Entropy Density Research Articles

Constant-roll warm inflation within Rastall gravity

This research paper used a newly proposed strategy for finding the exact inflationary solutions to the Friedman equations in the context of Rastall theory of gravity (RTG), which is known as constant-roll warm inflation (CRWI). The dissipative effects produced during WI are studied by introducing a dissipation factor Q=Γ3H, where Γ is the coefficient of dissipation. We establish the model to evaluate the inflaton field, effective potential requires to produce inflation, and entropy density. These physical quantities lead to developing the important inflationary observables like scalar/tensor power spectrum, scalar spectral index, tensor-to-scalar ratio, and running of spectral-index for two choices of obtained potential that are V0=0 and V0≠0. In this study, we focus on the effects of the theory parameter λ, CR parameter β, and dissipation factor Q (under a high dissipative regime for which Q=constant) on inflation, and are constrained to observe the compatibility of our model with Planck TT+lowP (2013), Planck TT, TE, EE+lowP (2015), Planck 2018 and BICEP/Keck 2021 bounds. The results are feasible and interesting up to the 2σ confidence level. Finally, we conclude that the CR technique produces significant changes in the early universe.

Entropies, level-density parameters and fission probabilities along the triaxially- and axially-symmetric fission paths in 296Lv

We investigate the variation of statistical properties of the fissile nucleus, especially entropy, and nuclear level density, along different fission paths. The calculations were focused on comparing axial and triaxial trajectories leading to fission of 296Lv. We observe that change of shell effects and their suppression rates with deformation can substantially influence fission dynamics. Furthermore, the fission process exhibits iso-entropic behavior at high excitation energies, while pronounced entropy variations are observed at lower energies. We derive a deformation-dependent level density parameter that plays a critical role in estimating the survival probability of a superheavy nucleus. The competition between different fission paths was further studied by employing a master equation approach, thereby demonstrating the critical role of entropy and thermodynamic properties in shaping fission dynamics within multidimensional deformation spaces.

Exactly solvable non-unitary time evolution in quantum critical systems I: effect of complex spacetime metrics

Abstract In this series of works, we study exactly solvable non-unitary time evolutions in one-dimensional quantum critical systems ranging from quantum quenches to time-dependent drivings. In this part I, we are motivated by the recent works of Kontsevich and Segal (2021 arXiv:2105.10161) and Witten (2021 arXiv:2111.06514) on allowable complex spacetime metrics in quantum field theories. In general, such complex spacetime metrics will lead to non-unitary time evolutions. In this work, we study the universal features of such non-unitary time evolutions based on exactly solvable setups. Various physical quantities including the entanglement Hamiltonian and entanglement spectrum, entanglement entropy, and energy density at an arbitrary time can be exactly solved. Due to the damping effect introduced by the complex time, the excitations in the initial state are gradually damped out in time. The non-equilibrium dynamics exhibit universal features that are qualitatively different from the case of real-time evolutions. For instance, for an infinite system after a global quench, the entanglement entropy of the semi-infinite subsystem will grow logarithmically in time, in contrast to the linear growth in a real-time evolution. Moreover, we study numerically the time-dependent driven quantum critical systems with allowable complex spacetime metrics. It is found that the competition between driving and damping leads to a steady state with an interesting entanglement structure.

Upside-Down Adsorption: The Counterintuitive Influences of Surface Entropy and Surface Hydroxyl Density on Hydrogen Spillover.

Although hydrogen spillover is often invoked to explain anomalies in catalysis, spillover remains a poorly understood phenomenon. Hydrogen spillover (H*) is best described as highly mobile H atom equivalents that arise when H2 migrates from a metal nanoparticle to an oxide or carbon support. In the 60 years since its discovery, few methods have become available to quantify or characterize H*-support interactions. We recently showed in situ infrared spectroscopy and volumetric chemisorption can quantify reversible H2 adsorption on Au/TiO2 catalysts, where adsorbed hydrogen exists as H* and interacts with titania surface hydroxyl (TiOH) groups. Here, we report parallel thermogravimetric analysis and Fourier transform infrared spectroscopy methods for systematically manipulating the surface TiOH density. We examine the role of surface hydroxylation on spillover thermodynamics using van't Hoff studies to determine apparent adsorption enthalpies and entropies at constant H* coverage, which is necessary to maintain constant H* translational entropy. Although surface TiOH groups are the likely adsorption sites, the data show removing hydroxyl groups increases spillover. This surprising finding─that adsorption increases as the adsorption site density decreases─is associated with improved thermodynamics on dehydroxylated surfaces. A strong adsorption enthalpy-entropy correlation implicates the changing surface entropy of the titania support itself (i.e., an initial state effect) is deeply intertwined with the H* configurational entropy. These effects are surprising and should apply to all low-coverage adsorbates where entropy terms dominate more traditional enthalpic considerations. Moreover, this study points toward a kinetic test for invoking spillover in a reaction mechanism: namely, in situ dehydroxylation should enhance spillover processes.

Using the total chemical potential to generalize the capillary pressure concept and therefrom derive a governing equation for two-phase flow in porous media

This work presents a governing equation (GE) for two-phase flow in porous media connecting capillary pressure to frictional pressure loss and external chemical potential supplied to a system in either stationary or diffusive equilibrium. It is based on the difference between non-wetting and wetting phase chemical potential (physically, pressure or energy density), which leads to a generalization of the capillary pressure concept. The difference in phase internal chemical potentials is characterized by changes in both interfacial areas and entropy densities due to variation in fluid saturations and is balanced by the system external chemical potential supplied. A definition of the capillary pressure concept is formulated based on the diffusive equilibrium criterion. The GE can explain the origin of the dynamic capillary pressure term, hysteresis, and connect the shift in the capillary pressure curve upon injecting water phases with varying salinities to all the other chemical potentials acting. It can connect, constrain, and potentially quantify all effects which can be formulated in terms of chemical potentials since it is based on a balance equation all two-phase flow systems must obey when either in stationary or diffusive equilibrium.

Shannon entropy variation as a global indicator of electron density contraction at interatomic regions in chemical reactions.

The negative of the Shannon entropy derivative is proposed to account for electron density contraction as the chemical bonds are breaking and forming during a chemical reaction. We called this property the electron density contraction index, EDC, which allows identifying stages in a reaction that are dominated by electron contraction or expansion. Four different reactions were analyzed to show how the EDC index changes along the reaction coordinate. The results indicate that the rate of change of Shannon entropy is directly related to the rate of change of the electron density at the bond critical points between all the atomic pairs in the molecular systems. It is expected that EDC will complement the detailed analysis of reaction mechanisms that can be performed with the theoretical tools available to date. Density functional theory calculations at the B3LYP/6-31G(d,p) level of theory were carried out using Gaussian 16 to analyze the reaction mechanisms of the four reactions studied. The reaction paths were obtained via the intrinsic reaction coordinate method, which served as the reaction coordinate to obtain the reaction force and the EDC profiles in each case. Shannon entropy and electron density at the bond critical points were calculated using the Multiwfn 3.7 package.

Chaotic dynamics of a delayed fractional order MLNCML system

Abstract We present a delayed fractional order spatiotemporal dynamical system using the mixed linear-nonlinear coupling connections between lattices. In the simulation experiments, the dynamical characteristics of the proposed model are looked into and analyzed by using bifurcation diagrams and metric entropy density. The proposed model has fewer periodic windows in its bifurcation diagrams, large key space and strong ergodicity due to the delay. These excellent properties are of great significance in encryption. Moreover, the parameter μ breaks its fixed range in the traditional logistic map, which can contribute to enlarge the key space of cryptosystem. Through numerical simulations and security analysis, it is found that the proposed model is applied for encryption.

A nonequilibrium statistical mechanics derivation of the hydrodynamic equations of simple fluids using a noncanonical form of the Poisson bracket

The continuum level hydrodynamic equations of a simple fluid were derived by Irving and Kirkwood directly from discrete particle dynamics using statistical mechanics almost 75 years ago. Their elegant derivation demonstrated the fundamental molecular basis of macroscopic fluid flow and culminated in molecular expressions for the stress tensor and heat current density that have since been employed in countless molecular simulations to date. In this article, an alternative derivation is presented, which leads to more general expressions for the fundamental transport relationships and which arrives at them in a more straightforward chain of consistency that ensues directly from the Principle of Least Action. The main point of departure from the Irving–Kirkwood derivation is the application of a transformation mapping of the total momentum of each individual particle onto the sum of its peculiar momentum and its momentum relative to the local velocity field. This mapping provides a phase-space distribution function applicable in the space of particle positions and peculiar momentum, from which a noncanonical Poisson bracket can be derived in terms of the same set of microscopic variables. For a given dynamic variable, expressed in terms of particle positions and peculiar momenta, the expectation value of the noncanonical Poisson bracket of the dynamic variable is shown to correspond to the evolution equation of the expectation value of the dynamic variable. This allows for a direct derivation of all macroscopic density evolution equations (mass, momentum, and energy density fields) using a systematic procedure free of assumptions concerning the macroscopic state of the system. Furthermore, an explicit expression of the time evolution of the entropy density at the hydrodynamic level is derived following the same procedure. Finally, in the limit of short-range interparticle interactions, a molecular-based expression for the local stress tensor as properly defined from continuum mechanics is developed at the hydrodynamic level that elucidates the continuum mechanics connection of the general stress expression of Irving and Kirkwood.

SMALE: Hyperspectral Image Classification via Superpixels and Manifold Learning

As an extremely efficient preprocessing tool, superpixels have become more and more popular in various computer vision tasks. Nevertheless, there are still several drawbacks in the application of hyperspectral image (HSl) processing. Firstly, it is difficult to directly apply superpixels because of the high dimension of HSl information. Secondly, existing superpixel algorithms cannot accurately classify the HSl objects due to multi-scale feature categorization. For the processing of high-dimensional problems, we use the principle of PCA to extract three principal components from numerous bands to form three-channel images. In this paper, a novel superpixel algorithm called Seed Extend by Entropy Density (SEED) is proposed to alleviate the seed point redundancy caused by the diversified content of HSl. It also focuses on breaking the dilemma of manually setting the number of superpixels to overcome the difficulty of classification imprecision caused by multi-scale targets. Next, a space–spectrum constraint model, termed Hyperspectral Image Classification via superpixels and manifold learning (SMALE), is designed, which integrates the proposed SEED to generate a dimensionality reduction framework. By making full use of spatial context information in the process of unsupervised dimension reduction, it could effectively improve the performance of HSl classification. Experimental results show that the proposed SEED could effectively promote the classification accuracy of HSI. Meanwhile, the integrated SMALE model outperforms existing algorithms on public datasets in terms of several quantitative metrics.

On interpretation of fluctuations of conserved charges at high T

Fluctuations of conserved charges calculated on the lattice which can be measured experimentally, are well reproduced by a hadron resonanse gas model at temperatures below Tch∼155\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T_{ch} \\sim 155$$\\end{document} MeV and radically deviate from the hadron resonance gas predictions above the chiral restoration crossover. This behaviour is typically interpreted as an indication of deconfinement in the quark-gluon plasma regime. We present an argument that this interpretation may be too simple. The argument is based on the scaling of quantities with the number of colors: demonstration of deconfinement and QGP requires observable that is sensitive to ∼Nc2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sim N_c^2$$\\end{document} gluons while the conserved charges are sensitive only to quarks and above Tch\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T_{ch}$$\\end{document} scale as Nc1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N_c^1$$\\end{document}. The latter scaling is consistent with the existence of an intermediate regime characterized by restored chiral symmetry and by approximate chiral spin symmetry which is a symmetry of confining interaction. In this regime the energy density, pressure and entropy density scale as Nc1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N_c^1$$\\end{document}. In the large Nc\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N_c$$\\end{document} limit this regime might become a distinct phase separated from the hadron gas and from QGP by phase transitions. A natural observable that associates with deconfinement and is directly sensitive to deconfined Nc2-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N_c^2-1$$\\end{document} gluons is the Polyakov loop; in the Nc=3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N_c=3$$\\end{document} world it remains very close to 0 at temperatures well above chiral crossover, reaches the value ∼0.5\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sim 0.5$$\\end{document} around ∼3Tch\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sim 3T_{ch}$$\\end{document} and the value close to 1 at temperatures ∼1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sim 1$$\\end{document} GeV.

Resting-state neural dynamics changes in older adults with post-COVID syndrome and the modulatory effect of cognitive training and sex.

Post-COVID syndrome manifests with numerous neurological and cognitive symptoms, the precise origins of which are still not fully understood. As females and older adults are more susceptible to developing this condition, our study aimed to investigate how post-COVID syndrome alters intrinsic brain dynamics in older adults and whether biological sex and cognitive training might modulate these effects, with a specific focus on older females. The participants, aged between 60 and 75years, were divided into three experimental groups: healthy old female, post-COVID old female and post-COVID old male. They underwent an adaptive task-switching training protocol. We analysed multiscale entropy and spectral power density of resting-state EEG data collected before and after the training to assess neural signal complexity and oscillatory power, respectively. We found no difference between post-COVID females and males before training, indicating that post-COVID similarly affected both sexes. However, cognitive training was effective only in post-COVID females and not in males, by modulating local neural processing capacity. This improvement was further evidenced by comparing healthy and post-COVID females, wherein the latter group showed increased finer timescale entropy (1-30ms) and higher frequency band power (11-40Hz) before training, but these differences disappeared following cognitive training. Our results suggest that in older adults with post-COVID syndrome, there is a pronounced shift from more global to local neural processing, potentially contributing to accelerated neural aging in this condition. However, cognitive training seems to offer a promising intervention method for modulating these changes in brain dynamics, especially among females.

Thermodynamic properties of a relativistic Bose gas under rigid rotation

We study the thermodynamic properties of a rigidly rotating relativistic Bose gas. First, we derive the solution of the equation of motion corresponding to a rotating complex Klein-Gordon field and determine the free propagator of this model utilizing the Fock-Schwinger proper-time method. Using this propagator, we then obtain the thermodynamic potential of this model in the zeroth and first perturbative level. In addition, we compute the nonperturbative ring contribution to this potential. Our focus is on the dependence of these expressions on the angular velocity, which effectively acts as a chemical potential. Using this thermodynamic potential, we calculate several quantities, including the pressure, angular momentum and entropy densities, heat capacity, speed of sound, and moment of inertia of this rigidly rotating Bose gas as functions of temperature (T), angular velocity (Ω), and the coupling constant (α). We show that certain thermodynamic instabilities appear at high temperatures and large couplings. They are manifested as zero and negative values of the above quantities, particularly the moment of inertia and heat capacity. Zero moment of inertia leads to the phenomenon of supervorticity at certain T or α. Supervortical temperatures (couplings) decrease with increasing coupling (temperature). We also observe superluminal sound velocities at high T and for large α. Published by the American Physical Society 2024

Nonlinear wave propagation in large extra spatial dimensions and the blackbody thermal laws

Abstract Nonlinear wave propagation in large extra spatial dimensions (on and above d = 2) is investigated in the context of nonlinear electrodynamics theories that depend exclusively on the invariant F ( = − ( 1 / 4 ) F μ ν F μ ν ) . In this vein, we consider propagating waves under the influence of external uniform electric and magnetic fields. Features related to the blackbody radiation in the presence of a background constant electric field such as the generalization of the spectral energy density distribution and the Stefan–Boltzmann law are obtained. Interestingly enough, anisotropic contributions to the frequency spectrum appear in connection to the nonlinearity of the electromagnetic field. In addition, the long wavelength regime and Wien’s displacement law in this situation are studied. The corresponding thermodynamics quantities at thermal equilibrium, such as energy, pressure, entropy, and heat capacity densities are contemplated as well.

Thermal Casimir effect for a Dirac field on flat space with a nontrivial circular boundary condition

This work investigates the thermal Casimir effect associated with a massive spinor field defined on a four-dimensional flat space with a circularly compactified spatial dimension whose periodicity is oriented along a vector in the xy plane. We employ the generalized zeta function method to establish a finite definition for the vacuum free energy density. This definition conveniently separates into the zero-temperature Casimir energy density and additional terms accounting for temperature corrections. The structure of existing divergences is analyzed from the asymptotic behavior of the spinor heat kernel function and removed in the renormalization by subtracting scheme. The only non-null heat coefficient is the one associated with the Euclidean divergence. We also address the need for a finite renormalization to treat the ambiguity in the zeta function regularization prescription associated with this Euclidean heat kernel coefficient and ensure that the renormalization procedure is unique. The high- and low-temperature asymptotic limits are also explored. In particular, we explicitly show that free energy density lacks a classical limit at high temperatures, and the entropy density agrees with the Nernst heat theorem at low temperatures. Published by the American Physical Society 2024

Endo- and exothermal mechanocaloric response in rubbers

AbstractWe investigated mechanocaloric properties of two silicone rubbers using an in-house made apparatus. Tension $$f$$ f and temperature change $$\Delta T$$ Δ T of the rubber samples in the form of tapes were measured as they were extended up to a normalized length $$\lambda \approx 2$$ λ ≈ 2 at a constant rate. Endothermal and exothermal components of the thermal response were observed and separated. The engineering stress and (decrease of) the entropy density derived from the data were analyzed. The number densities of the partial chains and the coefficients of the positive (endothermal) entropy contribution were determined as material constants of the rubbers. Non-idealities were revealed by the large difference between the work done on the rubber for the extension and the heat that evolved in the process. It decreased to a considerable extent when the heat was corrected for the endothermal effect arising from the above-mentioned endothermal entropy contribution. This may be understood as an indication of hidden near-ideality of silicone rubbers. Dissipation of the work into heat is quantified using the difference between the temperature changes on extension and contraction.

Jet transport coefficients by elastic and radiative scatterings in the strongly interacting quark-gluon plasma

We extend the investigation of jet transport coefficients within the effective dynamical quasiparticle model (DQPM)—constructed to describe nonperturbative QCD phenomena of the strongly interacting quark-gluon plasma (sQGP) in line with the lattice QCD equation of state—by accounting for inelastic 2→3 reactions with gluon radiation in addition to the elastic scattering of partons. The elastic and inelastic reactions are calculated explicitly within leading-order Feynman diagrams with effective propagators and vertices from the DQPM by accounting for all channels and their interferences. We present the results for the jet transport coefficients such as the transverse momentum transfer squared q̂ per unit length as well as the energy loss dE/dx per unit length in the sQGP and investigate their dependence on the temperature T and momentum of the jet parton depending on the choice of the strong coupling constant αs in thermal, jet parton, and radiative vertices. For the latter, we consider different scenarios used in the literature and find a very strong dependence of q̂ and dE/dx on the choice of αs. Moreover, we explore the relation of q̂/T3 to the ratio of specific shear viscosity to entropy density η/s and show that the ratio T3/q̂ to η/s has a strong T dependence—especially when approaching Tc—on the choice of αs in scattering vertices. Published by the American Physical Society 2024

Local thermodynamics and entropy for relativistic hydrostatic equilibrium

By refining the method proposed in Aoki et al. (2021) [5], entropy current and entropy density for a relativistic hydrostatic equilibrium system with spherical symmetry are constructed as a non-Nöther conserved charge in the Einstein gravity with cosmological constant. It is shown that the constructed entropy density satisfies both the local Euler relation and the first law of thermodynamics non-perturbatively with respect to the Newton constant. Finally the established relativistic thermodynamics is applied to one of the systems with uniform energy density as a crude model of a degenerate star and its local thermodynamic observables are determined analytically.

Dependence of thermodynamic quantities at freeze-out on pseudorapidity and collision energy in p-p collisions at LHC energies* *Supported by Princess Nourah bint Abdulrahman University Researchers Supporting Project number (PNURSP2024R106), Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia. In addition, the authors extend their appreciation to the Deanship of Scientific Research at Northern Border University, Arar, KSA for funding this research

The transverse momentum distributions of charged hadrons produced in proton-proton collisions at center-of-mass energies ( ) of 0.9 TeV and 2.36 TeV, as measured by the CMS detector at the Large Hadron Collider (LHC), have been analyzed within various pseudorapidity classes utilizing the thermodynamically consistent Tsallis distribution. The fitting procedure resulted in the key parameters, namely, effective temperature (T), non-extensivity parameter (q), and kinetic freezeout volume (V). Additionally, the mean transverse momentum ( ) and initial temperature (Ti ) of the particle source are determined through the fit function and string percolation method, respectively. An alternative method is employed to calculate the kinetic freezeout temperature ( ) and transverse flow velocity ( ) from T. Furthermore, thermodynamic quantities at the freezeout, including energy density (ε), particle density (n), entropy density (s), pressure (P), and squared speed of sound ( ), are computed using the extracted T and q. It is also observed that, with a decrease in pseudorapidity, all thermodynamic quantities except V and q increase. This trend is attributed to greater energy transfer along the mid pseudorapidity. q increases towards higher values of pseudorapidity, indicating that particles close to the beam axis are far from equilibrium. Meanwhile, V remains nearly independent of pseudorapidity. The excitation function of these parameters (q) shows a direct (inverse) correlation with collision energy. The ε, n, s, and P show a strong dependence on collision energies at low pseudorapidities. Explicit verification of the thermodynamic inequality suggests the formation of a highly dense droplet-like Quark-Gluon Plasma (QGP). Additionally, the inequality is explicitly confirmed, aligning with the evolution of the produced fireball.

Classical and quantum computing of shear viscosity for (2+1)D SU(2) gauge theory

We perform a nonperturbative calculation of the shear viscosity for (2+1)-dimensional SU(2) gauge theory by using the lattice Hamiltonian formulation. The retarded Green’s function of the stress-energy tensor is calculated from real time evolution via exact diagonalization of the lattice Hamiltonian with a local Hilbert space truncation, and the shear viscosity is obtained via the Kubo formula. When taking the continuum limit, we account for the renormalization group flow of the coupling but no additional operator renormalization. We find the ratio of the shear viscosity and the entropy density ηs is consistent with a well-known holographic result 14π at several temperatures on a 4×4 honeycomb lattice with the local electric representation truncated at jmax=12. We also find the ratio of the spectral function and frequency ρxy(ω)ω exhibits a peak structure when the frequency is small. Both the exact diagonalization method and simple matrix product state classical simulation method beyond jmax=12 on bigger lattices require exponentially growing resources. So we develop a quantum computing method to calculate the retarded Green’s function and analyze various systematics of the calculation including jmax truncation and finite size effects, Trotter errors and the thermal state preparation efficiency. Our thermal state preparation method still requires resources that grow exponentially with the lattice size, but with a very small prefactor at high temperature. We test our quantum circuit on both the Quantinuum emulator and the IBM simulator for a small lattice and obtain results consistent with the classical computing ones. Published by the American Physical Society 2024

Stairway to equilibrium entropy

We compute the time evolution of the nonequilibrium entropy in the homogeneous isotropization dynamics of the 1 R-Charge Black Hole model, which has a critical point in its conformal phase diagram defined at finite temperature and R-charge density. We also evaluate the time evolution of the pressure anisotropy and the scalar condensate of the medium. We disclose a new feature (not present in the Bjorken flow dynamics analyzed in previous works), which is observed for all the analyzed initial data: the formation of a periodic sequence of several close plateaus in the form of a stairway for the entropy density near thermodynamic equilibrium. We find that the period of plateau formation in the stairway is half the period of oscillations of the slowest quasinormal mode of the system, which is therefore strongly tied to the late-time dissipative dynamics of the system associated with the irreversibility of entropy production. For the particular case of the purely thermal Supersymmetric Yang-Mills plasma at zero density and vanishing scalar condensate, we find that the period of the stairway is half the period of oscillations of the slowest quasinormal mode associated with the late-time equilibration of the pressure anisotropy of the fluid, while at finite chemical potential the slowest quasinormal mode of the system is associated with the late-time equilibration of the scalar condensate. Published by the American Physical Society 2024