Equilibrium Correlation Research Articles

Dynamical scaling of Loschmidt echo in non-Hermitian systems

We show that non-Hermitian biorthogonal many-body phase transitions can be characterized by the enhanced decay of Loschmidt echo. The quantum criticality is numerically investigated in a non-Hermitian transverse field Ising model by performing the finite-size dynamical scaling of Loschmidt echo. We determine the equilibrium correlation length critical exponents that are consistent with previous results from the exact diagonalization. More importantly, we introduce a simple method to detect quantum phase transitions with the short-time average of rate function motivated by the critically enhanced decay behavior of Loschmidt echo. Our studies show how to detect equilibrium many-body phase transitions with biorthogonal Loschmidt echo that can be observed in future experiments via quantum dynamics after a quench.

Estimating linear mass transport coefficients in solid solutions via correlation splitting and a law of total diffusion

Directly computing linear mass transport coefficients in stochastic models entails integrating over time the equilibrium correlations between atomic displacements. Here, we show how to improve the accuracy of kinetic Monte Carlo simulations via correlation splitting and conditioning, which statistically amounts to estimating the mass transport coefficients through a law of total diffusion. We illustrate the approach with kinetic path sampling simulations of atomic diffusion in a random alloy model in which percolating solute clusters trap the mediating vacancy. There, Green functions serve to generate first-passage paths escaping the traps and to propagate the long-time dynamics. When they also serve to estimate mean-squared displacements via conditioning, colossal reductions of statistical errors are achieved.

Relativistic second-order dissipative hydrodynamics from Zubarev’s non-equilibrium statistical operator

We present a new derivation of relativistic second-order dissipative hydrodynamics for quantum systems using Zubarev’s non-equilibrium statistical-operator formalism. This is achieved by a systematic expansion of the energy–momentum tensor and the charge current to second order in deviations from equilibrium. As a concrete example, we obtain the relaxation equations for the shear-stress tensor, the bulk-viscous pressure, and the charge-diffusion currents required to close the set of equations of motion for relativistic second-order dissipative hydrodynamics. We also identify new transport coefficients which describe the relaxation of dissipative processes to second-order and express them in terms of equilibrium correlation functions, thus establishing new Kubo-type formulas for second-order transport coefficients.

Recent optimization and panelizing measures for green energy projects; insights into CO2 emission influencing to circular economy

Green energy projects (including wind, solar, biomass, hydro projects) are the major constituents of biofuel projects and primary need of global world which are directly concerned with economic growth and gross domestic products (GDP) development. In last few decades, fossil fuel consumption and carbon dioxide (CO2) emission have been increased due to more economic growth and growing population. Moreover, the objective of this research is to assess the consequence of biofuel including natural gas, environmentally friendly power projects (renewable-energy), and thermal power utilization on financial turn of events including GDP and CO2 in ten top countries. Multivariate climate countries with ubiquitous CO2 emission during the period of 1990–2018 were selected to examine the long-run flexibility as well as the path of causality between different variables, the panel co-integration test, panel heterogonous Dumitrescu and Hurlin causality evaluation and panel completely modified ordinary least squares were employed. The panel co-reconciliation test verify that variables have a long-run equilibrium correlation in their relationships. Long haul versatility and causality tests show that natural gas doesn't add to financial development or CO2 decreases. According to this present study, results can help to develop conservative policies regarding long-run and sustainable energy and design in energy development.

Correlations in superradiance of a two-dimensional system

The process of cooperative spontaneous emission in a system of two-level emitters interacting via electromagnetic field is analyzed using the Bogolyubov reduced description method, which provides the possibility of studying the state of the generated field. Field macrostates are described with electric and magnetic field amplitudes and binary correlation functions of their components. Since the previously obtained set of differential equations describing the Dicke system evolution with considering field correlations is very cumbersome, we must find some way of simplifying the model to make it accessible for numerical modeling. The general picture of correlation development can be elucidated with using one- and two-dimensional models. The paper presents the set of evolution equations for Dicke system with fixed orientation of dipole moments of emitters forming a two-dimensional structure. The material equations and equilibrium correlations are discussed. The transition to the Cauchy problem for ordinary differential equations is proposed.

Nonequilibrium Green-Kubo relations for hydrodynamic transport from an equilibrium-like fluctuation-response equality

Near equilibrium, Green-Kubo relations provide microscopic expressions for macroscopic transport coefficients in terms of equilibrium correlation functions. At their core, they are based on the intimate relationship between response and fluctuations as embodied by the equilibrium fluctuation-dissipation theorem, a connection generically broken far from equilibrium. In this work, we identify a class of perturbations whose response around far-from-equilibrium steady states is linked to steady-state correlation functions via an equilibrium-like fluctuation-response equality. We then utilize this prediction to substantiate linearized hydrodynamic transport equations that describe how spatial inhomogeneities in macroscopic nonequilibrium systems relax. As a consequence, we derive nonequilibrium Green-Kubo relations for the transport coefficients of two types of hydrodynamic variables: local conserved densities and broken-symmetry modes. A byproduct of this work is to provide a theoretical foundation for the validity of Onsager's regression hypothesis around nonequilibrium steady states. Our predictions are analytically and numerically corroborated for two model systems: density diffusion in a fluid of soft, spherical active Brownian particles and phase diffusion in the noisy Kuramoto model on a square lattice.

Equilibrium and nonequilibrium quantum correlations between two accelerated detectors

We quantify the quantum correlations between two accelerated detectors coupled to a scalar field in a cavity. It has been realized that an accelerated detector will experience a thermal bath, which is termed the Unruh effect. We examine the similarities and differences for quantum correlations regarding either temperature or acceleration. As the accelerations (resp. temperatures) of the detectors increase, the entanglement decreases to zero at some instant but the mutual information (resp. discord) can be amplified. As the accelerations increase but are in opposite directions, the quantum correlations decay. Importantly, we also reveal that larger quantum correlations can appear in certain nonequilibrium scenarios in which either the acceleration difference or the coupling difference becomes significant.

Dynamical conductivity of warm dense matter from correlation functions with account for interband transitions

Within the generalized linear response theory, the dynamical conductivity of charged particle systems is obtained from equilibrium correlation functions. Using the force–force correlation function approach, interband transitions in addition to phonon interaction and umklapp processes are taken into account for warm dense matter. For solid-density aluminum and copper plasmas, the results are shown for dynamical collision frequency, dynamical conductivity, and opacity as functions of laser frequency accounting for interband absorption. Calculated opacities for aluminum plasmas are compared with results of first-principles density functional theory–molecular dynamic (DFT-MD) simulations and recent experiments. The problem of underestimating the size of opacities by theoretical models in the vicinity of the L edge is discussed.

Adsorption and desorption equilibrium of Li4SiO4-based sorbents for high-temperature CO2 capture

The reversible CO2 adsorption/desorption by Li4SiO4-based sorbents under high temperature has attracted much attention in recent years due to its potential to capture CO2 with a high capacity and excellent cyclic stability. Implementation of the approach largely depends on the equilibrium between CO2 partial pressure and temperature of the sorbents. However, until now no research has been focused on revealing the experimental equilibrium correlation, despite some work alluding to potential effects by precursors or dopants. In this work, typical Li4SiO4-based sorbents with various silicon precursors, dopants of Ce/Fe/Na/K, and varying K contents were synthesized, and experimentally tested using thermogravimetry (TG) by changing the CO2 partial pressure in the range of 0.05–0.5 atm. Results show that experimental equilibrium temperatures are 30–60 °C higher than theoretical values, and pure silicon precursors and dopants of Ce/Fe impose only marginal effects on the adsorption/desorption equilibrium. Interestingly, equilibrium temperatures of sorbents with the presence of K/Na drop off significantly under 0.5 atm of CO2, and more K-dopant corresponds to a lower turnover temperature. This phenomenon is proposed to be the combined action of Li4SiO4 formation and eutectic materials at 500–750 °C. Finally, a correlation formula is established to describe the CO2 adsorption/desorption equilibrium of Li4SiO4-based sorbents by fitting experimental data according to thermodynamic laws.

Phase equilibrium measurements and correlation for {tetrafluoromethane (R14) + propane (R290)} system

In this work, a study on the (vapour + liquid) equilibrium (VLE) and (vapour + liquid + liquid) equilibrium (VLLE) for the tetrafluoromethane (R14) + propane (R290) system was carried out using an apparatus based recirculation method at temperatures ranging from (173.150–212.470) K. The uncertainties of the composition, temperature, and pressure were less than 0.005, 5 mK and 2% or 0.0008 MPa, respectively. All of the experimental data were correlated by the Peng–Robinson equation of state (PR EoS) with the Modified Huron–Vidal second-order (MHV2) mixing rule involving the non-random two-liquid (NRTL) activity coefficient model. The results show good agreement with the experimental data, and the maximum root mean square deviations for (R14 + R290) system are Rp =0.0239 MPa, Rx = 0.009, respectively.

Van der Waals cascade in supercritical turbulence near a critical point

We investigate a quite strong turbulence in a supercritical fluid near a gas-liquid critical point. Specifically, we consider a case in which the Kolmogorov scale is much smaller than the equilibrium correlation length $\xi$. Although equilibrium critical fluctuations are destroyed by turbulence, $\xi$ still provides a crossover length scale between two types of energy cascade. At scales much larger than $\xi$, the Richardson cascade becomes dominant, whereas at scales much smaller than $\xi$, another type of cascade, which we call the van der Waals cascade, is induced by density fluctuations. Experimental conditions required to observe the van der Waals cascade are also discussed.

Kinetics, equilibrium and thermodynamic investigations of methylene blue dye removal using Casuarina equisetifolia pines

Casuarina equisetifolia pines are degradable biopolymeric substance with dye-sequestering property was utilized as biosorbent to expel a cationic dye; methylene blue dye from simulated wastewater. The prepared adsorbent material was characterized for their structural, morphological and elemental features to understand their suitability in augmenting in dye-wastewater remediation. The results infer that 0.5 g/L biosorbent was proficient in removing 100 mg/L methylene blue (pH 7.0 ± 0.2) when agitated at 150 rpm for 120 min. Isothermal behavior were evaluated using non-linear isotherm models like Temkin, Langmuir and Freundlich models while the rate-limiting steps were found using kinetic models. Temkin isotherm and pseudo-first order model explained the removal mechanism among the models evaluated, which infers that the biosorption followed physisorption with the maximum adsorption capacity of 41.35 mg/g. Thermodynamic behavior of methylene blue removal by C. equisetifolia pines powder described the feasibility of biosorption as well as the type of heat involved. Equilibrium sorption capacities, rate constants and correlation coefficients explains that MB dye removal by C. equisetifolia pines is presumably physisorption, spontaneous and endothermic in nature.

Revisiting the Mazur bound and the Suzuki equality

Among the few known rigorous results for time-dependent equilibrium correlations, important for understanding transport properties, are the Mazur bound and the Suzuki equality. The Mazur inequality gives a lower bound, on the long-time average of the time-dependent auto-correlation function of observables, in terms of equilibrium correlation functions involving conserved quantities. On the other hand, Suzuki proposes an exact equality for quantum systems. In this paper, we discuss the relation between the two results and in particular, look for the analogue of the Suzuki result for classical systems. This requires us to examine as to what constitutes a complete set of conserved quantities required to saturate the Mazur bound. We present analytic arguments as well as illustrative numerical results from a number of different systems. Our examples include systems with few degrees of freedom as well as many-particle integrable models, both free and interacting.

Synchronous and Asynchronous Response in Dynamically Perturbed Proteins.

We present a dynamic perturbation-response model of proteins based on the Gaussian Network Model, where a residue is perturbed periodically, and the dynamic response of other residues is determined. The model shows that periodic perturbation causes a synchronous response in phase with the perturbation and an asynchronous response that is out of phase. The asynchronous component results from the viscous effects of the solvent and other dispersive factors in the system. The model is based on the solution of the Langevin equation in the presence of solvent, noise, and perturbation. We introduce several novel ideas: The concept of storage and loss compliance of the protein and their dependence on structure and frequency; the amount of work lost and the residues that contribute significantly to the lost work; new dynamic correlations that result from perturbation; causality, that is, the response of j when i is perturbed is not equal to the response of i when j is perturbed. As examples, we study two systems, namely, bovine rhodopsin and the class of nanobodies. The general results obtained are (i) synchronous and asynchronous correlations depend strongly on the frequency of perturbation, their magnitude decreases with increasing frequency, (ii) time-delayed mean-squared fluctuations of residues have only synchronous components. Asynchronicity is present only in cross correlations, that is, correlations between different residues, (iii) perturbation of loop residues leads to a large dissipation of work, (iv) correlations satisfy the hypothesis of pre-existing pathways according to which information transfer by perturbation rides on already existing equilibrium correlations in the system, (v) dynamic perturbation can introduce a selective response in the system, where the perturbation of each residue excites different sets of responding residues, and (vi) it is possible to identify nondissipative residues whose perturbation does not lead to dissipation in the protein. Despite its simplicity, the model explains several features of allosteric manipulation.

Fluctuation-dissipation relations far from equilibrium: a case study.

Fluctuation–dissipation relations or “theorems” (FDTs) are fundamental for statistical physics and can be rigorously derived for equilibrium systems. Their applicability to non-equilibrium systems is, however, debated. Here, we simulate an active microrheology experiment, in which a spherical colloid is pulled with a constant external force through a fluid, creating near-equilibrium and far-from-equilibrium systems. We characterize the structural and dynamical properties of these systems, and reconstruct an effective generalized Langevin equation (GLE) for the colloid dynamics. Specifically, we test the validity of two FDTs: The first FDT relates the non-equilibrium response of a system to equilibrium correlation functions, and the second FDT relates the memory friction kernel in the GLE to the stochastic force. We find that the validity of the first FDT depends strongly on the strength of the external driving: it is fulfilled close to equilibrium and breaks down far from it. In contrast, we observe that the second FDT is always fulfilled. We provide a mathematical argument why this generally holds for memory kernels reconstructed from a deterministic Volterra equation for correlation functions, even for non-stationary non-equilibrium systems. Motivated by the Mori–Zwanzig formalism, we therefore suggest to impose an orthogonality constraint on the stochastic force, which is in fact equivalent to the validity of this Volterra equation. Such GLEs automatically satisfy the second FDT and are unique, which is desirable when using GLEs for coarse-grained modeling.

Analyzing the effect of natural gas, nuclear energy and renewable energy on GDP and carbon emissions: A multi-variate panel data analysis

Internationally, the importance of clean energy is greatly appreciated in the context of sustainable development and to protect the atmosphere. Therefore, the objective of this article is to determine the effect of natural gas, renewable energy and nuclear energy consumption on economic growth and carbon dioxide emissions in the ten highest CO2 emitting countries within a multivariate context for the duration of 1990–2014. The panel co-integration test, panel fully modified ordinary least squares and panel heterogonous Dumitrescu and Hurlin causality assessment are used to analyze the estimation of long-run elasticity along with the course of causality among the variables. The panel co-integration test confirms the existence of a long-run equilibrium correlation among the variables. The findings of the long run elasticity and causality test reveal that natural gas does not contribute to economic growth and CO2 reduction like nuclear energy and renewable energy. However, except for natural gas, the expansion and improvement of renewable energy and nuclear energy are vital to avoid global warming and climate change as well as to promote economic growth.

Realization of the Landau definitions of effective Hamiltonian and nonequilibrium free energy in microscopic theory

Equilibrium fluctuations of some set of parameters in the states described by the canonical Gibbs distribution are investigated. In the theory of phase transitions of the second kind, these parameters are components of the order parameter. The microscopic realization of the Landau definition of the effective Hamiltonian of the system for studying the equilibrium fluctuations of the specified system of parameters is discussed in the terms of the probability density of their values. A general formula for this function is obtained and it is expressed through the equilibrium correlation functions of these parameters. An expression for the effective Hamiltonian in terms of deviations of the parameters from their equilibrium values is obtained. The deviations are considered small for conducting the calculations. The possibility of calculating the exact free energy of the system using the found effective Hamiltonian is discussed.
 In the microscopic theory, the implementation of the Landau definition of nonequilibrium thermodynamic potentials introduced in his phenomenological theory of phase transitions of the second kind is investigated. Nonequilibrium states of a fluctuating system described with some sets of parameters are considered. A general formula for nonequilibrium free energy expressed through the correlation functions of these parameters is obtained as for the effective Hamiltonian above. Like the previous case, the free energy expression via parameter deviations from the equilibrium values is obtained and small deviations are considered for calculations. The idea of the identity of the effective Hamiltonian of the system and its nonequilibrium free energy is discussed in connection with the Boltzmann distribution. The Gaussian approximation of both developed formalisms is considered.
 A generalization of the constructed theory for the case of spatially inhomogeneous states and the study of long-wave fluctuations are developed.

Correlation Lengths in the Language of Computable Information.

Computable information density (CID), the ratio of the length of a losslessly compressed data file to that of the uncompressed file, is a measure of order and correlation in both equilibrium and nonequilibrium systems. Here we show that correlation lengths can be obtained by decimation, thinning a configuration by sampling data at increasing intervals and recalculating the CID. When the sampling interval is larger than the system's correlation length, the data becomes incompressible. The correlation length and its critical exponents are thus accessible with no apriori knowledge of an order parameter or even the nature of the ordering. The correlation length measured in this way agrees well with that computed from the decay of two-point correlation functions g_{2}(r) when they exist. But the CID reveals the correlation length and its scaling even when g_{2}(r) has no structure, as we demonstrate by "cloaking" the data with a Rudin-Shapiro sequence.

Strongly coupled Yukawa trilayer liquid: Structure and dynamics.

The equilibrium structure and the dispersion relations of collective excitations in trilayer Yukawa systems in the strongly coupled liquid regime are examined. The equilibrium correlations reveal a variety of structures in the liquid phase, reminiscent of the corresponding structures in the solid phase. At small layer separation substitutional disorder becomes the governing feature. Theoretical dispersion relations are obtained by applying the quasilocalized charge approximation (QLCA) formalism, while numerical data are generated by microcanonical molecular dynamics simulations. The dispersions and polarizations of the collective excitations obtained through both of these methods are compared and discussed in detail. We find that the QLCA method is, in general, very satisfactory, but that there are phenomena not covered by the QLCA. In particular, by analyzing the dynamical longitudinal and transverse current fluctuation spectra we discover the existence of a structure not related to the collective mode spectra. This also provides insight into the long-standing problem of the gap frequency discrepancy, observed in strongly coupled layered systems in earlier studies.

Separation of azeotropic mixture (acetone + n-heptane) by extractive distillation with intermediate and heavy boiling entrainers: Vapour-liquid equilibrium measurements and correlation

Acetone and n-heptane are widely applied in pharmaceutical industry as benign solvents and are observed in the wastewater. Because acetone and n-hexane can form an azeotropic mixture, it is impossible to recover acetone and n-heptane with high purity from the wastewater using conventional distillation. In this research, for separating the azeotrope (acetone + n-heptane) by homogeneous extractive distillation, 1-chlorobutane and butyl propanoate were chosen as the intermediate and heavy boiling entrainers. The isobaric vapour-liquid equilibrium (VLE) behaviour for the three binary systems (acetone + 1-chlorobutane), (butyl propanoate + acetone) and (n-heptane + butyl propanoate) were reported at 101.3 kPa. The values of the excess Gibbs energy (GE) were calculated to explore the nonideal of the systems. The thermodynamic consistency of the determined VLE values was checked by the van Ness and Herington tests. In addition, the determined VLE data were fitted by the UNIQUAC, Wilson, and NRTL models. The parameters of those models were regressed, which are helpful for simulating the separation process with the intermediate and heavy boiling entrainers by extractive distillation.