Equilibrium Spectrum Research Articles

The Atmosphere of HD 149026b: Low Metal Enrichment and Weak Energy Transport

Recent JWST eclipse spectra of the high-density hot Saturn HD 149026b between 2.35 and 5.08 μm have allowed for in-depth study of its atmosphere. To understand its atmospheric properties, we have created a grid of 1D radiative-convective–thermochemical–equilibrium atmosphere models and spectra with PICASO 3.0. In agreement with previous work, we find that the presence of gaseous TiO creates a thermal inversion, which is inconsistent with the data. The presence of gaseous VO, however, which condenses at temperatures 200 K cooler, does not cause such inversions but alters the temperature–pressure profile of the atmosphere. We estimate an atmospheric metallicity of 14−8+12× solar without VO and 20−8+11× solar with VO, a factor of ∼10 times smaller than previous work from Bean et al., who relied on atmosphere retrievals. We attribute this significant difference in metallicity to a larger temperature gradient at low pressures in radiative equilibrium models. Such models with lower metallicities readily fit the strong CO2 feature at 4.3 μm. Our lower estimated metallicity makes HD 149026b more consistent with the mass–metallicity relationship for other giant planets. We find a C/O ratio of 0.67−0.27+0.06 with and without VO. The best-fit heat redistribution factor without VO is 1.17, a very high value suggesting very little dayside energy transport and no energy transport to the nightside. The heat redistribution factor shrinks to a more plausible value of 0.91−0.05+0.05 , with VO, which we regard as circumstantial evidence for the molecule in the atmosphere of HD 149026b.

Theoretical study of the electron-induced vibrational excitation of H2O

This study presents calculations for cross sections of the vibrational excitation of H2O(X1A1) via electron impact. The theoretical approach employed here is based on first principles only, combining electron-scattering calculations performed using the UK R-matrix codes for several geometries of the target molecule, three-dimensional (3D) vibrational states of H2O, and 3D vibrational frame transformation. The aim is to represent the scattering matrix for the electron incident of the molecule. The vibrational wave functions were obtained numerically, without the normal-mode approximation, so that the interactions and transitions between vibrational states assigned to different normal modes could be accounted for. The thermally averaged rate coefficients were derived from the calculated cross sections for temperatures in the 10–10 000 K interval and analytical fits for rate coefficients were also provided. We assessed the uncertainty estimations of the obtained data for subsequent applications of the rate coefficients in modelling the non-local thermal equilibrium (non-LTE) spectra of water in various astrophysical environments.

Inertial range scaling of inhomogeneous turbulence

We investigate how inhomogeneity influences the $k^{-5/3}$ inertial range scaling of turbulent kinetic energy spectra (with $k$ the wavenumber). For weak statistical inhomogeneity, the energy spectrum can be described as an equilibrium spectrum plus a perturbation. Theoretical arguments suggest that this latter contribution scales as $k^{-7/3}$ . This prediction is assessed using direct numerical simulations of three-dimensional Kolmogorov flow.

Corporate social responsibility and network externalities: a game-theoretic approach

This research revisits the pioneering work by Katz and Shapiro (Am Econom Rev 75:424–440, 1985) with network (consumption) externalities in a twofold way: first, it considers Corporate Socially Responsible (CSR), instead of profit-maximising, firms; second, it uses a game-theoretic approach and analyses the commitment decision game in which firms face the binary choice to credibly commit (C\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$C$$\\end{document}) or not to commit (NC\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$NC$$\\end{document}) themselves to an announced output level in the first decision-making stage. Competition at the market stage occurs à la Cournot. Results show a rich spectrum of sub-game perfect Nash equilibrium (SPNE) outcomes, ranging from the prisoner’s dilemma (self-interest and mutual benefit of output commitment conflict) to the anti-prisoner’s dilemma or deadlock (self-interest and mutual benefit of output commitment do not conflict), passing from the coordination to the anti-coordination game. These outcomes depend on the intensity of the social concern in the firm’s objective and the network size. The article also pinpoints the welfare outcomes corresponding to the SPNE and extends the analysis to a Stackelberg rivalry setting.

The blue supergiant Sher 25 revisited in the Gaia era

Aims. The evolutionary status of the blue supergiant Sher 25 and its membership to the massive cluster NGC 3603 are investigated. Methods. A hybrid non-local thermodynamic equilibrium (non-LTE) spectrum synthesis approach is employed to analyse a high-resolution optical spectrum of Sher 25 and five similar early B-type comparison stars in order to derive atmospheric parameters and elemental abundances. Fundamental stellar parameters are determined by considering stellar evolution tracks, Gaia Data Release 3 (DR3) data, and complementary distance information. Interstellar reddening and the reddening law along the sight line towards Sher 25 are constrained employing UV photometry for the first time in addition to optical and infrared data. The distance to NGC 3603 is reevaluated based on Gaia DR3 data of the innermost cluster O-stars. Results. The spectroscopic distance derived from the quantitative analysis implies that Sher 25 lies in the foreground of NGC 3603, which is found to have a distance of dNGC3603 = 6250 ± 150 pc. A cluster membership is also excluded as the hourglass nebula is unaffected by the vigorous stellar winds of the cluster stars and from the different excitation signatures of the hourglass nebula and the nebula around NGC 3603. Sher 25 turns out to have a luminosity of log L/L⊙ = 5.48 ± 0.14, equivalent to that of a ~27 M⊙ supergiant in a single-star scenario, which is about half of the mass assumed so far, bringing it much closer in its characteristics to Sk−69º202, the progenitor of SN 1987A. Sher 25 is significantly older than NGC 3603. Further arguments for a binary (merger) evolutionary scenario of Sher 25 are discussed.

Implications of reciprocity for the spectra of equilibrium and nonequilibrium Casimir forces

Implications of reciprocity for the spectra of equilibrium and nonequilibrium Casimir forces

Structural phases of classical 2D clusters with competing two-body and three-body interactions

In modeling systems of interacting particles, many-body terms beyond pairwise interactions are often overlooked. Nevertheless, in certain scenarios, even small contributions from three-body or higher-order terms can disrupt significant changes in their collective behavior. Here we investigate the effects of three-body interactions on the structure and stability of 2D, harmonically confined clusters. We consider clusters with three distinct pairwise interactions: , , and , thus covering a wide range of condensed and soft matter systems, such as vortices in mesoscopic superconductors, charged colloids, and dusty plasma. In each case, we evaluate the energetics and normal mode spectra of equilibrium and metastable configurations as the intensity of an attractive, Gaussian three-body potential is varied. We demonstrate that, above a threshold value of the three-body energy strength, the cluster shrinks and eventually becomes self-sustained, that is, it remains cohesive after the confinement potential is shut down. Depending on the strengths of the two-body and three-body interaction terms, this compaction can be continuous or abrupt. The latter case is characterized by a discontinuous jump in the particle density and coexsitence of the compact and non-compact phases as metastable states, as in a first-order phase transition. For some values of the particle number, the compaction is preceded by one or more structural changes, resulting in configurations not usually seen in purely pairwise-additive clusters.

An EDQNM study of the dissipation rate in isotropic non-equilibrium turbulence

The energy cascade from large to small scales is a robust feature of three-dimensional turbulence. In statistically steady turbulence, the average dissipation is in equilibrium with the energy injected in the system. A global quantity measuring the deviations from such a flux equilibrium is the normalised dissipation rate , corresponding to the viscous dissipation, normalised by quantities associated with the largest scales of the system. Recent investigations have pointed out how this normalised dissipation rate varies in unsteady flows. We focus on two test-cases to assess non-equilibrium in isotropic turbulence. These cases are, respectively, turbulence in the presence of a large-scale periodic forcing and turbulence with reversed initial conditions. We show, using the Eddy-Damped Quasi-Normal Markovian closure, that for turbulence in the presence of periodic forcing, a scaling is reproduced ( indicating the Taylor-scale Reynolds number) when the forcing-frequency is adjusted to be of the order of the inverse of the integral time-scale. It is shown that the spectrum can be decomposed into an equilibrium spectrum, governed by Kolmogorov scaling in the inertial range, and a perturbation spectrum, proportional to , k being the wavenumber. For reversed turbulence, a novel procedure is introduced to prescribe initial conditions for the nonlinear transfer. Subsequently a clear transient with a scaling is observed in the dynamics.

Does Electron Spectrum Affect TLD-100 Dose Response in 6 MV Photon Beam Irradiation?

In this study, the electron spectrum effect on the TLD-100 dosimeter response to a 6 MV photon beam in different media like water, aluminum, polystyrene, iron, copper, and lead using Monte Carlo and Burlin cavity theory was evaluated. To calculate and compare the dose to medium to dose to cavity correction factors (f), the electronic equilibrium spectrum produced by the 6 MV photon beam and its maximum electron energy in different media were used. The electronic equilibrium spectra were obtained using Beamdp Monte Carlo Simulation. Using two different methods, the cavity theory was applied to obtain the response of the TLD-100 to 6 MV photon beam in the media considered. In the first method, the average mass collision stopping power ratios and the average mass effective attenuation coefficients were calculated using the electron spectrum of 6 MV. In the second method, these parameters were calculated based on the maximum energy value of 6 MV. The maximum difference between the f values obtained using the two methods was about 10 % for lead, while it was less than 2.5 % for other media. Consequently, the differences between f factors calculated using these two methods were insignificant except for lead.

Ocean Surface Roughness from Satellite Observations and Spectrum Modeling of Wind Waves

Abstract Many wind wave spectrum models provide excellent wave height prediction given the input of wind speed and wave age. Their quantification of the surface roughness, on the other hand, varies considerably. The ocean surface roughness is generally represented by the mean square slope, and its direct measurement in open ocean remains a challenging task. Microwave remote sensing from space delivers ocean surface roughness information. Satellite platforms offer global coverage in a broad range of environmental conditions. This paper presents low-pass mean square slope (LPMSS) data obtained by spaceborne microwave altimeters and reflectometers operating at L, Ku, and Ka bands (about 1.6, 14, and 36 GHz). The LPMSS data represent the spectrally integrated ocean surface roughness with 11, 95, and 250 rad m−1 upper cutoff wavenumbers, and the maximum wind speeds are 80, 29, and 25 m s−1, respectively. A better understanding of the ocean surface roughness is important to the goal of improving wind wave spectrum modeling. The analysis presented in this paper shows that over two orders of magnitude of the wavenumber range (0.3–30 rad m−1), the spectral components follow a power function relating the dimensionless spectrum and the ratio between wind friction velocity and wave phase speed. The power function exponent is about 0.38, which is considerably smaller than unity as expected from the classical equilibrium spectrum function. It may suggest that wave breaking is not only an energy sink but also a source of roughness generation covering a wideband of wavelengths about 20 m and shorter. Significance Statement This paper presents low-pass mean square slope (LPMSS) data obtained by spaceborne microwave altimeters and reflectometers operating at L, Ku, and Ka bands (about 1.6, 14, and 36 GHz). The LPMSS data represent the spectrally integrated ocean surface roughness with 11, 95, and 250 rad m−1 upper cutoff wavenumbers, and the maximum wind speeds are 80, 29, and 25 m s−1, respectively. A better understanding of the ocean surface roughness is important to the goal of improving wind wave spectrum modeling that is critical to the investigation of air–sea interaction and ocean remote sensing. The analysis presented in this paper suggests that wave breaking is not only an energy sink but also a generation source of surface roughness covering a wide band of wavelengths about 20 m and shorter.

For how long are particles accelerated in shells of recurrent novae?

ABSTRACT Galactic novae are at present a well established class of γ-ray sources. We wonder for how long the mechanism of acceleration of electrons operates in the shells of novae. In order to put constraints on the time-scale of the electron acceleration, we consider a specific model for the injection and propagation of electrons within the shell of the recurrent nova RS Ophiuchi. We calculate the equilibrium spectra of electrons within the nova shell and the γ-ray fluxes produced by these electrons in the Comptonization of the soft radiation from the red giant within a nova binary system and also radiation from the nova photosphere. We investigate a two-component time-dependent model in which a spherically ejected nova shell propagates freely in the polar region of a nova binary system. However, the shell is significantly decelerated in the dense equatorial region of the binary system. We discuss the conditions under which electrons can produce γ-rays that might be detectable by present and/or future γ-ray observatories. It is concluded that freely expanding shells of novae in the optimal case (strongly magnetized shell and efficiency of acceleration of electrons of the order of 10 per cent) can produce TeV γ-rays within the sensitivity of the Cherenkov Telescope Array within 1–2 yr of explosion only. On the other hand, decelerated shells of novae have a chance to be detected during the whole recurrence period of RS Ophiuchi, i.e. ∼15 yr.

Doping effect on the light absorption and photoluminescence of Ge/Si quantum dots in the infrared spectral range

The results of comprehensive studies of near-infrared photoluminescence and mid-infrared equilibrium and photoinduced absorption spectra in structures with Ge/Si quantum dots with different doping levels at different optical pumping intensities and different temperatures are presented. Obtained dependences of interband photoluminescence spectra on temperature and optical pumping intensity are explained by the change in the intensities of direct and indirect in real space electron-hole recombination in Ge/Si quantum dots. The spectra of equilibrium and photoinduced absorption of polarized mid-infrared radiation demonstrate peaks associated with transitions of holes from the ground and excited states to continuum states above quantum dots and with optical transitions from the ground states to excited ones.

Checking of the condition of transformers and the efficiency of oil regeneration with RVM (return voltage measurement)

Up to now the insulation in HV power transformers has been made from oil/paper therefore the diagnosis of this kind of insulation will be also important in the next forty-fifty years. The lifetime of this equipment strongly depends on the condition of the insulation system. The ageing process of oil/paper insulating systems is a very complex and complicated phenomenon. In order to get a well-supported decision on the further operation of aged transformers, relevant information would be necessary on the condition of the oil-paper insulation. We also know that the oil-paper insulation has almost always inhomogeneous condition considering the temperature, moistening and ageing processes. The classical methods (insulation resistance, loss tangent, etc.) characterise the insulation by single measured value. This single value is not sufficient for relevant characterisation and diagnosis of such a complex system with lots of tons of insulation and with almost always inhomogeneous distribution of temperature, moisture and ageing product. If we measure the polarization spectra in three states (new insulation in equilibrium and uniform polarization spectrum, new insulation with not uniform distribution of polarization spectrum, later reaching again the uniform distributions) the shape of three polarization spectra will be different. Comparing the polarization and classical methods of this three case we can realize that sometimes the “classical single values” are almost the same but the polarization spectra are different. The three response methods provide very practical information about the insulation system (e.g. moisture, ageing). The moistening and accumulation of ageing by-products change the distribution of interfacial polarisation in the range of long time-constants. These promising response methods measure the polarisation distribution in the range of long time-constant (with other words, in the low frequency range). The three test methods were: Return Voltage measurement (RVM), the C and tgδ measurement in range of some tens of mHz to 50 Hz (FDS=Frequency Domain Spectroscopy), and the measurement of DC charging and discharging currents (PDC=polarisation and depolarization currents) up to some thousands of sec. These equivalent methods (RVM, FDS and PDC) are able to follow the changing of condition of insulation contrary to classical methods. Therefore a little bit surprising that until now the convenient standards is missing considering the polarization methods. In an earlier Hungarian research work (Budapest University of Technology) almost all the necessary measurements have been realized, consequently we are in possession of fundamental data considering the polarization methods. This paper would like to show a short review about the RVM technique, the correct interpretation of RVM data and a case study for the checking of the efficiency of the oil reclamation with RVM technique.

Stellar labels for hot stars from low-resolution spectra

We set out to determine stellar labels from low-resolution survey spectra of hot stars, specifically OBA stars with Teff ≳ 7500 K. This fills a gap in the scientific analysis of large spectroscopic stellar surveys such as LAMOST, which offers spectra for millions of stars at R ~ 1800 and covers 3800 Å ≤ λ ≤ 9000 Å. We first explore the theoretical information content of such spectra to determine stellar labels via the Cramér-Rao bound. We show that in the limit of perfect model spectra and observed spectra with signal-to-noise ratio ~50–100, precise estimates are possible for a wide range of stellar labels: not only the effective temperature, Teff, surface gravity, log g, and projected rotation velocity, vsin i, but also the micro-turbulence velocity,vmic, helium abundance, NHe/Ntot, and the elemental abundances [C/H], [N/H], [O/H], [Si/H], [S/H], and [Fe/H]. Our analysis illustrates that the temperature regime of Teff ~ 9500 K is challenging as the dominant Balmer and Paschen line strengths vary little with Teff. We implement the simultaneous fitting of these 11 stellar labels to LAMOST hot-star spectra using the Payne approach, drawing on Kurucz’s ATLAS12/SYNTHE local thermodynamic equilibrium spectra as the underlying models. We then obtain stellar parameter estimates for a sample of about 330 000 hot stars with LAMOST spectra, an increase by about two orders of magnitude in sample size. Among them, about 260 000 have good Gaia parallaxes (ω/σω > 5), and their luminosities imply that ≳95% of them are luminous stars, mostly on the main sequence; the rest are evolved lower luminosity stars, such as hot subdwarfs and white dwarfs. We show that the fidelity of the results, particularly for the abundance estimates, is limited by the systematics of the underlying models as they do not account for nonlocal thermodynamic equilibrium effects. Finally, we show the detailed distribution of vsin i of stars with 8000–15 000 K, illustrating that it extends to a sharp cutoff at the critical rotation velocity, vcrit, across a wide range of temperatures.

N2+fluorescence spectrum of comet C/2016 R2 (PanSTARRS)

Context.N2is rarely found in comets, or when it is present, it is found only in small quantities despite its abundance on the surfaces of different outer Solar System objects. A few comets presented N2+emission lines in their optical spectra. One of them, C/2016 R2, showed an unusually high abundance of this species in 2018, with dozens of bright N2+emission lines. A robust model of the N2+fluorescence in comets would permit us to perform a detailed quantitative analysis of this species and enlarge our comprehension of the surprisingly wide range of N2abundances in comets.Aims.The goal of this work is to provide the necessary tools to interpret N2+spectra. Computing production rates for a cometary species necessitates a good knowledge of the number of molecules located along the line of sight of the spectrometer. This in turn requires a good modeling of the emission spectrum with detailed fluorescence efficiencies for the different bands.Methods.We developed a model based on available laboratory data and new theoretical results relative to the N2+to compute the emission spectrum of this species observed in 8.2m Very Large Telescope high-resolution spectra of comet C/2016 R2. Because of some significant differences between spectra obtained on the nucleus and at a cometocentric distance of about 6000 km, it became apparent that a classic fluorescence equilibrium spectrum could not be used. A synthetic spectrum based on a Monte Carlo method and producing spectra at different times from an initial relative population was developed and compared to our observational data.Results.Our modeling of the cometary N2+emission spectrum satisfactorily fits our observed spectra of comet C/2016 R2, leading to the first modeling at high resolution. Different fluorescence efficiency factors are computed.

Visualizing spinon Fermi surfaces with time-dependent spectroscopy

Quantum simulation experiments have started to explore regimes that are not accessible with exact numerical methods. To probe these systems and enable new physical insights, the need for measurement protocols arises that can bridge the gap to solid-state experiments, and at the same time make optimal use of the capabilities of quantum simulation experiments. Here we propose applying time-dependent photoemission spectroscopy, an established tool in solid-state systems, in cold atom quantum simulators. Concretely, we suggest combining the method with large magnetic field gradients, unattainable in experiments on real materials, to drive Bloch oscillations of spinons, the emergent quasiparticles of spin liquids. We show in exact diagonalization simulations of the one-dimensional $t\text{\ensuremath{-}}J$ model with a single hole that the spinons start to populate previously unoccupied states in an effective band structure, thus allowing us to visualize states invisible in the equilibrium spectrum. The dependence of the spectral function on the time after the pump pulse reveals collective interactions among spinons. In numerical simulations of small two-dimensional systems, spectral weight appears at the ground-state energy at momentum $\mathbf{q}=(\ensuremath{\pi},\ensuremath{\pi})$, where the equilibrium spectral response is strongly suppressed up to higher energies, indicating a possible route toward solving the mystery of the Fermi arcs in the cuprate materials.

Equilibria and condensates in Rossby and drift wave turbulence

We study the thermodynamic equilibrium spectra of the Charney–Hasegawa–Mima (CHM) equation in its weakly nonlinear limit. In this limit, the equation has three adiabatic invariants, in contrast to the two invariants of the 2D Euler or Gross–Pitaevskii equations, which are examples for comparison. We explore how the third invariant considerably enriches the variety of equilibrium spectra that the CHM system can access. In particular we characterise the singular limits of these spectra in which condensates occur, i.e. a single Fourier mode (or pair of modes) accumulate(s) a macroscopic fraction of the total invariants. We show that these equilibrium condensates provide a simple explanation for the characteristic structures observed in CHM systems of finite size: highly anisotropic zonal flows, large-scale isotropic vortices, and vortices at small scale. We show how these condensates are associated with combinations of negative thermodynamic potentials (e.g. temperature).

Emission characteristics and dynamics of neutral, ionic and molecular species in a laser produced CaF2 plasma

The emission characteristics of a laser-ablated calcium fluoride CaF2 plasma have been investigated using time and space optical emission spectroscopy. The plasma-plume was produced by focusing 266 nm, 15 ns pulses from a Nd: YAG laser on a calcium fluoride crystal substrate placed in a vacuum chamber. The emission observed in the plasma region is due to electronic relaxation of excited neutral Ca and F, ionic fragments Ca2+, Ca+ and F+ and molecular features of CaF (A2Π- X2Σ+, B2Σ+- X2Σ+ and C2Π- X2Σ+) band systems. Plasma species were analyzed both as a function of the delay from the laser pulse incidence and location from the target surface. Spectroscopic diagnostics were employed to estimate time-resolved electron densities, electron temperatures and velocity expansion of different species. The results show a faster decay of the continuum emission, ionic F+, Ca2+, Ca+, F species than in the case of neutral Ca atoms and molecular species of CaF. Different excitation temperatures were measured by comparing Ca and F atomic/ionic Saha-local thermodynamic equilibrium (LTE) spectra with experimental ones at various delay times after the ablation event. Vibrational temperatures of CaF were assessed from the temporal analysis of the A2Π - X2Σ+ Δv = 0 band sequence molecular emission. We observed a non-equilibrium plasma although the plasma is found to maintain partial LTE.

Conformational equilibrium, IR and Raman vibrational spectra of the quercetin molecule in different solvents: A comprehensive quantum-chemical investigation

This study represents comprehensive investigation by the quantum-chemical calculations at the MP2/6-311++G(2df,pd)//B3LYP/6-311++G(d,p) level of theory of the conformational equilibrium, IR and Raman vibrational spectra of all 48 conformers of the quercetin molecule in the isolated state (ε=1.0) and various solvents, such as: continuum with ε=4.0, ethanol (ε=24.3), methanol (ε=32.7), DMSO (ε=47.2) and water (ε=80.4). It has been established their characteristic features, which are closely related to the microstructural mechanisms of the biological action of the quercetin molecule. It was shown that, independently from the value of the dielectric constant ε of the solvent, conformational equilibrium of the quercetin molecule is determined by the co-existence of planar structures of conformers 1–8, which population consist 99 % among all 48 conformers. In the IR and Raman vibrational spectra of the conformers of the isolated quercetin molecule it was defined vibrational markers, which enable to determine their belonging to one of the four conformational subfamilies and to precisely identify each of them. It was discussed characteristics of the transformations of the vibrational spectra at the transition of the quercetin molecule into the polar solvents. It was established that altogether quercetin molecule possesses 90 vibrational modes in its vibrational spectra, including low-frequency vibrations (⁓ 4 cm−1) or so-called soft modes. It was established that different solvents lead to the increasing of the intensities of the IR and Raman vibrational spectra. It was solved the task of the detection of the belonging of the conformers of the quercetin molecules to the conformational subfamilies and precise identification each of them by the IR and Raman vibrational portraits. It was analyzed in detail the possibility of the experimental fixation of the conformational equilibrium of the quercetin molecule both in the isolated state and in the polar solutions. Possible applications of the obtained results have been also considered.

Heat Transfer and Entanglement–Non‐Equilibrium Correlation Spectra of Two Quantum Oscillators

AbstractThe non‐equilibrium state of two oscillators with a mutual interaction and coupled to separate heat baths is discussed. Bosonic baths are considered, and an exact spectral representation for the elements of the covariance matrix is provided analytically. A wide class of spectral densities for the relevant bath modes is allowed for. The validity of the fluctuation‐dissipation relation is established for global equilibrium (both baths at the same temperature) in the stationary state. Spectral measures of entanglement are suggested by comparing to the equilibrium spectrum of zero‐point fluctuations. No rotating‐wave approximation is applied, and anomalous heat transport from cold to hot bath, as reported in earlier work, is demonstrated not to occur.