Thermodynamic Derivation of Scaling at the Liquid–Vapor Critical Point

With the use of thermodynamics and general equilibrium conditions only, we study the entropy of a fluid in the vicinity of the critical point of the liquid–vapor phase transition. By assuming a general form for the coexistence curve in the vicinity of the critical point, we show that the functional dependence of the entropy as a function of energy and particle densities necessarily obeys the scaling form hypothesized by Widom. Our analysis allows for a discussion of the properties of the corresponding scaling function, with the interesting prediction that the critical isotherm has the same functional dependence, between the energy and the number of particles densities, as the coexistence curve. In addition to the derivation of the expected equalities of the critical exponents, the conditions that lead to scaling also imply that, while the specific heat at constant volume can diverge at the critical point, the isothermal compressibility must do so.     

Condensation and Crystal Nucleation in a Lattice Gas with a Realistic Phase Diagram

We reconsider model II of Orban et al. (J. Chem. Phys. 1968, 49, 1778–1783), a two-dimensional lattice-gas system featuring a crystalline phase and two distinct fluid phases (liquid and vapor). In this system, a particle prevents other particles from occupying sites up to third neighbors on the square lattice, while attracting (with decreasing strength) particles sitting at fourth- or fifth-neighbor sites. To make the model more realistic, we assume a finite repulsion at third-neighbor distance, with the result that a second crystalline phase appears at higher pressures. However, the similarity with real-world substances is only partial: Upon closer inspection, the alleged liquid–vapor transition turns out to be a continuous (albeit sharp) crossover, even near the putative triple point. Closer to the standard picture is instead the freezing transition, as we show by computing the free-energy barrier relative to crystal nucleation from the “liquid”.     

Inequalities for Jensen–Sharma–Mittal and Jeffreys–Sharma–Mittal Type f–Divergences

In this paper, we introduce new divergences called Jensen–Sharma–Mittal and Jeffreys–Sharma–Mittal in relation to convex functions. Some theorems, which give the lower and upper bounds for two new introduced divergences, are provided. The obtained results imply some new inequalities corresponding to known divergences. Some examples, which show that these are the generalizations of Rényi, Tsallis, and Kullback–Leibler types of divergences, are provided in order to show a few applications of new divergences.     

Improvement of Bobrovsky–Mayor–Wolf–Zakai Bound

This paper presents a difference-type lower bound for the Bayes risk as a difference-type extension of the Borovkov–Sakhanenko bound. The resulting bound asymptotically improves the Bobrovsky–Mayor–Wolf–Zakai bound which is difference-type extension of the Van Trees bound. Some examples are also given.     

A Quantitative Comparison between Shannon and Tsallis–Havrda–Charvat Entropies Applied to Cancer Outcome Prediction

In this paper, we propose to quantitatively compare loss functions based on parameterized Tsallis–Havrda–Charvat entropy and classical Shannon entropy for the training of a deep network in the case of small datasets which are usually encountered in medical applications. Shannon cross-entropy is widely used as a loss function for most neural networks applied to the segmentation, classification and detection of images. Shannon entropy is a particular case of Tsallis–Havrda–Charvat entropy. In this work, we compare these two entropies through a medical application for predicting recurrence in patients with head–neck and lung cancers after treatment. Based on both CT images and patient information, a multitask deep neural network is proposed to perform a recurrence prediction task using cross-entropy as a loss function and an image reconstruction task. Tsallis–Havrda–Charvat cross-entropy is a parameterized cross-entropy with the parameter α . Shannon entropy is a particular case of Tsallis–Havrda–Charvat entropy for α=1 . The influence of this parameter on the final prediction results is studied. In this paper, the experiments are conducted on two datasets including in total 580 patients, of whom 434 suffered from head–neck cancers and 146 from lung cancers. The results show that Tsallis–Havrda–Charvat entropy can achieve better performance in terms of prediction accuracy with some values of α .     

Statistical Physics Approach to Liquid Crystals: Dynamics of Mobile Potts Model Leading to Smectic Phase,Phase Transition by Wang–Landau Method

We study the nature of the smectic–isotropic phase transition using a mobile 6-state Potts model. Each Potts state represents a molecular orientation. We show that with the choice of an appropriate microscopic Hamiltonian describing the interaction between individual molecules modeled by a mobile 6-state Potts spins, we observe the smectic phase dynamically formed when we cool the molecules from the isotropic phase to low temperatures (T). In order to elucidate the order of the transition and the low-T properties, we use the high-performance Wang–Landau flat energy-histogram technique. We show that the smectic phase goes to the liquid (isotropic) phase by melting/evaporating layer by layer starting from the film surface with increasing T. At a higher T, the whole remaining layers become orientationally disordered. The melting of each layer is characterized by a peak of the specific heat. Such a succession of partial transitions cannot be seen by the Metropolis algorithm. The successive layer meltings/evaporations at low T are found to have a first-order character by examining the energy histogram. These results are in agreement with experiments performed on some smectic liquid crystals.     

Thermal–Statistical Odd–Even Fermions’ Staggering Effect and the Order–Disorder Disjunction

We review thermal–statistical considerations on the odd–even staggering effect (OES) in fermions. There is a well known OES in nuclear binding energies at zero temperature. We discuss here a thermal OES (finite temperatures) that establishes links with the order–disorder disjunction. The present thermal considerations cannot be found in the nuclear literature.     

Two-Step Measurement of Water–Energy–Food Symbiotic Coordination and Identification of Key Influencing Factors in the Yangtze River Basin

With the intensification of people’s production and life behaviors, the systemic risks of water, energy and food in the Yangtze River Basin have become increasingly prominent, which has become a bottleneck for sustainable development of social, economic and ecological in the basin. Therefore, studying the symbiotic coordination between water, energy and food is of great significance to promoting regional sustainable development. First, from the perspective of water–energy–food symbiosis, with the water–energy–food ecosystem conceptual model as the nexus, the two-step measurement model of the symbiotic index and the symbiotic level index is used to study the water–energy–food symbiosis of the Yangtze River. Then, we use the BP-DEMATEL-GTCW model to identify the key influencing factors that affect the symbiotic security of the water–energy–food ecosystem. In this research, it is found that the average value of the symbiotic degree of the water–energy–food ecosystem of the 11 provinces or municipalities in the Yangtze River Basin only reached the risk grade. It can also be seen from the identification results of key influencing factors that energy microsystem-related indicators have a greater impact on the symbiotic development of the entire WEF ecosystem. Therefore, special attention needs to be paid to increasing energy sources and reducing expenditure. Relevant departments need to effectively develop primary energy production and expand energy-saving investment through multiple channels to expand energy self-sufficiency and ultimately promote the coordinated and effective development of water, energy and food in the Yangtze River Basin.     

Quantum Weak Invariants: Dynamical Evolution of Fluctuations and Correlations

Weak invariants are time-dependent observables with conserved expectation values. Their fluctuations, however, do not remain constant in time. On the assumption that time evolution of the state of an open quantum system is given in terms of a completely positive map, the fluctuations monotonically grow even if the map is not unital, in contrast to the fact that monotonic increases of both the von Neumann entropy and Rényi entropy require the map to be unital. In this way, the weak invariants describe temporal asymmetry in a manner different from the entropies. A formula is presented for time evolution of the covariance matrix associated with the weak invariants in cases where the system density matrix obeys the Gorini–Kossakowski–Lindblad–Sudarshan equation.     

Information–Theoretic Aspects of Location Parameter Estimation under Skew–Normal Settings

In several applications, the assumption of normality is often violated in data with some level of skewness, so skewness affects the mean’s estimation. The class of skew–normal distributions is considered, given their flexibility for modeling data with asymmetry parameter. In this paper, we considered two location parameter (μ) estimation methods in the skew–normal setting, where the coefficient of variation and the skewness parameter are known. Specifically, the least square estimator (LSE) and the best unbiased estimator (BUE) for μ are considered. The properties for BUE (which dominates LSE) using classic theorems of information theory are explored, which provides a way to measure the uncertainty of location parameter estimations. Specifically, inequalities based on convexity property enable obtaining lower and upper bounds for differential entropy and Fisher information. Some simulations illustrate the behavior of differential entropy and Fisher information bounds.     

Discrete Versions of Jensen–Fisher,Fisher and Bayes–Fisher Information Measures of Finite Mixture Distributions

In this work, we first consider the discrete version of Fisher information measure and then propose Jensen–Fisher information, to develop some associated results. Next, we consider Fisher information and Bayes–Fisher information measures for mixing parameter vector of a finite mixture probability mass function and establish some results. We provide some connections between these measures with some known informational measures such as chi-square divergence, Shannon entropy, Kullback–Leibler, Jeffreys and Jensen–Shannon divergences.     

Entropy Estimation Using a Linguistic Zipf–Mandelbrot–Li Model for Natural Sequences

Entropy estimation faces numerous challenges when applied to various real-world problems. Our interest is in divergence and entropy estimation algorithms which are capable of rapid estimation for natural sequence data such as human and synthetic languages. This typically requires a large amount of data; however, we propose a new approach which is based on a new rank-based analytic Zipf–Mandelbrot–Li probabilistic model. Unlike previous approaches, which do not consider the nature of the probability distribution in relation to language; here, we introduce a novel analytic Zipfian model which includes linguistic constraints. This provides more accurate distributions for natural sequences such as natural or synthetic emergent languages. Results are given which indicates the performance of the proposed ZML model. We derive an entropy estimation method which incorporates the linguistic constraint-based Zipf–Mandelbrot–Li into a new non-equiprobable coincidence counting algorithm which is shown to be effective for tasks such as entropy rate estimation with limited data.     

Effect of Shear Flow on Nanoparticles Migration near Liquid Interfaces

The effect of shear flow on spherical nanoparticles (NPs) migration near a liquid–liquid interface is studied by numerical simulation. We have implemented a compact model through which we use the diffuse interface method for modeling the two fluids and the molecular dynamics method for the simulation of the motion of NPs. Two different cases regarding the state of the two fluids when introducing the NPs are investigated. First, we introduce the NPs randomly into the medium of the two immiscible liquids that are already separated, and the interface is formed between them. For this case, it is shown that before applying any shear flow, 30% of NPs are driven to the interface under the effect of the drag force resulting from the composition gradient between the two fluids at the interface. However, this percentage is increased to reach 66% under the effect of shear defined by a Péclet number Pe = 0.316. In this study, different shear rates are investigated in addition to different shearing times, and we show that both factors have a crucial effect regarding the migration of the NPs toward the interfacial region. In particular, a small shear rate applied for a long time will have approximately the same effect as a greater shear rate applied for a shorter time. In the second studied case, we introduce the NPs into the mixture of two fluids that are already mixed and before phase separation so that the NPs are introduced into the homogenous medium of the two fluids. For this case, we show that in the absence of shear, almost all NPs migrate to the interface during phase separation, whereas shearing has a negative result, mainly because it affects the phase separation.     

Exergy Analysis of a Bio-System: Soil–Plant Interaction

This paper explains a thorough exergy analysis of the most important reactions in soil–plant interactions. Soil, which is a prime mover of gases, metals, structural crystals, and electrolytes, constantly resembles an electric field of charge and discharge. The second law of thermodynamics reflects the deterioration of resources through the destruction of exergy. In this study, we developed a new method to assess the exergy of soil and plant formation processes. Depending on the types of soil, one may assess the efficiency and degradation of resources by incorporating or using biomass storage. According to the results of this study, during different processes from the mineralization process to nutrient uptake by the plant, about 62.5% of the input exergy will be destroyed because of the soil solution reactions. Most of the exergy destruction occurs in the biota–atmosphere subsystem, especially in the photosynthesis reaction, due to its low efficiency (about 15%). Humus and protonation reactions, with 14% and 13% exergy destruction, respectively, are the most exergy destroying reactions. Respiratory, weathering, and reverse weathering reactions account for the lowest percentage of exergy destruction and less than one percent of total exergy destruction in the soil system. The total exergy yield of the soil system is estimated at about 37.45%.     

Arbitrary-Order Finite-Time Corrections for the Kramers–Moyal Operator

With the aim of improving the reconstruction of stochastic evolution equations from empirical time-series data, we derive a full representation of the generator of the Kramers–Moyal operator via a power-series expansion of the exponential operator. This expansion is necessary for deriving the different terms in a stochastic differential equation. With the full representation of this operator, we are able to separate finite-time corrections of the power-series expansion of arbitrary order into terms with and without derivatives of the Kramers–Moyal coefficients. We arrive at a closed-form solution expressed through conditional moments, which can be extracted directly from time-series data with a finite sampling intervals. We provide all finite-time correction terms for parametric and non-parametric estimation of the Kramers–Moyal coefficients for discontinuous processes which can be easily implemented—employing Bell polynomials—in time-series analyses of stochastic processes. With exemplary cases of insufficiently sampled diffusion and jump-diffusion processes, we demonstrate the advantages of our arbitrary-order finite-time corrections and their impact in distinguishing diffusion and jump-diffusion processes strictly from time-series data.     

Analysis on International Competitiveness of Service Trade in the Guangdong–Hong Kong–Macao Greater Bay Area Based on Using the Entropy and Gray Correlation Methods

Based on the analysis and measurement of the overall situation, import and export structure and international competitiveness of the various sectors of service trade in the Guangdong–Hong Kong–Macao Greater Bay Area, with the help of MATLAB and Gray System Modeling software, the synergy degree model was established to quantitatively analyze the synergy level of service trade in the Greater Bay Area with the help of grey correlation analysis method and entropy weight method. The results show that the overall development trend of service trade in the Guangdong–Hong Kong–Macao Greater Bay Area is good. The service trade industries in different regions are highly complementary and have a high degree of correlation. The potential for the coordinated development of internal service trade is excellent, and the overall situation of service trade in the Greater Bay Area is in a stage of transition from a moderate level of synergy to a high level of synergy. The Greater Bay Area can achieve industrial synergy by accelerating industrial integration and green transformation, establishing a coordinated development mechanism, sharing market platform, strengthening personnel security, and further enhancing the international competitiveness of service trade. The established model better reflects the current coordination of service trade in the Guangdong–Hong Kong–Macao Greater Bay Area and has good applicability. In the future, more economic, technological, geographic, and policy data and information can be comprehensively used to study the spatial pattern, evolution rules, and mechanisms of coordinated development in the broader area.     

Effects of pressure on flame propagation in a premixture containing fine fuel droplets

Combustion experiments on fuel droplet–vapor–air mixtures have been performed with a rapid expansion apparatus which generates monodispersed droplet clouds with narrow diameter distribution using the condensation method. The effects of fine fuel droplets on flame propagation were investigated for ethanol droplet–vapor–air mixtures at various pressures from 0.2 to 1.0 MPa. A stagnant fuel droplet–vapor–air mixture, generated in a rapid expansion chamber, was ignited at the center of the chamber using an ignition wire. Spherical flame propagation under constant-pressure conditions was observed with a high-speed video camera and flame speed was measured. Total equivalence ratio, and the ratio of liquid fuel mass to total fuel mass, was varied from 0.6 to 1.4 and from zero to 56%, respectively. The mean droplet diameter of fuel droplet–vapor–air mixtures was set at 8.5 and 11 μm. It was found that the flame speed of droplet–vapor–air mixtures less than 0.9 in the total equivalence ratio exceeds that of premixed gases of the same total equivalence ratio at all pressures. The flame speed of fuel droplet–vapor–air mixtures decreases as the pressure increases in all total equivalence ratios. At large ratios of liquid fuel mass to total fuel mass, the normalized flame speed (the flame speed of droplet–vapor–air mixtures divided by the flame speed of the premixed gas with the same total equivalence ratio), increases with the increase in pressure for fuel-lean mixtures, and it decreases for fuel-rich mixtures. The outcome is reversed at small ratios of liquid fuel mass to total fuel mass; the normalized flame speed decreases with the increase in pressure for fuel-lean mixtures, and increases for fuel-rich mixtures. The results suggest that the increase in pressure promotes droplet evaporation in the preheat zone.     

Reliability Analysis of the New Exponential Inverted Topp–Leone Distribution with Applications

The inverted Topp–Leone distribution is a new, appealing model for reliability analysis. In this paper, a new distribution, named new exponential inverted Topp–Leone (NEITL) is presented, which adds an extra shape parameter to the inverted Topp–Leone distribution. The graphical representations of its density, survival, and hazard rate functions are provided. The following properties are explored: quantile function, mixture representation, entropies, moments, and stress–strength reliability. We plotted the skewness and kurtosis measures of the proposed model based on the quantiles. Three different estimation procedures are suggested to estimate the distribution parameters, reliability, and hazard rate functions, along with their confidence intervals. Additionally, stress–strength reliability estimators for the NEITL model were obtained. To illustrate the findings of the paper, two real datasets on engineering and medical fields have been analyzed.     

Multi-Particle Interference in an Electronic Mach–Zehnder Interferometer

The development of dynamic single-electron sources has made it possible to observe and manipulate the quantum properties of individual charge carriers in mesoscopic circuits. Here, we investigate multi-particle effects in an electronic Mach–Zehnder interferometer driven by a series of voltage pulses. To this end, we employ a Floquet scattering formalism to evaluate the interference current and the visibility in the outputs of the interferometer. An injected multi-particle state can be described by its first-order correlation function, which we decompose into a sum of elementary correlation functions that each represent a single particle. Each particle in the pulse contributes independently to the interference current, while the visibility (given by the maximal interference current) exhibits a Fraunhofer-like diffraction pattern caused by the multi-particle interference between different particles in the pulse. For a sequence of multi-particle pulses, the visibility resembles the diffraction pattern from a grid, with the role of the grid and the spacing between the slits being played by the pulses and the time delay between them. Our findings may be observed in future experiments by injecting multi-particle pulses into a Mach–Zehnder interferometer.     

Null Wave Front and Ryu–Takayanagi Surface

The Ryu–Takayanagi formula provides the entanglement entropy of quantum field theory as an area of the minimal surface (Ryu–Takayanagi surface) in a corresponding gravity theory. There are some attempts to understand the formula as a flow rather than as a surface. In this paper, we consider null rays emitted from the AdS boundary and construct a flow representing the causal holographic information. We present a sufficient and necessary condition that the causal information surface coincides with Ryu–Takayanagi surface. In particular, we show that, in spherical symmetric static spacetimes with a negative cosmological constant, wave fronts of null geodesics from a point on the AdS boundary become extremal surfaces and therefore they can be regarded as the Ryu–Takayanagi surfaces. In addition, from the viewpoint of flow, we propose a wave optical formula to calculate the causal holographic information.