable smeared Wilson loops. We circumvent this problem by studying the smeared non-local class operators in the enlarged non-gauge invariant Hilbert space. This provides a generic approach for smeared operators in gauge theories and explicit formulas at weak coupling. In this approach, the Wilson and ’t Hooft loops are labeled by the full weight and co-weight lattices respectively. We study generic Lie groups and discuss couplings with matter fields. Smeared magnetic operators, as opposed to the usual infinitely thin ones, have expectation values that approach one at weak coupling. The corresponding entropic order parameter saturates to its maximum topological value, except for an exponentially small correction, which we compute. On the other hand, smeared ’t Hooft loops and their entropic disorder parameter are exponentially small. We verify that both behaviors match the certainty relation for the relative entropies. In particular, we find upper and lower bounds (that differ by a factor of 2) for the exact coefficient of the linear perimeter law for thin loops at weak coupling. This coefficient is unphysical/non-universal for line operators. We end with some comments regarding the RG flows of entropic parameters through perturbative beta functions.

Proof of the universal density of charged states in QFT

We prove a recent conjecture by Harlow and Ooguri concerning a universal formula for the charged density of states in QFT at high energies for global symmetries associated with finite groups. An equivalent statement, based on the entropic order parameter associated with charged operators in the thermofield double state, was proven in a previous article by Casini, Huerta, Pontello, and the present author. Here we describe how the statement about the entropic order parameter arises, and how it gets transformed into the universal density of states. The use of the certainty principle, relating the entropic order and disorder parameters, is crucial for the proof. We remark that although the immediate application of this result concerns charged states, the origin and physics of such density can be understood by looking at the vacuum sector only. We also describe how these arguments lie at the origin of the so-called entropy equipartition in these type of systems, and how they generalize to QFT’s on non-compact manifolds.

Modelling the occurrence and spatial distribution of screwworm species in Northern Pakistan.

We use binomial kriging to model the spatial distribution of myiasis by three species namely Chrysomya bezziana, Wohlfahrtia magnifica and Lucilia cuprina in the livestock of Khyber Pakhtunkhwa, Pakistan. Traditional species distribution models are usually based on assumption of independence of observations. Species data often come in presence-only form for which background points are generated based on some covariates using statistical and machine learning techniques such as MaxEnt. We assume a symmetric binomial distribution based on the principle of maximum entropy in order to decide the number of pseudo-absences. Our results showed that the spatial models fitted very well and prediction distributions were estimated with excellent accuracy. Moreover kriging maps were more accurate as most of the non-spatial variation has been picked up by external drift with higher values of the sensitivity focusing partial AUC for all the three species. Land-use-land-cover was a common factor significantly affecting spatial distribution of all the three species suggesting that for established species anthropogenic factors such as land use become a strong determinant of their spatial distribution. Our results also revealed that for invading species like W. magnifica elevation acts as a barrier to species dispersal and therefore is more limiting to distribution. Furthermore the higher overall prediction accuracy demonstrated that our models performed well in predicting the distributions of the three species, which would lead to better understanding and management of the larval infestation.

Nonergodic dynamics of the one-dimensional Bose-Hubbard model with a trapping potential

We investigate nonergodic behavior of the one-dimensional Bose-Hubbard model, which emerges in the unitary quantum dynamics starting with initial-state $|\ensuremath{\psi}(0)\ensuremath{\rangle}=|\ensuremath{\cdots}2020\ensuremath{\cdots}\ensuremath{\rangle}$ in the presence of a trapping potential. We compute the level spacing statistic, the time evolution of the number imbalance between the odd and the even sites, and the entanglement entropy in order to show that the system exhibits nonergodicity in a strongly interacting regime. The trapping potential enhances nonergodicity even when the trapping potential is weak compared to the hopping energy. We derive the effective spin-1/2 $XXZ$ Hamiltonian for the strongly interacting regimes by using a perturbation method. On the basis of the effective Hamiltonian, we show that the trapping potential is effectively strengthened by the on-site interaction, leading to the enhancement of the nonergodic behavior. We also calculate the real-time dynamics under the effective Hamiltonian and find that the entanglement entropy grows logarithmically in time.

Entropy of pair condensed bosons at finite temperatures in optical lattices with bond-charge interaction

This work contains a quantum rotor analysis of the bond-charge interaction extended Bose–Hubbard model. Adding extended interactions to bosonic optical lattice models reveals new phases of matter to observe and study. Many-body correlations further widen the scope of possible discoveries. The U(1) quantum rotor method used in this work preserves three-body correlations, uncovering the presence of pair condensation in this model. Phase transitions between the normal state and both single and pair bosonic condensation are examined through the lens of the thermal behavior of the two superfluid order parameters and entropy, as well as the impact of bond-charge interaction on the properties of Bose–Einstein condensation in the presence of many-body correlations. At low temperatures and high densities, bond-charge interaction reinforces coherence, improving the critical temperature of Bose–Einstein condensation. It also exhibits a temperature-independent dissipative influence on the system.

A novel method for classification of multi-class motor imagery tasks based on feature fusion

Motor imagery based brain computer interface (MI-BCI) has the advantage of strong independence that can rely on the spontaneous brain activity of the user to operate external devices. However, MI-BCI still has the problem of poor control effect, which requires more effective feature extraction algorithms and classification methods to extract distinctly separable features from electroencephalogram (EEG) signals. This paper proposes a novel framework based on Bispectrum, Entropy and common spatial pattern (BECSP). Here we use three methods of bispectrum in higher order spectra, entropy and CSP to extract MI-EEG signal features, and then select the most contributing features through tree-based feature selection algorithm. By comparing the classification results of SVM, Random Forest, Naive Bayes, LDA, KNN, Xgboost and Adaboost, we finally decide to use the SVM algorithm based on RBF kernel function which obtained the best result among them for classification. The proposed method is applied to the BCI competition IV data set 2a and BCI competition III data set IVa. On data set 2a, the highest accuracy on the evaluation data set reaches 85%. The experiment on data set IVa can also achieve good results. Compared with other algorithms that use the same data set, the performance of our algorithm has also been improved.

Qubit-efficient entanglement spectroscopy using qubit resets

One strategy to fit larger problems on NISQ devices is to exploit a tradeoff between circuit width and circuit depth. Unfortunately, this tradeoff still limits the size of tractable problems since the increased depth is often not realizable before noise dominates. Here, we develop qubit-efficient quantum algorithms for entanglement spectroscopy which avoid this tradeoff. In particular, we develop algorithms for computing the trace of the n-th power of the density operator of a quantum system, Tr(ρn), (related to the Rényi entropy of order n) that use fewer qubits than any previous efficient algorithm while achieving similar performance in the presence of noise, thus enabling spectroscopy of larger quantum systems on NISQ devices. Our algorithms, which require a number of qubits independent of n, are variants of previous algorithms with width proportional to n, an asymptotic difference. The crucial ingredient in these new algorithms is the ability to measure and reinitialize subsets of qubits in the course of the computation, allowing us to reuse qubits and increase the circuit depth without suffering the usual noisy consequences. We also introduce the notion of effective circuit depth as a generalization of standard circuit depth suitable for circuits with qubit resets. This tool helps explain the noise-resilience of our qubit-efficient algorithms and should aid in designing future algorithms. We perform numerical simulations to compare our algorithms to the original variants and show they perform similarly when subjected to noise. Additionally, we experimentally implement one of our qubit-efficient algorithms on the Honeywell System Model H0, estimating Tr(ρn) for larger n than possible with previous algorithms.

Replenishment Model with Entropic Order Quantity for Deteriorating Items under Inflation

The purpose of the current paper is to determine an optimal order quantity so as to minimize the total cost of the inventory system of a business enterprise. The model is developed for deteriorating items with stock and selling price dependent demand under inflation without permitting shortage. Optimal solution is achieved by cost minimization strategy considering replenishment cost, purchase cost, holding cost and deterioration cost with a special approach to entropy cost for bulk size purchasing units. The effectiveness of the proposed model has been avowed through empirical investigation. Sensitivity analysis has been accomplished to deduce managerial insights. Findings suggest that an increased inflationary effect results in increment in the system total cost. The paper can be extended by allowing shortage. The model can be utilized in the business firms dealing with bulk purchasing units of electric equipments, semiconductor devices, photographic films and many more.

Service Evaluation of Electric Vehicle Charging Station: An Application of Improved Matter-Element Extension Method

To reach the targets of carbon peaking and neutral, China needs to develop electric vehicles extensively. The service level of electric vehicle charging stations (EVCSs) notably decides the promotion of electric vehicles. Given the current unsatisfactory service performance of charging stations, this paper established a multi-criteria evaluation system for the electric vehicle charging stations. We conducted a survey in 2020 by distributing questionnaires to experts and charging station users. Firstly, from the perspective of the subject and object of charging station service, the evaluation system of 16 indexes for operator service and customer service was constructed. Secondly, the order relation method and entropy weight method were used to determine the subjective weight and objective weight of the indexes, respectively. It was concluded that charging price and parking cost have a great influence on the service evaluation. Then, a comprehensive evaluation model based on the improved matter-element extension method was established to appraise three charging stations in Beijing. Sensitive analysis and comparative analysis were implemented to further demonstrate the effectiveness and stability of the proposed evaluation method. Finally, the evaluation results provided implications for improving the charging service performance.

HEMP: High-order entropy minimization for neural network compression

We formulate the entropy of a quantized artificial neural network as a differentiable function that can be plugged as a regularization term into the cost function minimized by gradient descent. Our formulation scales efficiently beyond the first order and is agnostic of the quantization scheme. The network can then be trained to minimize the entropy of the quantized parameters, so that they can be optimally compressed via entropy coding. We experiment with our entropy formulation at quantizing and compressing well-known network architectures over multiple datasets. Our approach compares favorably over similar methods, enjoying the benefits of higher order entropy estimate, showing flexibility towards non-uniform quantization (we use Lloyd-max quantization), scalability towards any entropy order to be minimized and efficiency in terms of compression. We show that HEMP is able to work in synergy with other approaches aiming at pruning or quantizing the model itself, delivering significant benefits in terms of storage size compressibility without harming the model’s performance.

Entanglement wedge cross section inequalities from replicated geometries

We generalize the constructions for the multipartite reflected entropy in order to construct spacetimes capable of representing multipartite entanglement wedge cross sections of differing party number as Ryu-Takayanagi surfaces on a single replicated geometry. We devise a general algorithm for such constructions for arbitrary party number and demonstrate how such methods can be used to derive novel inequalities constraining mulipartite entanglement wedge cross sections.

Testing homogeneity of the galaxy distribution in the SDSS using Renyi entropy

We analyze a set of volume limited sample of galaxies from the SDSS to study the issue of cosmic homogeneity. We use the Renyi entropy of different order to probe the inhomogeneties present in the galaxy distributions. We also calculate the Renyi diveregence to quantify the deviations of the galaxy distribution from a homogeneous Poisson distribution on different length scales. We separately carry out the analysis using the overlapping spheres and the independent voxels. Our analysis suggests that the scale of homogeneity is underestimated in the smaller galaxy samples due to the suppression of inhomogeneities by the overlapping of the measuring speheres. We find that an analysis with the independent voxels and/or use of a significantly larger galaxy sample can help to circumvent or mitigate this problem. Combining the results from these analyses, we find that the galaxy distribution in the SDSS becomes homogeneous on a length scale beyond 140 h -1 Mpc.

A Two Parameter Odd Exponentiated Skew-T Distribution With J-Shaped Hazard Rate Function

A new generalization of the skew-t distribution was proposed. The two-parameter lifetime model called the odd exponentiated skew-t distribution has the ability of fitting skewed, long and heavy tailed datasets. It is considered to be more flexible than the skew-t distribution as it contains it as a special case. Some basic properties of the distribution such as the order statistics, entropy, asymptotic behaviour, moment, incomplete moment, characteristic function and quantile function were derived. The odd exponentiated skew-t distribution parameter estimates were derived using the maximum likelihood estimation method and simulation studies performed to evaluate the finite sample performance of these parameter estimates showed that the parameter estimates were consistent and approached the arbitrary selected parameter values as the sample size is increased. The application using a real-life dataset indicated that the new distribution outperformed the other competing distributions. The hazard rate shape of the odd exponentiated skew-t distribution was found to be increasing and J-shaped which was also reflected in the application result.

Thermodynamics of real polymer solutions in the new Rényi and Tsallis formalism

The generalized non-ideality factor of systems (GNF) was introduced into the Renyi and Tsallis information entropy equations, and new expressions were obtained for information and thermodynamic entropies with a fractional moment of the order entropy gS and thermodynamic gth nonideality factors. Equations in formalism of Renyi and Tsallis: The equations describe self-organized structures of essentially non-equilibrium systems and can be used in studying the topological and conformational properties of solutions of high-molecular compounds. GNF: where is are relative average characteristics (pi are statistical probabilities) of opposite processes. Factor g varies in the range 0 ≤ g ≤ 2 and depends on which of the competitive processes prevails. An algorithm for calculating the thermodynamic functions of the state of the system under study is presented. The equations are intended for calculating the thermodynamic functions of objects of fractal nature, including real solutions of synthetic and natural highmolecular compounds of plant and animal origin (hyper branched structures, dendrimers, lignins, biological systems, dendrites, systems of internal organs, blood vessels, etc.).