Evolution Of Entropy Research Articles

Rate dependent free energy formulations for dynamically excited superelastic SMA wires

AbstractSuperelastic shape memory alloys (SMAs) are metallic two‐phase polycrystal alloys. The transformation between austenite and martensite phases allows superelastic SMAs unique hysteretic energy dissipation capacity, which is particularly interesting for the development of new‐type of intelligent vibration control systems for structures. However, in structural control, most of the vibrations occur in high strain rate regimes, which interfere the release of self‐generated heat and cause atomic lattice destabilization and thus influence the hysteretic dissipation. The present work proposes two different strain rate dependent free energy formulations and aims to improve the accuracy of existing one‐dimensional macroscopic models of SMA wires. The approaches are developed and implemented in different continuum thermomechanical frameworks, without impairing the simplicity and robustness of the solution process. The first approach introduces an additional control variable for the entropy evolution. The second approach uses a phenomenological formulation of the latent heat evolution. The proposed formulations are validated by cyclic tensile tests conducted on SMA wires. The results show that the calculations using the new formulations can represent the superelastic SMA wire response more accurately.

Application of Shannon Entropy Implementation Into a Novel Fractional Particle Swarm Optimization Gravitational Search Algorithm (FPSOGSA) for Optimal Reactive Power Dispatch Problem

Optimal reactive power dispatch (ORPD) intended for reducing the real power losses of the transmission scheme remains one of the supreme concerns for the research community to explore the competence of power schemes. Numerous systems have been deliberate to increase the performance of the optimization method in tunning the operational variables as well as explored through estimating the final results. The research offering a novel approach based on the entropy evolution technique implemented into Fractional PSOGSA algorithm to solve the optimal reactive power dispatch problem. To alleviate the drawback of PSOGSA the fractional and entropy techniques are implemented into the algorithm which enhanced memory effect, stability and robustness of the algorithm. The novel design of FPSOGSA-Entropy is further tested for the optimal reactive power dispatch problems on IEEE-30 and IEEE-57 bus standards to find the two objective functions; minimization of power line losses and voltage deviation. The superior performance of the proposed FPSOGSA-Entropy is further verified with the results of simple FPSOGSA for both single and multiple runs through comparative analysis study with state of art counterparts for each scenario of optimal reactive power dispatch problems.

An effective mesh-free fission source convergence indicator for Monte Carlo k-Eigenvalue problems

In Monte Carlo k-eigenvalue problems, the entropy of the fission site distribution is calculated after each fission cycle and its evolution over the entire fission cycles is examined. Here, the entropy evolution equilibrates as soon as the fission source distribution converges. Unfortunately, the standard entropy calculation requires space discretization with an additional effort to assign the fission sites into the space bins. Plus, the decision on choosing the number of spatial bins is subjective and based on code users’ experience. Therefore, a consistent mesh-free convergence indicator is proposed as an alternative to the conventional entropy indicator. The indicator utilizes the fundamental mode coefficient of the Fourier series expansion of the fission site distribution. Also, it eliminates the need for user specification on spatial meshing for the purpose of entropy calculation. The numerical tests conducted in this paper indicates that the new indicator is as reliable as the conventional entropy indicator and able to indicate the instance where the source distribution has converged.

Entropy in multiple equilibria. Argon and nitrogen adsorption isotherms of nonporous, microporous, and mesoporous materials

Analysis of multiple equilibria of compounds with different coordination sites is extended to the description of adsorption isotherms with focus on the low relative pressure range. The entropy evolution is described using the particle distribution theory which also holds for adsorbents consisting of materials bearing more than one type of sites and applies for the condition that the adsorptive-adsorbent binding strength is larger than the adsorptive-adsorbate binding strength, so that monolayer coverage is favored. This allows to accurately determine the adsorption enthalpy. No assumption concerning the growth mechanism and specifics regarding the structure of the surface is needed. We find on a rigorous basis that this leads to Langmuir's equation for each site independently, that the total fractional amount of bound adsorptive can be described as a linear combination of individual Langmuir isotherms, and that such a linear combination has never the shape of the original Langmuir isotherms. The results are successfully applied to argon and nitrogen adsorption isotherms of nonporous, microporous, and mesoporous adsorbents which allows comparing systems for which the properties of the active surface span a large range. We observe that all experimental data can accurately be described by means of a linear combination of two Langmuir isotherms in the low relative pressure range up to a coverage of 60%–95%. This means that the shape of all adsorption isotherms is essentially determined by the entropy decrease with increasing coverage. The two site interactions involved exhibit substantially different adsorption enthalpies. Interestingly the Ar enthalpy of adsorption Δ a d s H 1 ∅ of the sites 1 for the Stöber-type silica and of the three investigated MCM-41 adsorbents (with pore size of 2.7 nm, 4.1 nm, and 4.4 nm) are similar, namely −11 kJ/mol. The situation is analogous for the enthalpy of adsorption Δ a d s H 2 ∅ for the sites 2, which amounts to −8 kJ/mol. A significantly larger enthalpy of adsorption Δ a d s H 1 ∅ for the sites 1, namely −14.3 kJ/mol, and Δ a d s H 2 ∅ = − 11.7 kJ / mol for the sites 2 is measured for potassium zeolite L thus reflecting the more polar nature of this adsorbent. The measured specific surface area for these samples ranges from 14 m 2 /g for the Stöber-type silica up to 1100 m 2 /g for the MCM-41(4.1 nm) adsorbent. The information provided by the lc2-L (linear combination of 2 Langmuir functions) analysis allows calculating the evolution of the coverage of site 1 and of site 2 as a function of increasing pressure. The inflection points of the isotherms, which mark the point where the curvature changes sign, were determined by numerically evaluating the second derivatives which vanish at this point and are compared with values obtained using BET analysis.

Uncovering patterns of the evolution of genomic sequence entropy and complexity.

The lack of consensus concerning the biological meaning of entropy and complexity of genomes and the different ways to assess these data hamper conclusions concerning what are the causes of genomic entropy variation among species. This study aims to evaluate the entropy and complexity of genomic sequences of several species without using homologies to assess relationships among these variables and non-molecular data (e.g., the number of individuals) to seek a trigger of interspecific genomic entropy variation. The results indicate a relationship among genomic entropy, genome size, genomic complexity, and the number of individuals: species with a small number of individuals harbors large genome, and hence, low entropy but a higher complexity. We defined that the complexity of a genome relies on the entropy of each DNA segment within genome. Then, the entropy andcomplexity of a genome reflects its organization solely. Exons of vertebrates harbor smaller entropies than non-exon regions (likely by the repeats that accumulated from duplications), whereas other taxonomic groups do not present this pattern. Our findings suggest that small initial population might have defined current genomic entropy and complexity:actual genomes are lesscomplex than ancestral ones. Besides, our data disagree with the relationship between phenotype and genomic entropies previously established. Finally, by establishing the relationship between genomic entropy/complexity with the number of individuals and genome size, under an evolutive perspective, ideas concerning the genomic variability may emerge.

Nonlinear entanglement growth in inhomogeneous space-times

Entanglement has become central for the characterization of quantum matter both in and out of equilibrium. In a dynamical context entanglement exhibits universal linear temporal growth in generic systems, which stems from the underlying linear light cones as they occur in planar geometries. Inhomogeneous spacetimes can lead, however, to strongly bent trajectories. While such bent trajectories crucially impact correlation spreading and therefore the light-cone structure, it has remained elusive how this influences the entanglement dynamics. In this work we investigate the real-time evolution of the entanglement entropy in one-dimensional quantum systems after quenches which change the underlying spacetime background of the Hamiltonian. Concretely, we focus on the Rindler space describing the spacetime in close vicinity to a black hole. As a main result we find that entanglement grows sublinearly in a generic fashion both for interacting and noninteracting quantum matter. We further observe that the asymptotic relaxation becomes exponential, as opposed to algebraic for planar Minkowski spacetimes, and that in the vicinity of the black hole the relaxation time for large subsystems becomes independent of the subsystem size. We study entanglement dynamics both for the case of noninteracting fermions, allowing for exact numerical solutions, and for random unitary circuits representing a paradigmatic class of ergodic systems.

Multiregion entanglement in locally scrambled quantum dynamics

We study the evolution of multi-region bipartite entanglement entropy under locally scrambled quantum dynamics. We show that the multi-region entanglement can significantly modify the growth of single-region entanglement, whose effect has been largely overlooked in the existing literature. We developed a novel theoretical framework, called the entanglement feature formalism, to organize all the multi-region entanglement systematically as a sign-free many-body state. We further propose a two-parameter matrix product state (MPS) ansatz to efficiently capture the exponentially many multi-region entanglement features. Using these tools, we are able to study the multi-region entanglement dynamics jointly and represent the evolution in the MPS parameter space. By comparing the dynamical constraints on the motion of entanglement cuts, we are able to identify different quantum dynamics models in a unifying entanglement feature Hamiltonian. Depending on the quantum dynamics model, we find that multi-region effects can dominate the single region entanglement growth and only vanish for Haar random circuits. We calculate the operator-averaged out-of-time-order correlator based on the entanglement feature Hamiltonian and extract the butterfly velocity from the result. We show that the previously conjectured bound between the entanglement velocity and the butterfly velocity holds true even under the influence of multi-region entanglement. These developments could enable more efficient numerical simulations and more systematic theoretical understandings of the multi-region entanglement dynamics in quantum many-body systems.

Entropy production due to adiabatic particle creation in a holographic dissipative cosmology

Cosmological adiabatic particle creation results in the generation of irreversible entropy. The evolution of this entropy is examined in a flat Friedmann--Robertson--Walker universe at late times, using a dissipative model with a power-law term (proportional to the power of the Hubble parameter $H$). In a dissipative universe, the irreversible entropy included in the Hubble volume is found to be proportional to $H^{-1}$, unlike for the case of the Bekenstein--Hawking entropy on the horizon of the universe. In addition, the evolution of the horizon entropy is examined, extending the previous analysis of a non-dissipative universe [Phys.\ Rev.\ D \textbf{100}, 123545 (2019) (arXiv:1911.08306)]. In the present model, the generalized second law of thermodynamics is always satisfied, whereas the maximization of entropy is satisfied under specific conditions. The dissipative universe should be constrained by the entropy maximization as if the universe behaves as an ordinary, isolated macroscopic system. The thermodynamic constraints are likely to be consistent with constraints on a transition from a decelerating universe to an accelerating universe.

Configurational entropy in f(T) gravity

The evolution of the configurational entropy of the universe relies on the growth rate of density fluctuations and on the Hubble parameter. In this work, I present the evolution of configurational entropy for the power-law $f(T)$ gravity model of the form $f(T) = \zeta (-T)^ b$, where, $\zeta = (6 H_{0}^{2})^{(1-s)}\frac{\Omega_{P_{0}}}{2 s -1}$ and $b$ a free parameter. From the analysis, I report that the configurational entropy in $f(T)$ gravity is negative and decreases with increasing scale factor and therefore consistent with an accelerating universe. The decrease in configurational entropy is the highest when $b$ vanishes since the effect of dark energy is maximum when $b=0$. Additionally, I find that as the parameter $b$ increases, the growth rate, growing mode, and the matter density parameter evolve slowly whereas the Hubble parameter evolves rapidly. The rapid evolution of the Hubble parameter in conjunction with the growth rate for the $b=0$ may provide an explanation for the large dissipation of configurational entropy.

Evolution of entropy in the outer heliosphere

Entropy is an important thermodynamic quantity. Based on the conservation equations of a coupled solar wind and turbulence model, and using measurements from Voyager 2, Pioneer 10 and New Horizons, we investigate the solar wind entropy throughout the heliosphere. Observations from Voyager 2, Pioneer 10, and the NH SWAP instrument show different radial profiles of the entropy as a function of heliocentric distance. We find that the entropy measured by (i) Voyager 2 increases by about 12.84% at 75 au, (ii) NH SWAP increases by about 7.8% at 46.37 au, and (iii) Pioneer 10 increases by about 6.5% at 56.82 au. Voyager 2 and NH SWAP made measurements in the upwind direction and Pioneer 10 is in the downwind direction. We compare directly the theoretical results with Voyager 2 measurements only, and find good agreement between them.

Formularization of entropy and anticipation of metastable states using mutual information in one-dimensional traffic flow

Both macro and micro states of Newtonian particles are used to define entropy. However, in previous research studies, which focused on traffic flow from the perspective of thermodynamics and information theory, researchers did not fully determine how entropy can be defined for self-driven particles that do not satisfy Newton’s laws. One attempt to formularize entropy in a one-dimensional traffic flow has been based on information theory. Entropy has been defined by focusing only on the location variation of the vehicles but not on the velocity variation of the vehicles. Moreover, no study has succeeded in considering the time evolution of entropy in a self-driven particle system. In this study, we redefine the entropy and mutual information in one-dimensional traffic flow from the information theoretical perspective, focusing on the velocity variation of vehicles. Moreover, we advance the thermodynamic analysis of one-dimensional traffic flow by examining the time evolution of the new formularized entropy. To observe the time evolution of the formularized entropy, we conducted numerical simulations using both stochastic optimal velocity (SOV) and zero-range process with a slow-start-rule (ZRP+SLS) models that can reproduce a metastable state, which occurs before the congestion begins at a high average velocity and short headway. Moreover, we used the mutual information to anticipate a metastable state – a sign of congestion – by calculating experimental data from three following vehicles on a real expressway to demonstrate the practical application of the formularized mutual information. Thus, we analyzed traffic flow both macroscopically and microscopically using the new formularized entropy to contribute to the studies of self-driven particle systems in both ways of thermodynamics and statistical mechanics or information theory.

Entropy in Spin Relaxation, Spintronics, and Magnetic Resonance

The entropy change during spin relaxation for a realistic model system is studied, whose spin dynamics can be handled with the Boltzmann equation. The time evolution of the von Neumann entropy is monitored during the process and is compared with the recently introduced concept of the Loschmidt echo envelope. The time evolution of the two quantities is remarkably similar which helps to distinguish reversible and irreversible changes to the ensemble spin state. The method is also demonstrated for a toy model of nuclear magnetic resonance, where the usual π spin echo is performed numerically, and the echo envelope also follows the time evolution of the von Neumann entropy. The numerical approach highlights the utility of the entropy concept in analyzing various processes which occur during spin relaxation.

Onset of inverse magnetocaloric effect in multiferroic FeVO4 below the antiferromagnetic transition temperature TN1

We investigated the evolution of magnetic entropy in a triclinic FeVO4 multiferroic using temperature and magnetic field dependent magnetic measurements at magnetic transitions. The observed antiferromagnetic transitions are at TN1 = 22 K and TN2 = 15 K, together with the paramagnetic phase above TN1. A magnetic field induced maximum magnetic entropy change (ΔSM = 0.37 J kg−1K−1 at H = 50 kOe) at multiferroic transition, 15 K is observed in conjunction with a crossover from the negative to positive in ΔSM(T) data at TN1 towards TN2. The crossover of magnetic entropy substantiates the onset of inverse magnetocaloric effect below the antiferromagnetic transition temperature at TN1 together with maximum ΔSM at TN2.

The dynamics of entropy in the COVID-19 outbreaks

With the unfolding of the COVID-19 pandemic, mathematical modelling of epidemics has been perceived and used as a central element in understanding, predicting, and governing the pandemic event. However, soon it became clear that long-term predictions were extremely challenging to address. In addition, it is still unclear which metric shall be used for a global description of the evolution of the outbreaks. Yet a robust modelling of pandemic dynamics and a consistent choice of the transmission metric is crucial for an in-depth understanding of the macroscopic phenomenology and better-informed mitigation strategies. In this study, we propose a Markovian stochastic framework designed for describing the evolution of entropy during the COVID-19 pandemic together with the instantaneous reproductive ratio. Then, we introduce and use entropy-based metrics of global transmission to measure the impact and the temporal evolution of a pandemic event. In the formulation of the model, the temporal evolution of the outbreak is modelled by an equation governing the probability distribution that describes a nonlinear Markov process of a statistically averaged individual, leading to a clear physical interpretation. The time-dependent parameters are formulated by adaptive basis functions, leading to a parsimonious representation. In addition, we provide a full Bayesian inversion scheme for calibration together with a coherent strategy to address data unreliability. The time evolution of the entropy rate, the absolute change in the system entropy, and the instantaneous reproductive ratio are natural and transparent outputs of this framework. The framework has the appealing property of being applicable to any compartmental epidemic model. As an illustration, we apply the proposed approach to a simple modification of the susceptible–exposed–infected–removed model. Applying the model to the Hubei region, South Korean, Italian, Spanish, German, and French COVID-19 datasets, we discover significant difference in the absolute change of entropy but highly regular trends for both the entropy evolution and the instantaneous reproductive ratio.

The Relativistic Boltzmann Equation and Two Times.

We discuss a covariant relativistic Boltzmann equation which describes the evolution of a system of particles in spacetime evolving with a universal invariant parameter . The observed time t of Einstein and Maxwell, in the presence of interaction, is not necessarily a monotonic function of . If increases with , the worldline may be associated with a normal particle, but if it is decreasing in , it is observed in the laboratory as an antiparticle. This paper discusses the implications for entropy evolution in this relativistic framework. It is shown that if an ensemble of particles and antiparticles, converge in a region of pair annihilation, the entropy of the antiparticle beam may decreaase in time.

Matter-geometry entanglement in quantum cosmology

We present a study of the evolution of entanglement entropy of matter and geometry in quantum cosmology. For a variety of Gaussian initial states and their linear combinations, and with evolution defined with respect to a relational time, we show numerically that (i) entanglement entropy increases rapidly at very early times, and subsequently saturates to a constant non-zero value, and (ii) that the saturation value of this entropy is a linear function of the energy associated to the quantum state: . These results suggest a remnant of quantum entanglement in the macroscopic Universe from the era of the Big Bang, independent of the initial state parameters, and a ‘First Law’ associated with matter-gravity entanglement entropy in quantum gravity.

The unpredictability of the basins of attraction in photogravitational Chermnykh’s problem

This paper deals with the photogravitational circular restricted three-body problem, including the effect of circular cluster of material points. The parametric evolution of the position of equilibrium points and the existence of a different number of equilibrium points are illustrated using graphs. A detailed investigation to find out the influence of the radiation pressure $q$ , mass ratio $\mu $ and the circular cluster of material points $M_{b}$ on the geometry of basins of attraction is carried out. Further, the number of iterations required to obtain the desired level of accuracy is recorded and presented using probability distribution diagram. The correlations between the domain of convergence of equilibrium points and the corresponding number of the iterations required to obtain the desired level of accuracy are explained. We monitor the parametric evolution of the basin entropy to reveal the unpredictability in the basins of attractions. It is found that unpredictable (fractal) regions exist in the vicinity of boundaries of the basins of attraction.

Holographic subregion complexity under a thermal quench in an Einstein-Maxwell-axion theory with momentum relaxation

We investigate the evolution of holographic entanglement entropy (HEE) and holographic complexity (HC) under a thermal quench in Einstein-Maxwell-axion theory, which is dual to a field theory with momentum relaxation on the boundary. A strip-shaped boundary geometry is utilized to calculate HEE and HC via ``$\text{entropy}=\text{surface}$'' and ``$\text{complexity}=\text{volume}$'' conjecture, respectively. By fixing other parameters, we claim that either large enough black hole charge or width of the strip will introduce swallow-tail behaviors in HEE and multivalues in HC due to the discontinuity of the minimum Hubeny-Rangamani-Takayanagi surface. Meanwhile, we explore the effects of momentum relaxation on the evolution of HEE and HC. The results present that the momentum relaxation will suppress the discontinuity to occur as it increases. For large enough momentum relaxation, the continuity of HEE and HC will be recovered.

Black Holes Often Saturate Entanglement Entropy the Fastest.

There is a simple bound on how fast the entanglement entropy of a subregion of a many-body quantum system can saturate in a quench: t_{sat}≥R/v_{B}, where t_{sat} is the saturation time, R the radius of the largest inscribed sphere, and v_{B} the butterfly velocity characterizing operator growth. By combining analytic and numerical approaches, we show that in systems with a holographic dual, the saturation time is equal to this lower bound for a variety of differently shaped entangling surfaces, implying that the dual black holes saturate the entanglement entropy as fast as possible. This finding adds to the growing list of tasks that black holes are the fastest at. We furthermore analyze the complete time evolution of entanglement entropy for large regions with a variety of shapes, yielding more detailed information about the process of thermalization in these systems.

An efficient lattice Boltzmann method for compressible aerodynamics on D3Q19 lattice

An efficient lattice Boltzmann (LB) model relying on a hybrid recursive regularization (HRR) collision operator on D3Q19 stencil is proposed for the simulation of three-dimensional high-speed compressible flows in both subsonic and supersonic regimes. An improved thermal equilibrium distribution function on D3Q19 lattice is derived to reduce the complexity of correcting terms. A simple shock capturing scheme and an upwind biased discretization of correction terms are implemented for supersonic flows with shocks. Mass and momentum equations are recovered by an efficient streaming, collision and forcing process on D3Q19 lattice. Then a non-conservative formulation of the entropy evolution equation is used, that is solved using a finite volume method. The proposed method is assessed considering the simulation of i) 2D isentropic vortex convection, ii) 3D non-isothermal acoustic pulse, iii) 2D supersonic flow over a bump, iv) 3D shock explosion in a box, v) 2D vortex interaction with shock wave, vi) 2D laminar flows over a flat plate at Ma of 0.5, 1.0 and 1.5.