Entropy Scaling Research Articles

Entropy scaling framework for transport properties using molecular-based equations of state

Modeling transport properties is important for many applications. In this work, an entropy scaling framework for modeling transport properties using molecular-based equations of state (EOS) is presented. It can be applied for modeling the viscosity, thermal conductivity, and self-diffusion coefficients. The framework is formulated in a general way such that it can be coupled with various EOS. It is demonstrated that the model, when coupled to molecular-based EOS, provides not only good descriptions of existing data but also reasonable predictions in a wide range of states covering liquid, gaseous, supercritical, and meta-stable regions. Moreover, the model can be used for reliably predicting transport properties of mixtures. The universal parameters of the model were fitted to computer experiment data of the Lennard-Jones fluid. This procedure provides inherently a robust form of the basic scaling function. Thereby, only few data points are required for the determination of the component-specific model parameters. The applicability of the developed framework is demonstrated for model fluids as well as for a wide variety of real substances including non-polar, polar, and associating pure fluids and mixtures.

Progress in the lattice evaluation of entanglement entropy of three-dimensional Yang-Mills theories and holographic bulk reconstruction

A construction of a gravity dual to a physical gauge theory requires confronting data. We establish a proof-of-concept for precision holography, i.e., the explicit reconstruction of the dual background metric functions directly from the entanglement entropy (EE) of strip subregions that we extract from pure glue Yang-Mills theory discretized on a lattice. Our main focus is on a three-dimensional Euclidean SU2 theory in the deconfining phase. Holographic EE suggests, and we find evidence for, that the scaling of the thermal entropy with temperature is to power 7/3 and that it approaches smoothly the critical point, consistent with black hole thermodynamics. In addition, we provide frugal results on the potential between quenched quarks by the computation of the Polyakov loop correlators on the lattice. Holographic arguments pique curiosity in the substratum of Debye screening at strong coupling.

Entanglement area law violation from field-curvature coupling

We investigate the ground state entanglement entropy of a massive scalar field nonminimally coupled to spacetime curvature, assuming a static, spherically symmetric background. We first discretize the field Hamiltonian by introducing a lattice of spherical shells and imposing a cutoff in the radial direction. We then study the ground state of the field and quantify deviations from area law due to nonminimal coupling, focusing in particular on Schwarzschild-de Sitter and Hayward spacetimes, also discussing de Sitter spacetime as a limiting case. We show that large positive coupling constants can significantly alter the entropy scaling with respect to the boundary area, in case of coordinate-dependent spacetime curvature. Our outcomes are interpreted in view of black hole entropy production and early universe scenarios.

Strain Energy and Entropy Based Scaling of Buckling Modes.

A new utilization of entropy in the context of buckling is presented. The novel concept of connecting the strain energy and entropy for a pin-ended strut is derived. The entropy of the buckling mode is extracted through a surrogate model by decomposing the strain energy into entropy and virtual temperature. This concept rationalizes the ranking of buckling modes based on their strain energy under the assumption of given entropy. By assigning identical entropy to all buckling modes, they can be ranked according to their deformation energy. Conversely, with identical strain energy assigned to all the modes, ranking according to entropy is possible. Decreasing entropy was found to represent the scaling factors of the buckling modes that coincide with the measurement of the initial out-of-straightness imperfections in IPE160 beams. Applied to steel plane frames, scaled buckling modes can be used to model initial imperfections. It is demonstrated that the entropy (scale factor) for a given energy roughly decreases with the inverse square of the mode index. For practical engineering, this study presents the possibility of using scaled buckling modes of steel plane frames to model initial geometric imperfections. Entropy proves to be a valuable complement to strain energy in structural mechanics.

Aperiodic spin chains at the boundary of hyperbolic tilings

In view of making progress towards establishing a holographic duality for theories defined on a discrete tiling of the hyperbolic plane, we consider a recently proposed boundary spin chain Hamiltonian with aperiodic couplings that are chosen such as to reflect the inflation rule, i.e. the construction principle, of the bulk tiling. As a remnant of conformal symmetry, the spin degrees of freedom are arranged in multiplets of the dihedral group under which the bulk lattice is invariant. For the boundary Hamiltonian, we use strong-disorder RG techniques and evaluate correlation functions, the entanglement entropy and mutual information for the case that the ground state is in an aperiodic singlet phase. We find that two-point functions decay as a power-law with exponent equal to one. Furthermore, we consider the case that the spin variables transform in the fundamental representation of SO(N), leading to a gapless system, and find that the effective central charge obtained from the entanglement entropy scales as lnN, reflecting the number of local degrees of freedom. We also determine the dependence of this central charge on the parameters specifying the bulk tiling. Moreover, we obtain an analytical expression for the mutual information, according to which there is no phase transition at any finite value of the distance between the two intervals involved.

Multiscale Cumulative Residual Dispersion Entropy with Applications to Cardiovascular Signals.

Heart rate variability (HRV) is used as an index reflecting the adaptability of the autonomic nervous system to external stimuli and can be used to detect various heart diseases. Since HRVs are the time series signal with nonlinear property, entropy has been an attractive analysis method. Among the various entropy methods, dispersion entropy (DE) has been preferred due to its ability to quantify the time series' underlying complexity with low computational cost. However, the order between patterns is not considered in the probability distribution of dispersion patterns for computing the DE value. Here, a multiscale cumulative residual dispersion entropy (MCRDE), which employs a cumulative residual entropy and DE estimation in multiple temporal scales, is presented. Thus, a generalized and fast estimation of complexity in temporal structures is inherited in the proposed MCRDE. To verify the performance of the proposed MCRDE, the complexity of inter-beat interval obtained from ECG signals of congestive heart failure (CHF), atrial fibrillation (AF), and the healthy group was compared. The experimental results show that MCRDE is more capable of quantifying physiological conditions than preceding multiscale entropy methods in that MCRDE achieves more statistically significant cases in terms of p-value from the Mann-Whitney test.

Group Contribution Method for the Residual Entropy Scaling Model for Viscosities of Branched Alkanes

In this work it is shown how the entropy scaling paradigm introduced by Rosenfeld (Phys Rev A 15:2545–2549, 1977, https://doi.org/10.1103/PhysRevA.15.2545) can be extended to calculate the viscosities of branched alkanes by group contribution methods (GCM), making the technique more predictive. Two equations of state (EoS) requiring only a few adjustable parameters (Lee–Kesler–Plöcker and PC-SAFT) were used to calculate the thermodynamic properties of linear and branched alkanes. These EOS models were combined with first-order and second-order group contribution methods to obtain the fluid-specific scaling factor allowing the scaled viscosity values to be mapped onto the generalized correlation developed by Yang et al. (J Chem Eng Data 66:1385–1398, 2021, https://doi.org/10.1021/acs.jced.0c01009) The second-order scheme offers a more accurate estimation of the fluid-specific scaling factor, and overall the method yields an AARD of 10 % versus 8.8 % when the fluid-specific scaling factor is fit directly to the experimental data. More accurate results are obtained when using the PC-SAFT EoS, and the GCM generally out-performs other estimation schemes proposed in the literature for the fluid-specific scaling factor.

Empirical models of thermal conductivity of cis-1,3,3,3-tetrafluoropropene (R1234ze(Z)) with measurements using transient hot-wire method

This article represents the empirical modeling for thermal conductivity of cis-1,3,3,3-tetrafluoropropene (R1234ze(Z)) with new experimental measurements conducted in liquid and vapor phases using the well-established transient hot-wire method. These new experimental data, covering a temperature range of 313 to 414 K for liquid and 354 to 452 K for vapor phase at a pressure range of 0.20 to 4.0 MPa, have an expanded uncertainty of less than 2.17% for liquid and 2.41 % for vapor measurements at a 95 % confidence level (k = 2). The thermal conductivity model of this fluid is presented using the extended corresponding states (ECS) and modified fluid specific residual entropy scaling (RES) techniques with the help of recently published respective viscosity models. Using the adjustable parameters found during the modeling process, the extended corresponding states and the residual entropy scaling technique model equations can represent the experimental data within reported uncertainties. Furthermore, the average absolute deviations for thermal conductivity were found to be 0.96 % and 0.72 % using the ECS and the RES methods, respectively.

A comparative study between Helmholtz and entropy scaling approaches for viscosity of natural gas mixtures based on the GERG-2008 equation of state

A comparative study between Helmholtz and entropy scaling approaches for viscosity of natural gas mixtures based on the GERG-2008 equation of state

Understanding dynamics in coarse-grained models. III. Roles of rotational motion and translation-rotation coupling in coarse-grained dynamics.

This paper series aims to establish a complete correspondence between fine-grained (FG) and coarse-grained (CG) dynamics by way of excess entropy scaling (introduced in Paper I). While Paper II successfully captured translational motions in CG systems using a hard sphere mapping, the absence of rotational motions in single-site CG models introduces differences between FG and CG dynamics. In this third paper, our objective is to faithfully recover atomistic diffusion coefficients from CG dynamics by incorporating rotational dynamics. By extracting FG rotational diffusion, we unravel, for the first time reported to our knowledge, a universality in excess entropy scaling between the rotational and translational diffusion. Once the missing rotational dynamics are integrated into the CG translational dynamics, an effective translation-rotation coupling becomes essential. We propose two different approaches for estimating this coupling parameter: the rough hard sphere theory with acentric factor (temperature-independent) or the rough Lennard-Jones model with CG attractions (temperature-dependent). Altogether, we demonstrate that FG diffusion coefficients can be recovered from CG diffusion coefficients by (1) incorporating "entropy-free" rotational diffusion with translation-rotation coupling and (2) recapturing the missing entropy. Our findings shed light on the fundamental relationship between FG and CG dynamics in molecular fluids.

Diffusion of hydrocarbons diluted in supercritical carbon dioxide

Mutual diffusion of six hydrocarbons (methane, ethane, isobutane, benzene, toluene or naphthalene) diluted in supercritical carbon dioxide ({hbox {CO}}_{2}) is studied by molecular dynamics simulation near the Widom line, i.e., in the temperature range from 290 to 345 K along the isobar 9 MPa. The {hbox {CO}}_{2} + aromatics mixtures are additionally sampled at 10 and 12 MPa and an experimental database with Fick diffusion coefficient data for those systems is provided. Taylor dispersion experiments of {hbox {CO}}_{2} with benzene, toluene, n-dodecane and 1,2,3,4-tetrahydronaphthalene are conducted along the p = 10 MPa isobar. Maxwell–Stefan and Fick diffusion coefficients are analyzed, together with the thermodynamic factor that relates them. It is found that the peculiar behavior of the Fick diffusion coefficient of some {hbox {CO}}_{2} mixtures in the extended critical region is a consequence of the thermodynamic factor minimum due to pronounced clustering on the molecular scale. Further, the strong dependence of the Fick diffusion coefficient on the molecular mass of the solute as well as the breakdown of the Stokes–Einstein relation near the Widom line are confirmed. Eleven correlations for the prediction of the Fick diffusion coefficient of {hbox {CO}}_{2} mixtures are assessed. An alternative two-step approach for the prediction of the infinite dilution Fick diffusion coefficient of supercritical {hbox {CO}}_{2} mixtures is proposed. It requires only the state point in terms of temperature and pressure (or density) as well as the molecular solute mass as input parameters. First, entropy scaling is applied to estimate the self-diffusion coefficient of {hbox {CO}}_{2}. Subsequently, this coefficient is used to determine the infinite dilution Fick diffusion coefficient of the mixture, based on the finding that these two diffusion coefficients exhibit a linear relationship, where the slope depends only on the molecular solute mass.

Relating non-Hermitian and Hermitian quantum systems at criticality

We demonstrate three types of transformations that establish connections between Hermitian and non-Hermitian quantum systems at criticality, which can be described by conformal field theories (CFTs). For the transformation preserving both the energy and the entanglement spectra, the corresponding central charges obtained from the logarithmic scaling of the entanglement entropy are identical for both Hermitian and non-Hermitian systems. The second transformation, while preserving the energy spectrum, does not perserve the entanglement spectrum. This leads to different entanglement entropy scalings and results in different central charges for the two types of systems. We demonstrate this transformation using the dilation method applied to the free fermion case. Through this method, we show that a non-Hermitian system with central charge c = -4c=−4 can be mapped to a Hermitian system with central charge c = 2c=2. Lastly, we investigate the Galois conjugation in the Fibonacci model with the parameter \phi \to - 1/\phiϕ→−1/ϕ, in which the transformation does not preserve both energy and entanglement spectra. We demonstrate the Fibonacci model and its Galois conjugation relate the tricritical Ising model/3-state Potts model and the Lee-Yang model with negative central charges from the scaling property of the entanglement entropy.

Coupled Fredkin and Motzkin chains from quantum six- and nineteen-vertex models

We generalize the area-law violating models of Fredkin and Motzkin spin chains into two dimensions by building quantum six- and nineteen-vertex models with correlated interactions. The Hamiltonian is frustration free, and its projectors generate ergodic dynamics within the subspace of height configuration that are non negative. The ground state is a volume- and color-weighted superposition of classical bi-color vertex configurations with non-negative heights in the bulk and zero height on the boundary. The entanglement entropy between subsystems has a phase transition as the qq-deformation parameter is tuned, which is shown to be robust in the presence of an external field acting on the color degree of freedom. The ground state undergoes a quantum phase transition between area- and volume-law entanglement phases with a critical point where entanglement entropy scales as a function L\log LLlogL of the linear system size LL. Intermediate power law scalings between L\log LLlogL and L^2L2 can be achieved with an inhomogeneous deformation parameter that approaches 1 at different rates in the thermodynamic limit. For the q>1q>1 phase, we construct a variational wave function that establishes an upper bound on the spectral gap that scales as q^{-L^3/8}q−L3/8.

Quantum entropic effects in the liquid viscosities of hydrogen, deuterium, and neon

Extremely low temperatures have limited the availability and accuracy of experimental thermophysical property measurements for cryogens, particularly transport properties. Traditional scaling techniques, such as the theory of corresponding states, have long been known to be inaccurate for fluids with strong quantum effects. To address this need, this paper investigates how quantum effects impact thermodynamics and momentum transfer (shear viscosity) in the fluid phases of hydrogen, deuterium, and neon. We utilize experimental viscosity measurements and reference empirical equations of state to show that conventional entropy scaling is inadequate for quantum-dominated systems. We then provide a simple empirical correction to entropy scaling based on the ratio of quantum to packing length scale that accounts for the deviations.

Scaling theories for predicting the viscosity of binary and ternary refrigerant mixtures

Modeling the viscosity of potential replacements for refrigerants like hydrofluorocarbons (HFCs) and hydrofluoroolefins (HFOs) is important because this information can be used to determine which refrigerants are suitable for use in different refrigeration systems and to guide decisions about system design, operation, and maintenance. In this work, the viscosities of four selected refrigerants, two HFCs and two HFOs, and their mixtures were calculated using two similar approaches, namely entropy scaling and Helmholtz scaling. In both cases, the polar perturbed-chain statistical associating fluid theory (PPC-SAFT) EoS provides the molecular parameters and the entropy or Helmholtz energy dependency required. Results indicate good predictive capabilities for both models, with comparable error to the available experimental data. Even so, the Helmholtz scaling exhibits superior overall robustness, given its extra adjustable parameter. However, predictive results tend to be the same or less quality than those given by the entropy scaling approach.

Entanglement blossom in a simplex matryoshka

Exotic entanglement entropy scaling properties usually present interesting entanglement structures in real space and novel metrics of the spacetime lattice. One prominent example is the rainbow chain where lattice sites which are symmetric about the center form entangled Bell pairs due to an effective long-range coupling in the strong inhomogeneity regime. This manuscript generalizes the rainbow chain to a Hausdorff dimension one lattice embedded in higher dimensional space and enlarged local Hilbert space keeping the Hamiltonian frustration free. The effective Hamiltonian from the Schrieffer–Wolff transformation is given by a stacking of layers of k-simplices with 0-dimensional (all-to-all interacting) antiferromagnetic Hamiltonians, which can be diagonalized analytically with Young operators. The original lattice can be obtained by introducing disinclination defects in a regular k-dimensional cubical lattice, which introduces curvature at the center of the lattice. The model interpolates between the SYK model and the free-fermionic XX spin chain, and hence might be potentially useful in understanding black hole physics and holography.

The nonlinearity of pupil diameter fluctuations in an insight task as criteria for detecting children who solve the problem from those who do not.

Insights, characterized by sudden discoveries following unsuccessful problem-solving attempts, are fascinating phenomena. Dynamic systems perspectives argue that insight arises from self-organizing perceptual and motor processes. Entropy and fractal scaling are potential markers for emerging new and effective solutions. This study investigated whether specific features associated with self-organization in dynamical systems can distinguish between individuals who succeed and those who fail in solving insight tasks. To achieve this, we analyzed pupillary diameter fluctuations of children aged 6 to 12 during the 8-coin task, a well-established insight task. The participants were divided into two groups: successful (n = 24) and unsuccessful (n = 43) task completion. Entropy, determinism, recurrence ratio, and the β scaling exponent were estimated using Recurrence Quantification and Power Spectrum Density analyses. The results indicated that the solver group exhibited more significant uncertainty and lower predictability in pupillary diameter fluctuations before finding the solution. Recurrence Quantification Analysis revealed changes that went unnoticed by mean and standard deviation measures. However, the β scaling exponent did not differentiate between the two groups. These findings suggest that entropy and determinism in pupillary diameter fluctuations can identify early differences in problem-solving success. Further research is needed to determine the exclusive role of perceptual and motor activity in generating insights and investigate these results' generalizability to other tasks and populations.

Nonlocality and entanglement in measured critical quantum Ising chains

We study the effects of measurements, performed with a finite density in space, on the ground state of the one-dimensional transverse-field Ising model at criticality. Local degrees of freedom in critical states exhibit long-range entanglement, and as a result, local measurements can have highly nonlocal effects. Our analytical investigation of correlations and entanglement in the ensemble of measured states is based on properties of the Ising conformal field theory (CFT), where measurements appear as $(1+0)$-dimensional defects in the $(1+1)$-dimensional Euclidean spacetime. So that we can verify our predictions using large-scale free-fermion numerics, we restrict ourselves to parity-symmetric measurements. To describe their averaged effects analytically we use a replica approach, and we show that the defect arising in the replica theory is an irrelevant perturbation to the Ising CFT. Strikingly, the asymptotic scalings of averaged correlations and entanglement entropy are therefore unchanged relative to the ground state. In contrast, the defect generated by postselecting on the most likely measurement outcomes is exactly marginal. We then find that the exponent governing postmeasurement order parameter correlations, as well as the ``effective central charge'' governing the scaling of entanglement entropy, vary continuously with the density of measurements in space. Our work establishes connections between the effects of measurements on many-body quantum states and of physical defects on low-energy equilibrium properties.

Getting over the hump with KAMEL-LOBE: Kernel-averaging method to eliminate length-of-bin effects in radial distribution functions.

Radial distribution functions (RDFs) are widely used in molecular simulation and beyond. Most approaches to computing RDFs require assembling a histogram over inter-particle separation distances. In turn, these histograms require a specific (and generally arbitrary) choice of discretization for bins. We demonstrate that this arbitrary choice for binning can lead to significant and spurious phenomena in several commonplace molecular-simulation analyses that make use of RDFs, such as identifying phase boundaries and generating excess entropy scaling relationships. We show that a straightforward approach (which we term Kernel-Averaging Method to Eliminate Length-Of-Bin Effects) mitigates these issues. This approach is based on systematic and mass-conserving mollification of RDFs using a Gaussian kernel. This technique has several advantages compared to existing methods, including being useful for cases where the original particle kinematic data have not been retained, and the only available data are the RDFs themselves. We also discuss the optimal implementation of this approach in the context of several application areas.

Measurement-induced entanglement phase transition on a superconducting quantum processor with mid-circuit readout

Quantum many-body systems subjected to unitary evolution with the addition of interspersed measurements exhibit a variety of dynamical phases that do not occur under pure unitary evolution. However, these systems remain challenging to investigate on near-term quantum hardware owing to the need for numerous ancilla qubits or repeated high-fidelity mid-circuit measurements, a capability that has only recently become available. Here we report the realization of a measurement-induced entanglement phase transition with a hybrid random circuit on up to 14 superconducting qubits with mid-circuit readout capability. We directly observe extensive and sub-extensive scaling of entanglement entropy in the volume- and area-law phases, respectively, by varying the rate of the measurements. We also demonstrate phenomenological critical behaviour by performing a data collapse of the measured entanglement entropy. Our work establishes the use of mid-circuit measurement as a powerful resource for quantum simulation on near-term quantum computers. The interplay of quantum measurements and unitary evolution is expected to produce dynamical phases with different entanglement properties. An entanglement phase transition has now been detected with hybrid quantum circuits in a superconducting processor.