Equilibrium Correlation Research Articles

Effect of capital market on economic growth: An analysis using the autoregressive distributed lag (ARDL) approach

The limits testing method known as ARDL (Autoregressive Distributed Lag) examines Nigerian capital market improvement and monetary development. Relevant indicators about the capital market are taken into account during analysis while considering influencing factors as well. This study aims to explore the relationship between the capital market and financial development in Nigeria. The study’s theoretical framework, which is based on the ARDL framework, includes both short- and long-term dynamics. The data used in this analysis was collected from the Central Bank of Nigeria (CBN), the World Bank database, and the Nigerian Stock Exchange (NSE). In this study, the Nigerian All-Share Index, foreign direct investment, currency exchange rates, and inflation rates are the free factors, while the increase in GDP is the dependent factor. Through cointegration analysis using the ARDL framework, it was discovered that in Nigeria there’s a lengthy equilibrium correlation between economic expansion and financial development. The coefficients determined allow for a deeper understanding of how capital market factors affect economic growth over time. Furthermore, utilizing an error correction model derived from the ARDL analysis offers insight into both brief dynamics and modified speed toward reaching a lasting state of balance. By utilizing the ARDL approach, this study adds to the continuing discourse surrounding how capital markets impact growth in Nigeria. Its empirical evidence provides valuable knowledge for policymakers and stakeholders looking to utilize capital markets effectively toward achieving long-lasting economic development within the country.

Nonlinear Langevin functionals for a driven probe.

When a probe particle immersed in a fluid with nonlinear interactions is subject to strong driving, the cumulants of the stochastic force acting on the probe are nonlinear functionals of the driving protocol. We present a Volterra series for these nonlinear functionals by applying nonlinear response theory in a path integral formalism, where the emerging kernels are shown to be expressed in terms of connected equilibrium correlation functions. The first cumulant is the mean force, the second cumulant characterizes the non-equilibrium force fluctuations (noise), and higher order cumulants quantify non-Gaussian fluctuations. We discuss the interpretation of this formalism in relation to Langevin dynamics. We highlight two example scenarios of this formalism. (i) For a particle driven with the prescribed trajectory, the formalism yields the non-equilibrium statistics of the interaction force with the fluid. (ii) For a particle confined in a moving trapping potential, the formalism yields the non-equilibrium statistics of the trapping force. In simulations of a model of nonlinearly interacting Brownian particles, we find that nonlinear phenomena, such as shear-thinning and oscillating noise covariance, appear in third- or second-order response, respectively.

Correlation functions from tensor network influence functionals: The case of the spin-boson model.

We investigate the application of matrix product state (MPS) representations of the influence functionals (IFs) for the calculation of real-time equilibrium correlation functions in open quantum systems. Focusing specifically on the unbiased spin-boson model, we explore the use of IF-MPSs for complex time propagation, as well as IF-MPSs for constructing correlation functions in the steady state. We examine three different IF approaches: one based on the Kadanoff-Baym contour targeting correlation functions at all times, one based on a complex contour targeting the correlation function at a single time, and a steady state formulation, which avoids imaginary or complex times, while providing access to correlation functions at all times. We show that within the IF language, the steady state formulation provides a powerful approach to evaluate equilibrium correlation functions.

Effect of capital market on economic growth: An analysis using the autoregressive distributed lag (ARDL) approach

The limits testing method known as ARDL (Autoregressive Distributed Lag) examines Nigerian capital market improvement and monetary development. Relevant indicators about the capital market are taken into account during analysis while considering influencing factors as well. This study aims to explore the relationship between the capital market and financial development in Nigeria. The study’s theoretical framework, which is based on the ARDL framework, includes both short- and long-term dynamics. The data used in this analysis was collected from the Central Bank of Nigeria (CBN), the World Bank database, and the Nigerian Stock Exchange (NSE). In this study, the Nigerian All-Share Index, foreign direct investment, currency exchange rates, and inflation rates are the free factors, while the increase in GDP is the dependent factor. Through cointegration analysis using the ARDL framework, it was discovered that in Nigeria there’s a lengthy equilibrium correlation between economic expansion and financial development. The coefficients determined allow for a deeper understanding of how capital market factors affect economic growth over time. Furthermore, utilizing an error correction model derived from the ARDL analysis offers insight into both brief dynamics and modified speed toward reaching a lasting state of balance. By utilizing the ARDL approach, this study adds to the continuing discourse surrounding how capital markets impact growth in Nigeria. Its empirical evidence provides valuable knowledge for policymakers and stakeholders looking to utilize capital markets effectively toward achieving long-lasting economic development within the country.

Large deviations for out of equilibrium correlations in the symmetric simple exclusion process

Large deviations for out of equilibrium correlations in the symmetric simple exclusion process

Quantum correlation functions through tensor network path integral.

Tensor networks have historically proven to be of great utility in providing compressed representations of wave functions that can be used for the calculation of eigenstates. Recently, it has been shown that a variety of these networks can be leveraged to make real time non-equilibrium simulations of dynamics involving the Feynman-Vernon influence functional more efficient. In this work, a tensor network is developed for non-perturbatively calculating the equilibrium correlation function for open quantum systems using the path integral methodology. These correlation functions are of fundamental importance in calculations of rates of reactions, simulations of response functions and susceptibilities, spectra of systems, etc. The influence of the solvent on the quantum system is incorporated through an influence functional, whose unconventional structure motivates the design of a new optimal matrix product-like operator that can be applied to the so-called path amplitude matrix product state. This complex-time tensor network path integral approach provides an exceptionally efficient representation of the path integral, enabling simulations for larger systems strongly interacting with baths and at lower temperatures out to longer time. The derivation, design, and implementation of this method are discussed along with a wide range of illustrations ranging from rate theory and symmetrized spin correlation functions to simulation of response of the Fenna-Matthews-Olson complex to light.

Statistics of the number of renewals, occupation times, and correlation in ordinary, equilibrium, and aging alternating renewal processes.

The renewal process is a point process where an interevent time between successive renewals is an independent and identically distributed random variable. Alternating renewal process is a dichotomous process and a slight generalization of the renewal process, where the interevent time distribution alternates between two distributions. We investigate statistical properties of the number of renewals and occupation times for one of the two states in alternating renewal processes. When both means of the interevent times are finite, the alternating renewal process can reach an equilibrium. On the other hand, an alternating renewal process shows aging when one of the means diverges. We provide analytical calculations for the moments of the number of renewals, occupation time statistics, and the correlation function for several case studies in the interevent-time distributions. We show anomalous fluctuations for the number of renewals and occupation times when the second moment of interevent time diverges. When the mean interevent time diverges, distributional limit theorems for the number of events and occupation times are shown analytically. These are known as the Mittag-Leffler distribution and the generalized arcsine law in probability theory.

Green recovery determination: Interlinkage of international trade, crude oil price volatility, and economic performance

This research delves into the intricate web of relationships between green economic growth, global trade, crude oil price volatility, and economic output. We use a complex econometric framework, the Autoregressive Distributed Lag (ARDL) model, to examine the long-term equilibrium correlations between these variables. When subjected to the Johansen co-integration test, strong long-term ties are shown to be present. The Error Correction Model (ECM) extension of the ARDL model reveals short-term dynamics and corrects deviations from equilibrium values. According to the results of the research, there is a connection between Green economic growth and international trade and economic performance. Economic performance is further dampened by the uncertainty surrounding crude oil prices. Policymakers in today's increasingly globalizing economy would do well to take note of these findings, as they highlight the vital role the factors mentioned above play in creating the Green recovery. The research provides further evidence that it is critical to integrate environmental factors into economic and trade policy in order to promote sustainable development. Based on the study's shreds of evidence, multiple policy implications are recommended for the associated stakeholders.

Active and passive microrheology with large tracers in hard colloids.

The dynamics of a tracer particle in a bath of quasi-hard colloidal spheres is studied by Langevin dynamics simulations and mode coupling theory (MCT); the tracer radius is varied from equal to up to seven times larger than the bath particles radius. In the simulations, two cases are considered: freely diffusing tracer (passive microrheology) and tracer pulled with a constant force (active microrheology). Both cases are connected by linear response theory for all tracer sizes. It links both the stationary and transient regimes of the pulled tracer (for low forces) with the equilibrium correlation functions; the velocity of the pulled tracer and its displacement are obtained from the velocity auto-correlation function and the mean squared displacement, respectively. The MCT calculations give insight into the physical mechanisms: At short times, the tracer rattles in its cage of neighbours, with the frequency increasing linearly with the tracer radius asymptotically. The long-time tracer diffusion coefficient from passive microrheology, which agrees with the inverse friction coefficient from the active case, arises from the transport of transverse momentum around the tracer. It can be described with the Brinkman equation for the transverse flow field obtained in extension of MCT, but cannot be recovered from the MCT kernel coupling to densities only. The dynamics of the bath particles is also studied; for the unforced tracer the dynamics is unaffected. When the tracer is pulled, the velocity field in the bath follows the prediction of the Brinkman model, but different from the case of a Newtonian fluid.

Isothermal (Vapour + Liquid) Equilibrium Measurements and Correlation of the Binary Mixture {3,3,3-Trifluoropropene (HFO-1243zf) + 2,3,3,3-tetrafluoropropene (HFO-1234yf)} at Temperatures from 283.15 K to 323.15 K

The many constrains introduced by the F-gas Regulation and the Kigali Amendment to the Montreal Protocol have resulted in an intense search for alternatives to fluorinated greenhouses gases for air conditioning and refrigeration purposes (Mota-Babiloni A, Makhnatch P, in Int J Refrig 127:101–110, 2021). With respect to the urge of new low-GWP and low-ODP refrigerants, blends composed of hydrofluoroolefins (HFO) are considered promising possible substitutes to hydrofluorocarbons (HFCs) and hydrochlorofluorocarbons (HCFCs) for HVAC&R applications (Sovacool et al., in Renew Sustain Energy Rev 141:110759), but thermophysical properties data for these blends are still scarce (Bell et al., in: J Chem Eng Data, 2021). In the present study, the vapor–liquid equilibrium (VLE) for the binary system (HFO-1243zf + HFO-1234yf), for which just one set of data on the VLE is available to date in literature, has been experimentally studied by means of a vapor recirculation apparatus. The measurements have been performed at isothermal conditions in the range of temperatures between 283.15 K and 323.15 K, while the composition of both the phases in equilibrium has been measured by gas-chromatographic analysis. The experimental VLE data have been correlated by two different equations of state (EoS): the Peng-Robinson (PR) EoS combined with Mathias–Copeman (MC) alpha function and van der Waals (vdW) mixing rules, and the Helmoltz EoS with dedicated binary interaction parameters. Correlated results showed a good agreement with the experimental data for the binary system.

Inertial dynamics and equilibrium correlation functions of magnetization at short times

The method of moments is developed and employed to analyze the equilibrium correlation functions of the magnetization of ferromagnetic nanoparticles in the case of inertial magnetization dynamics. The method is based on the Taylor series expansion of the correlation functions and the estimation of the expansion coefficients. This method significantly reduces the complexity of analysis of equilibrium correlation functions. Analytical expressions are derived for the first three coefficients for the longitudinal and transverse correlation functions for the uniaxial magnetocrystalline anisotropy of ferromagnetic nanoparticles with a longitudinal magnetic field. The limiting cases of very strong and negligibly weak external longitudinal fields are considered. The Gordon sum rule for inertial magnetization dynamics is discussed. In addition, we show that finite analytic series can be used as a simple and satisfactory approximation for the numerical calculation of correlation functions at short times.

ТРЕВОЖНОСТЬ ЗРЕЛИЩА И ЖЕСТОКОСТЬ ОЩУЩЕНИЯ В КАРТИНЕ Ф. БЭКОНА «ПОРТРЕТ ПАПЫ ИННОКЕНТИЯ X» (ЭТЮД №7)

The article will consider the problem of the concept of physicality in the "spirit of the times". The time that will be discussed is commonly called modernity and post-modernity, a prominent representative of which is the artist Francis Bacon. Such a traditional problem of philosophical thought as the correlation of the human soul and body, in the interpretation of Francis Bacon, acquires a completely new discourse. Francis Bacon is an artist who thinks in philosophical categories in line with the problems of human existence as such. Human existence should arrive in an equilibrium correlation of categories: space, time and life, death. The narrative of the works of F. Bacon is the irony of human existence that breaks through pain and screaming. Through the observation of material signs - corporeality and their essence – the spiritual, Francis Bacon proposes to understand the question of the correlation of the corporeal and the spiritual, a discourse in the spirit of postmodernism. By means of the analysis of the painting "Portrait of Pope Innocent X" (etude No. 7), the concept of the corporeal as a structure is revealed, which should be perceived and understood in the context of the totality: the body as an individual, the body as an artificial construct and the body as a socio-cultural construct. Physicality as the sum of the three toposes of the body. The rejection of a stable, uniform understanding of the corporeal and the perception of its image as a stream that cannot be fixed in principle, allows us to identify the ideological program of the representative in its new senses. The ceremonial portrait of Pope Innocent X in the interpretation of Diego Velasquez is the essence of the bodily category, the portrait of Francis Bacon is the splitting of the bodily and the essence of the spiritual category. This is a discourse about a dichotomy, the basis of which is the splitting of subjectivity - the separation of the symbolic plane of corporeality from physical reality.

KELLY TRADING AND MARKET EQUILIBRIUM

The Kelly framework is the natural multi-period extension of the one-period mean-variance model of Markowitz in the sense that the efficient frontier is characterized by trading strategies having maximal instantaneous Sharpe ratio. We show that Kelly traders naturally trade in such a way as to induce an equilibrium for the instantaneous covariance matrix. This equilibrium, arising from trading alone, has the property that the equilibrium correlation can be described as the saddle point of a stochastic differential game. However, because the game is not necessarily a zero-sum game the equilibrium volatility is shown to be lower than what is predicted from the game. The covariance equilibrium is fully specified by the rate of logarithmic return, the interest rate and the aggregate willingness to leverage seen in the market.

Continuum mechanics of nonideal crystals: Microscopic approach based on projection-operator formalism.

We present a microscopic derivation of the laws of continuum mechanics of nonideal ordered solids including dissipation, defect diffusion, and heat transport. The starting point is the classical many-body Hamiltonian. The approach relies on the Zwanzig-Mori projection operator formalism to connect microscopic fluctuations to thermodynamic derivatives and transport coefficients. Conservation laws and spontaneous symmetry breaking, implemented via Bogoliubov's inequality, determine the selection of the slow variables. Density fluctuations in reciprocal space encode the displacement field and the defect concentration. Isothermal and adiabatic elastic constants are obtained from equilibrium correlations, while transport coefficients are given as Green-Kubo formulas, providing the basis for their measurement in atomistic simulations or colloidal experiments. The approach to the linearized continuum mechanics and results are compared to others from the literature.

Measurement and correlation of liquid-liquid equilibrium for the ternary system (water + 1,2-dichloroethane + sulfolane) at 288.15, 298.15, and 308.15 K

Sulfolane is an important aprotic polar solvent. Liquid-liquid equilibrium (LLE) data for the ternary systems of water + 1,2-dichloroethane + sulfolane were measured at temperatures of 288.15, 298.15 and 308.15 K under the atmospheric pressure. The distribution coefficient and selectivity were determined from the measured LLE data, which showed that 1,2-dichloroethane is a suitable extractant for the recovery of sulfolane from its aqueous solution. The nonrandom two-liquid (NRTL) model and the universal quasi-chemical (UNIQUAC) model were utilized to correlate the experimental LLE data. The low values of RMSD indicated that the ternary system could be fitted well by the NRTL and UNIQUAC models. The consistency of the binary interaction parameters for the two thermodynamic models obtained was confirmed by the topological information contained in the Gibbs energy of mixing function ( G M / RT ).

Kinetic coefficient for ice–water interface from simulated non-equilibrium relaxation at coexistence

In the theory of solidification, the kinetic coefficient multiplies the local supercooling to give the solid-liquid interface velocity. The same coefficient should drive interface migration at the coexistence temperature in proportion to a curvature force. This work computes the ice-water kinetic coefficient from molecular simulations starting from a sinusoidal ice-water interface at the coexistence temperature. We apply this method to the basal and prismatic ice planes and compare results to previous estimates from equilibrium correlation functions and simulations at controlled supercooling.

Equilibrium and nonequilibrium quantum correlations between two detectors in curved spacetime

We investigate the equilibrium and nonequilibrium quantum information correlations encoded in a two-qubit system in curved spacetime near the horizon of a Kerr black hole. We study the impact of mass and the angular momentum and further the local curvature or accelerations on the behaviors of the quantum correlations between the two qubits. We show that the quantum information of the two qubits is encoded in the spacetime structure. Concretely, the quantum correlations in the two-qubit system vary non-monotonically with the mass of the black hole and are amplified by the angular momentum, while the curvature suppresses the quantum correlations in the system. We show that the nonequilibrium can also contribute to the quantum correlations. Remarkably, the nonequilibrium can lead to the increase of quantum correlations in the steady state under the curved spacetime shown in this black hole example.

Solid–Liquid Equilibrium and Solubility Determination and Correlation of Dyclonine Hydrochloride in Eight Pure Solvents and Four Binary Mixed Solvents at T = 278.15–323.15 K

Solid–Liquid Equilibrium and Solubility Determination and Correlation of Dyclonine Hydrochloride in Eight Pure Solvents and Four Binary Mixed Solvents at <i>T</i> = 278.15–323.15 K

Mechanisms for the emergence of Gaussian correlations

We comprehensively investigate two distinct mechanisms leading to memory loss of non-Gaussian correlations after switching off the interactions in an isolated quantum system undergoing out-of-equilibrium dynamics. The first mechanism is based on spatial scrambling and results in the emergence of locally Gaussian steady states in large systems evolving over long times. The second mechanism, characterized as `canonical transmutation', is based on the mixing of a pair of canonically conjugate fields, one of which initially exhibits non-Gaussian fluctuations while the other is Gaussian and dominates the dynamics, resulting in the emergence of relative Gaussianity even at finite system sizes and times. We evaluate signatures of the occurrence of the two candidate mechanisms in a recent experiment that has observed Gaussification in an atom-chip controlled ultracold gas and elucidate evidence that it is canonical transmutation rather than spatial scrambling that is responsible for Gaussification in the experiment. Both mechanisms are shown to share the common feature that the Gaussian correlations revealed dynamically by the quench are already present though practically inaccessible at the initial time. On the way, we present novel observations based on the experimental data, demonstrating clustering of equilibrium correlations, analyzing the dynamics of full counting statistics, and utilizing tomographic reconstructions of quantum field states. Our work aims at providing an accessible presentation of the potential of atom-chip experiments to explore fundamental aspects of quantum field theories in quantum simulations.

Identification of topological measures of visibility graphs for analyzing transitions in complex time series

In this paper, we investigate signatures of variation in the behavior of correlated time series by analyzing changes in the topological properties of the corresponding visibility graph. Variations in six different network measures: assortativity, average path length, clustering, transitivity, density, and the average of the mean link length, are explored. We construct visibility graphs from the original and the magnitude and sign of its increment series. Both the horizontal and the natural visibility graphs are studied. Through extensive numerical studies on the time series of fractional Brownian motion (fBm), we first identify network measures that can reflect the changes in correlations in the time series. The efficacy of these markers is examined to identify the transitions in two systems, a two-dimensional (2D) Ising spin system and EEG data with seizures. While all the identified network measures capture the change in the thermal equilibrium correlations for the Ising spin system, they have limited success in the case of the time-dependent fluctuations in the EEG data. We identify some markers relevant to detecting seizures in the EEG data set.