Entropy Scaling Research Articles

The Dynamic Diversity and Invariance of Ab Initio Water.

Comprehending water dynamics is crucial in various fields, such as water desalination, ion separation, electrocatalysis, and biochemical processes. While ab initio molecular dynamics (AIMD) accurately portray water's structure, computing its dynamic properties over nanosecond time scales proves cost-prohibitive. This study employs machine learning potentials (MLPs) to accurately determine the dynamic properties of liquid water with ab initio accuracy. Our findings reveal diversity in the calculated diffusion coefficient (D) and viscosity of water (η) across different methodologies. Specifically, while the GGA, meta-GGA, and hybrid functional methods struggle to predict dynamic properties under ambient conditions, methods on the higher level of Jacob's ladder of DFT approximation perform significantly better. Intriguingly, we discovered that both D and η adhere to the established Stokes-Einstein (SE) relation for all of the ab initio water. The diversity observed across different methods can be attributed to distinct structural entropy, affirming the applicability of excess entropy scaling relations across all functionals. The correlation between D and η provides valuable insights for identifying the ideal temperature to accurately replicate the dynamic properties of liquid water. Furthermore, our findings can validate the rationale behind employing artificially high temperatures in the simulation of water via AIMD. These outcomes not only pave the path to designing better functionals for water but also underscore the significance of water's many-body characteristics.

Entanglement fractalization

We numerically explore the interplay of fractal geometry and quantum entanglement by analyzing the von Neumann entropy (known as entanglement entropy) and the entanglement contour in the scaling limit. Adopting quadratic fermionic models on Sierpinski carpet, we uncover intriguing findings. For gapless ground states exhibiting a finite density of states at the chemical potential, we reveal a super-area law characterized by the presence of a logarithmic correction for area law in the scaling of entanglement entropy. This extends the well-established super-area law observed on translationally invariant Euclidean lattices where the Gioev-Klich-Widom conjecture regarding the asymptotic behavior of Toeplitz matrices holds significant influence. Furthermore, different from the fractal structure of the lattice, we observe the emergence of a self-similar and universal pattern termed an “entanglement fractal” in the entanglement contour data as we approach the scaling limit. Remarkably, this pattern bears resemblance to intricate Chinese paper-cutting designs. We provide general rules to artificially generate this fractal, offering insights into the universal scaling of entanglement entropy. Meanwhile, as the direct consequence of the entanglement fractal and beyond a single scaling behavior of entanglement contour in translation-invariant systems, we identify two distinct scaling behaviors in the entanglement contour of fractal systems. For gapped ground states, we observe that the entanglement entropy adheres to a generalized area law, with its dependence on the Hausdorff dimension of the boundary between complementary subsystems. Published by the American Physical Society 2024

Monitoring Age-Related Changes in Gait Complexity in the Wild with a Smartphone Accelerometer System.

Stride-to-stride fluctuations during walking reflect age-related changes in gait adaptability and are estimated with nonlinear measures that confine data collection to controlled settings. Smartphones, with their embedded accelerometers, may provide accessible gait analysis throughout the day. This study investigated age-related differences in linear and nonlinear gait measures estimated from a smartphone accelerometer (SPAcc) in an unconstrained, free-living environment. Thirteen young adults (YA) and 11 older adults (OA) walked within a shopping mall with a SPAcc placed in their front right pants pocket. The inter-stride interval, calculated as the time difference between ipsilateral heel contacts, was used for dependent measures calculations. One-way repeated-measures analysis of variance revealed significant (p < 0.05) age-related differences (mean: YA, OA) for stride-time standard deviation (0.04 s, 0.05 s) and coefficient of variation (3.47%, 4.16%), sample entropy (SaEn) scale 1 (1.70, 1.86) and scale 3 (2.12, 1.80), and statistical persistence decay (31 strides, 23 strides). The fractal scaling index was not different between groups (0.93, 0.95), but exceeded those typically found in controlled settings, suggesting an upregulation in adaptive behaviour likely to accommodate the increased challenge of free-living walking. These findings support the SPAcc as a viable telehealth instrument for remote monitoring of gait dynamics, with implications for unsupervised fall-risk assessment.

A Picture is Worth a Thousand Timesteps: Excess Entropy Scaling for Rapid Estimation of Diffusion Coefficients in Molecular-Dynamics Simulations of Fluids.

In molecular-dynamics simulations of fluids, the Einstein-Helfand (EH) and Green-Kubo (GK) relationships are frequently used to compute a variety of transport coefficients, including diffusion coefficients. These relationships are formally valid in the limit of infinite sampling time: The error in the estimate of a transport coefficient (relative to an infinitely long simulation) asymptotically approaches zero as more dynamics are simulated and recorded. In practice, of course, one can only simulate a finite number of particles for a finite amount of time. In this work, we show that in this pre-asymptotic regime, an approach for estimating diffusion coefficients based upon excess entropy scaling (EES) achieves a significantly lower error than either EH or GK relationships at fixed online sampling time. This approach requires access only to structural information at the level of the radial distribution function (RDF). We further demonstrate that the use of a recently developed RDF mollification scheme significantly reduces the amount of sampling time needed to converge to the long-time value of the diffusion coefficient. We also demonstrate favorable sample-to-sample variances in the diffusion coefficient estimate obtained using EES as compared to those obtained using EH and GK.

Implication of heart rhythm complexity in predicting long-term outcomes in pulmonary hypertension

Pulmonary hypertension (PH) is a serious disease, however simple tools to predict outcomes are lacking. In our previous investigation, we found that heart rate variability (HRV) and heart rhythm complexity (HRC) were associated with the detection and severity of PH, however their association with PH mortality remains unclear.The aim of this study was to investigate these metrics as a tool for determining long-term outcomes in PH patients. We enrolled 74 Asian PH patients with WHO PH group 1 or 4 at a single hospital in Taiwan between March 2012 and June 2018. After a median follow-up duration of 58 months (to January 2023), 22 patients had died. The patients who died had a significantly lower lean body mass index (BMI), impaired renal function, higher N-terminal pro B-type natriuretic peptide (NT-proBNP) level, lower very low-frequency (VLF), lower short-term detrended fluctuation analysis α1 (DFAα1), and lower multiscale entropy scale 5 value. In multivariable analysis, BMI, VLF and multiscale entropy scale 5 were significantly associated with survival. The best cut-off VLF and scale 5 values were 115.13 and 0.738, respectively. We then categorized the study population into three groups: both elevated VLF/scale 5 (group 1), either depressed VLF or depressed scale 5 (group 2), and both depressed VLF/scale 5 (group 3). The results showed that group 1 had the best outcomes, whereas group 3 had the worst survival (P < 0.001).Combining HRV and HRC metrics appears to be a good non-invasive tool to predict the long-term outcomes of patients with PH.

Coupling cubic equations of state with the concept of entropy scaling to model the viscosity of ionic liquids

This short paper investigates the applicability of our previously developed entropy scaling model to pure ionic liquids and concludes that it can be used without any modification and leads to very satisfactory results when coupled with the Peng-Robinson or Soave-Redlich-Kwong cubic equations of state. For the considered ionic liquids, the average deviations between calculated and experimental viscosities were found to be around 4.6 and 5.8% for the two cubic equations of state, respectively.

Linking Thermal Conductivity to Equations of State Using the Residual Entropy Scaling Theory.

In recent years, the application of the residual entropy scaling (RES) method for modeling transport properties has become increasingly prominent. Based on Yang et al. (Ind. Eng. Chem. Res. 2021, 60, 13052) in modeling the thermal conductivity of refrigerants, we present here an RES model that extends Yang et al.'s approach to a wider range of pure fluids and their mixtures. All fluids available in the REFPROP 10.0 software, i.e., those with reference equations of state (EoS), were studied. A total of 71,554 experimental data of 125 pure fluids and 16,702 experimental data of 164 mixtures were collected from approximately 647 references, mainly based on the NIST ThermoData Engine (TDE) database 10.1. As a result, over 68.2% (corresponding to the standard deviation of a normal distribution) of the well-screened experimental data agree with the developed RES model within 3.1% and 4.6% for pure fluids and mixtures, respectively. Comparative analysis against the various models implemented in the REFPROP 10.0 (one of the state-of-the-art software packages for thermophysical property calculations) reveals that our RES model demonstrates analogous statistical agreement with experimental data yet with much fewer parameters. Regarding the average absolute value of the relative deviation (AARD) from experimental values to model predictions, the developed RES model shows a smaller or equal AARD for 74 pure fluids out of 125 and 76 mixtures out of 164. Besides, a detailed examination of the impact of the critical enhancement term on mixture calculations was conducted. To use our model easily, a software package written in Python is provided in the Supporting Information.

Modelling of wall-bounded cavitating flow and spray mixing in multi-component environments using the PC-SAFT equation of state

This work introduces a numerical multiphase model for multi-component mixtures, utilizing tabulated data for physical and transport properties across a spectrum of conditions from near-vacuum pressures to supercritical states. The property data are derived using Perturbed Chain Statistical Associating Fluid Theory (PC-SAFT), vapor-liquid equilibrium (VLE) calculations, entropy scaling methodologies, and Group Contribution (GC) methods. These techniques accurately reflect the thermodynamic behaviors of real fluids, avoiding the empirical estimation of Equation of State (EoS) input parameters. Implemented in OpenFOAM, the fluid dynamics solver is designed to address the three-dimensional Navier-Stokes equations for multi-component mixtures. The methodology integrates operator splitting to manage hyperbolic and parabolic steps distinctively. Hyperbolic terms are solved using the HLLC (Harten-Lax-van Leer-Contact) solver with temporal integration performed via a third-order Strong-Stability-Preserving Runge–Kutta (SSP-RK3) method. Viscous stress tensor contributions in the momentum equation are handled through an implicit velocity correction equation, while parabolic terms in the energy equation are explicitly solved. The simulation efficiency is further enhanced by adaptive Local Time Stepping and the Immersed Boundary (IB) method, which addresses interactions between the fluid and solid boundaries. Turbulence is resolved using the Wall Adaptive Large Eddy (WALE) model. Applied to high-pressure diesel fuel spray injections into non-reacting (nitrogen) gas environments, the model has been validated against Engine Combustion Network (ECN) data for the Spray-C configuration, featuring a fully cavitating multi-hole orifice. Results demonstrate that the model achieves accurate predictions across a broad range of tested conditions without the need for tuning or calibration parameters.

Many-Body Non-Hermitian Skin Effect for Multipoles.

In this Letter, we investigate the fate of the non-Hermitian skin effect in one-dimensional systems that conserve the dipole moment and higher moments of an associated global U(1) charge. Motivated by field theoretical arguments and lattice model calculations, we demonstrate that the key feature of the non-Hermitian skin effect for m-pole conserving systems is the generation of an (m+1)th multipole moment. For example, in contrast to the conventional skin effect where charges are anomalously localized at one boundary, the dipole-conserving skin effect results in charges localized at both boundaries, in a configuration that generates an extremal quadrupole moment. In addition, we explore the dynamical consequences of the m-pole skin effect, focusing on charge and entanglement propagation. Both numerically and analytically, we provide evidence that long-time steady states have Fock-space localization and an area-law scaling of entanglement entropy, which serve as quantum indicators of the skin effect.

Entropy of strongly coupled Yukawa fluids.

The entropy of strongly coupled Yukawa fluids is discussed from several perspectives. First, it is demonstrated that a vibrational paradigm of atomic dynamics in dense fluids can be used to obtain a simple and accurate estimate of the entropy without any adjustable parameters. Second, it is explained why a quasiuniversal value of the excess entropy of simple fluids at the freezing point should be expected, and it is demonstrated that a remaining very weak dependence of the freezing point entropy on the screening parameter in the Yukawa fluid can be described by a simple linear function. Third, a scaling of the excess entropy with the freezing temperature is examined, a modified form of the Rosenfeld-Tarazona scaling is put forward, and some consequences are briefly discussed. Fourth, the location of the Frenkel line on the phase diagram of Yukawa systems is discussed in terms of the excess entropy and compared with some predictions made in the literature. Fifth, the excess entropy scaling of the transport coefficients (self-diffusion, viscosity, and thermal conductivity) is reexamined using the contemporary datasets for the transport properties of Yukawa fluids. The results could be of particular interest in the context of complex (dusty) plasmas, colloidal suspensions, electrolytes, and other related systems with soft pairwise interactions.

Dynamical Transition Due to Feedback-Induced Skin Effect.

The traditional dynamical phase transition refers to the appearance of singularities in an observable with respect to a control parameter for a late-time state or singularities in the rate function of the Loschmidt echo with respect to time. Here, we study the many-body dynamics in a continuously monitored free fermion system with conditional feedback under open boundary conditions. We surprisingly find a novel dynamical transition from a logarithmic scaling of the entanglement entropy to an area-law scaling as time evolves. The transition, which is noticeably different from the conventional dynamical phase transition, arises from the competition between the bulk dynamics and boundary skin effects. In addition, we find that while quasidisorder or disorder cannot drive a transition for the steady state, a transition occurs for the maximum entanglement entropy during the time evolution, which agrees well with the entanglement transition for the steady state of the dynamics under periodic boundary conditions.

Theoretical study and experimental verification of the viscosities of azeotropic refrigerant R515B

One essential aspect of the studies on the refrigeration and heat pump technology is to search for new alternative working fluids. Meanwhile, the azeotropic mixtures of hydrofluorocarbons (HFCs)/hydrofluoroolefins (HFOs) have attracted researchers not only in fundamentals research field but also in the industry fields due to its good performance and applicability. Therefore, to promote application research, this study is focused on the characteristics of viscosity for azeotrope R515B, which is widely recognized and studied from the thermodynamic aspect. Hence, the high-pressure density and viscosity in liquid phase of R515B were measured with a vibrating-wire viscosimeter within the temperature range in 253 K to 363 K when pressure changes from 1 MPa to 12 MPa. The combined expended uncertainties with a confidence level of 0.95 (k = 2) of density and viscosity are 0.2 % and 2 %, respectively. In addition, a modified viscosity model is proposed with combining the parameterization method of thermodynamic equation of state (EoS) in previous work and the modified entropy variable as well as reduced viscosity reference term of residual entropy scaling (RES) theory. Furthermore, the systematical comparison results among this model and three benchmark viscosity models available illustrate that the RES model proposed in this research is robust and precise in a wide range of operation condition.

A novel fatigue driving detection method based on whale optimization and Attention-enhanced GRU

Fatigue driving has emerged as the predominant causative factor for road traffic safety accidents. The fatigue driving detection method, derived from laboratory simulation data, faces challenges related to imbalanced data distribution and limited recognition accuracy in practical scenarios. In this study, we introduce a novel approach utilizing a gated recurrent neural network method, employing whale optimization algorithm for fatigue driving identification. Additionally, we incorporate an attention mechanism to enhance identification accuracy. Initially, this study focuses on the driver's operational behavior under authentic vehicular conditions. Subsequently, it employs wavelet energy entropy, scale entropy, and singular entropy analysis to extract the fatigue-related features from the driver's operational behavior. Subsequently, this study adopts the cross-validation recursive feature elimination method to derive the optimal fatigue feature index about operational behavior. To effectively capture long-range dependence relationships, this study employs the gated recurrent unit neural network method. Lastly, an attention mechanism is incorporated in this study to concentrate on pivotal features within the data sequence of driving behavior. It assigns greater weight to crucial information, mitigating information loss caused by the extended temporal sequence. Experimental results obtained from real vehicle data demonstrate that the proposed method achieves an accuracy of 89.84% in third-level fatigue driving detection, with an omission rate of 10.99%. These findings affirm the feasibility of the approach presented in this study.

Viscosity of Hydrogen and Methane Blends: Experimental and Modelling Investigations

Understanding of thermophysical and transport properties of H2-NG blends are needed for the gradual introduction of hydrogen into the national gas grid. A capillary tube viscometer was used to measure the viscosity of hydrogen + methane blends (with hydrogen mole fraction = 0, 0.1000, 0.1997, 0.5019, and 1) at temperatures from 213 to 324 K and pressures up to 31 MPa. A total 147 experimental viscosity measurements were made for the three H2 + CH4 blends and compared against the predictions of five different viscosity models: a one-reference corresponding states (Pedersen) model, a two-reference corresponding states (CS2) model, an extended corresponding states (ECS) model, a corresponding states model derived from molecular dynamic simulations of Lennard Jones (LJ) fluids, and a residual entropy scaling (SRES) method. All the model predictions showed a relatively low deviation compared to the measured viscosities. The density required for viscosity model predictions were computed using Multi-Fluid Helmholtz Energy Approximation (MFHEA) equations of state (EoS). To check the experimental procedure and applicability of the viscometer equipment, viscosity validation measurements were carried out for propane, hydrogen, and methane. The measured viscosities of the pure components were in good agreement with the respective viscosity models with AARD of 0.24%, 0.25%, and 0.58% for propane, hydrogen, and methane, respectively.Graphical

Understanding dynamics in coarse-grained models. IV. Connection of fine-grained and coarse-grained dynamics with the Stokes-Einstein and Stokes-Einstein-Debye relations.

Applying an excess entropy scaling formalism to the coarse-grained (CG) dynamics of liquids, we discovered that missing rotational motions during the CG process are responsible for artificially accelerated CG dynamics. In the context of the dynamic representability between the fine-grained (FG) and CG dynamics, this work introduces the well-known Stokes-Einstein and Stokes-Einstein-Debye relations to unravel the rotational dynamics underlying FG trajectories, thereby allowing for an indirect evaluation of the effective rotations based only on the translational information at the reduced CG resolution. Since the representability issue in CG modeling limits a direct evaluation of the shear stress appearing in the Stokes-Einstein and Stokes-Einstein-Debye relations, we introduce a translational relaxation time as a proxy to employ these relations, and we demonstrate that these relations hold for the ambient conditions studied in our series of work. Additional theoretical links to our previous work are also established. First, we demonstrate that the effective hard sphere radius determined by the classical perturbation theory can approximate the complex hydrodynamic radius value reasonably well. Furthermore, we present a simple derivation of an excess entropy scaling relationship for viscosity by estimating the elliptical integral of molecules. In turn, since the translational and rotational motions at the FG level are correlated to each other, we conclude that the "entropy-free" CG diffusion only depends on the shape of the reference molecule. Our results and analyses impart an alternative way of recovering the FG diffusion from the CG description by coupling the translational and rotational motions at the hydrodynamic level.

Eigen-entropy based time series signatures to support multivariate time series classification

Most current algorithms for multivariate time series classification tend to overlook the correlations between time series of different variables. In this research, we propose a framework that leverages Eigen-entropy along with a cumulative moving window to derive time series signatures to support the classification task. These signatures are enumerations of correlations among different time series considering the temporal nature of the dataset. To manage dataset’s dynamic nature, we employ preprocessing with dense multi scale entropy. Consequently, the proposed framework, Eigen-entropy-based Time Series Signatures, captures correlations among multivariate time series without losing its temporal and dynamic aspects. The efficacy of our algorithm is assessed using six binary datasets sourced from the University of East Anglia, in addition to a publicly available gait dataset and an institutional sepsis dataset from the Mayo Clinic. We use recall as the evaluation metric to compare our approach against baseline algorithms, including dependent dynamic time warping with 1 nearest neighbor and multivariate multi-scale permutation entropy. Our method demonstrates superior performance in terms of recall for seven out of the eight datasets.

Is EEG Entropy a Useful Measure for Alzheimer's Disease?

The number of individuals diagnosed with Alzheimer's disease (AD) has increased, and it is estimated to continue rising in the coming years. The diagnosis of this disease is challenging due to variations in onset and course, its diverse clinical manifestations, and the indications for measuring deposit biomarkers. Hence, there is a need to develop more precise and less invasive diagnostic tools. Multiple studies have considered using electroencephalography (EEG) entropy measures as an indicator of the onset and course of AD. Entropy is deemed suitable as a potential indicator based on the discovery that variations in its complexity can be associated with specific pathologies such as AD. Following PRISMA guidelines, a literature search was conducted in 4 scientific databases, and 40 articles were analyzed after discarding and filtering. There is a diversity in entropy measures; however, Sample Entropy (SampEn) and Multiscale Entropy (MSE) are the most widely used (21/40). In general, it is found that when comparing patients with controls, patients exhibit lower entropy (20/40) in various areas. Findings of correlation with the level of cognitive decline are less consistent, and with neuropsychiatric symptoms (2/40) or treatment response less explored (2/40), although most studies show lower entropy with greater severity. Machine learning-based studies show good discrimination capacity. There is significant difficulty in comparing multiple studies due to their heterogeneity; however, changes in Multiscale Entropy (MSE) scales or a decrease in entropy levels are considered useful for determining the presence of AD and measuring its severity.

Emerging entanglement on network histories

We show that quantum fields confined to Lorentzian histories of freely falling networks in Minkowski spacetime probe entanglement properties of vacuum fluctuations that extend unrestricted across spacetime regions. Albeit instantaneous field configurations are localized on one-dimensional edges, angular momentum emerges on these network histories and establish the celebrated area scaling of entanglement entropy. Published by the American Physical Society 2024

Multicomponent entropic cosmology model with generalized entropy

Entropic cosmology provides a concrete physical understanding of the late accelerated expansion of the universe. The acceleration appears to be a consequence of entropy associated with information storage in the universe. Therefore, the assumption of an ad-hoc dark energy is not necessary. In this paper, we investigate the implications of a multicomponent model (radiation and non-relativistic matter) that includes a subdominant power-law term within a thermodynamically admissible model. We use a generic power-law entropy and the temperature of the universe horizon results from the requirement that the Legendre structure of thermodynamics is preserved. We analyse the behaviour for different combinations of the parameters and compare them with other cosmological models, the observed redshift dependencies of the Hubble parameter H and the luminosity distance data obtained from supernovae. This is an early attempt to analyse a multicomponent entropic cosmological model. Furthermore, the analysis is based on a entropy scaling with an arbitrary power of the Hubble radius instead of a specific entropy. This allows us to simultaneously infer different models, compare them and conserve the scaling exponent as a parameter that can be fitted with the observational data, thus providing information about the form of the actual cosmological entropy and temperature. We show that the introduced correction term is able to explain different acceleration and deceleration periods in the late-time universe by solving the model numerically. We discuss the advantages and disadvantages of entropic models compared to mainstream cosmology.

Many-Body Dynamics in Monitored Atomic Gases without Postselection Barrier.

We study the properties of a monitored ensemble of atoms driven by a laser field and in the presence of collective decay. The properties of the quantum trajectories describing the atomic cloud drastically depend on the monitoring protocol and are distinct from those of the average density matrix. By varying the strength of the external drive, a measurement-induced phase transition occurs separating two phases with entanglement entropy scaling subextensively with the system size. Incidentally, the critical point coincides with the superradiance transition of the trajectory-averaged dynamics. Our setup is implementable in current light-matter interaction devices, and most notably, the monitored dynamics is free from the postselection measurement problem, even in the case of imperfect monitoring.