Dissipation Theorem Research Articles

White dwarf eccentricity fluctuation and dissipation by AGB convection

ABSTRACT Millisecond pulsars with white dwarf companions have typical eccentricities $e\sim 10^{-6}{\!-\!}10^{-3}$. The eccentricities of helium white dwarfs are explained well by applying the fluctuation–dissipation theorem to convective eddies in their red giant progenitors. We extend this theory to more massive carbon–oxygen (CO) white dwarfs with asymptotic giant branch (AGB) progenitors. Due to the radiation pressure in AGB stars, the dominant factor in determining the remnant white dwarf’s eccentricity is the critical residual hydrogen envelope mass $m_{\rm env}$ required to inflate the star to giant proportions. Using a suite of mesa stellar evolution simulations with $\Delta m_{\rm c}=10^{-3}\, {\rm M}_{\odot }$ core-mass intervals, we resolved the AGB thermal pulses and found that the critical $m_{\rm env}\propto m_{\rm c}^{-6}$. The resulting eccentricity $e\sim 3\times 10^{-3}$ is almost independent of the remnant CO white dwarf’s mass $m_{\rm c}$. Nearly all of the measured eccentricities lie below this robust theoretical limit, indicating that the eccentricity is damped during the common-envelope inspiral that follows the unstable Roche lobe overflow of the AGB star. Specifically, we focused on white dwarfs with median masses $m_{\rm c}\gt 0.6\, {\rm M}_{\odot }$. These massive white dwarfs begin their inspiral with practically identical orbital periods and eccentricities, eliminating any dependence on the initial conditions. For this sub-sample, we find an empirical relation $e\propto P^{3/2}$ between the final period and eccentricity that is much tighter than previous studies – motivating theoretical work on the eccentricity evolution during the common envelope phase. The eccentricities of lower mass CO white dwarfs may be explained by alternative formation channels.

Highly efficient spectrum-splitting solar energy utilization based on near- and far-field thermophotovoltaics

Improving the efficiency of solar energy utilization systems is of great importance in solar energy utilization. Near-field thermophotovoltaic cells can achieve a high power density and, therefore, efficiently utilize radiative heat transfer. An efficient spectrum-splitting solar energy utilization system based on near- and far-field thermophotovoltaics was proposed. The input solar energy was divided by the splitter, and the two parts of the energy were utilized differently. The concentration ratio can determine the energy input of the system, which can affect the photoelectric conversion efficiency of the system. Further, the vacuum distance can modulate the near-field radiative heat transfer, thus significantly impacting system performance. Based on the fluctuation dissipation theorem and Maxwell's equations, a system model was constructed and calculated using the optimal design method, and the effects of these parameters were investigated. Moreover, the optimal efficiency was obtained under different operating conditions. The optimal cascade system efficiency reached 39.93 % at a concentration ratio of 3000, which was 15.59 % higher than that of a single photovoltaic system. Thus, this study proposes a method for the efficient utilization of solar energy. In addition, it provides guidance for the subsequent design and construction of spectrum-splitting cascade systems based on near- and far-field thermophotovoltaics.

A new method to calculate broadband dielectric spectra of solvents from molecular dynamics simulations demonstrated with polarizable force fields.

Simulating the dielectric spectra of solvents requires the nuanced definition of inter- and intra-molecular forces. Non-polarizable force fields, while thoroughly benchmarked for dielectric applications, do not capture all the spectral features of solvents, such as water. Conversely, polarizable force fields have been largely untested in the context of dielectric spectroscopy but include charge and dipole fluctuations that contribute to intermolecular interactions. We benchmark non-polarizable force fields and the polarizable force fields AMOEBA03 and HIPPO for liquid water and find that the polarizable force fields can capture all the experimentally observed spectral features with varying degrees of accuracy. However, the non-polarizable force fields miss at least one peak. To diagnose this deficiency, we decompose the liquid water spectra from polarizable force fields at multiple temperatures into static and induced dipole contributions and find that the peak originates from induced dipole contributions. Broadening our inquiry to other solvents parameterized with the AMOEBA09 force field, we demonstrate good agreement between the experimental and simulated dielectric spectra of methanol and formamide. To produce these spectra, we develop a new computational approach to calculate the dielectric spectrum via the fluctuation dissipation theorem. This method minimizes the error in both the low and high frequency portions of the spectrum, improving the overall accuracy of the simulated spectrum and broadening the computed frequency range.

Investigation into the thermal noise propagation mechanism within composite materials for gravitational wave detection systems

The thermal transmission properties of polymer-based composites, commonly used in satellites, are crucial for high-precision thermal management applications. The study constructed the structures of polyimide polymers and polyimide/graphene interfaces based on molecular dynamics and fluctuation dissipation theorem. Optical parameters were determined through first-principles calculations, and the thermal transport from a microthermal source was simulated using Reverse Non-Equilibrium Molecular Dynamics (RNEMD) and the modified four-dimensional transfer matrix method (M4D-TMM). Simulations of polymers, interface structures, and interfacial thermal radiation models investigated the transmission dynamics of microthermal sources during heat transport. Findings showed that the differences in the temperature fields formed within the polymer from microthermal heat sources were less than 20 K for heat source inputs ranging from 0.002 W/m² to 20 GW/m². With a microthermal source, the heat diffusion was extensive, the heat transport was continuous, and the temperature field remained stable. At the level of the heat source up to the intermolecular energy level, the temperature field distribution showed significant instability, leading to nonlinear effects. Within the interface structure, the continuity of heat diffusion increased as the heat source intensified. The interface structure demonstrated enhanced temperature sensitivity and improved stability, with minimal fluctuations of only 0.59 %. The increase in heat flux perpendicular to the interface structure was ascribed to near-field radiative heat transfer. As the temperature difference decreased to less than 0.1 K, the influence of evanescent waves on radiative heat flux nearly disappeared. Phonon polaritons maintained temperature stability during thermal transport through micro- and nanoscale gaps. Integrating thermal conduction principles in polyimide polymers and interface structures with near-field thermal radiation provides a theoretical framework for high-precision thermal management in gravitational wave detection.

Turbulence and Rossby Wave Dynamics with Realizable Eddy Damped Markovian Anisotropic Closure

The theoretical basis for the Eddy Damped Markovian Anisotropic Closure (EDMAC) is formulated for two-dimensional anisotropic turbulence interacting with Rossby waves in the presence of advection by a large-scale mean flow. The EDMAC is as computationally efficient as the Eddy Damped Quasi Normal Markovian (EDQNM) closure, but, in contrast, is realizable in the presence of transient waves. The EDMAC is arrived at through systematic simplification of a generalization of the non-Markovian Direct Interaction Approximation (DIA) closure that has its origin in renormalized perturbation theory. Markovian Anisotropic Closures (MACs) are obtained from the DIA by using three variants of the Fluctuation Dissipation Theorem (FDT) with the information in the time history integrals instead carried by Markovian differential equations for two relaxation functions. One of the MACs is simplified to the EDMAC with analytical relaxation functions and high numerical efficiency, like the EDQNM. Sufficient conditions for the EDMAC to be realizable in the presence of Rossby waves are determined. Examples of the numerical integration of the EDMAC compared with the EDQNM are presented for two-dimensional isotropic and anisotropic turbulence, at moderate Reynolds numbers, possibly interacting with Rossby waves and large-scale mean flow. The generalization of the EDMAC for the statistical dynamics of other physical systems to higher dimension and higher order nonlinearity is considered.

Energetics of the dissipative quantum oscillator

In this paper, we discuss some aspects of the energetics of a quantum Brownian particle placed in a harmonic trap, also known as the dissipative quantum oscillator. Based on the fluctuation–dissipation theorem, we analyze two distinct notions of thermally-averaged energy that can be ascribed to the oscillator. These energy functions, respectively dubbed hereafter as the mean energy and the internal energy, are found to be inequivalent for arbitrary system–bath coupling strength when the dissipation kernel has a non-zero memory timescale, as in the case of a Drude bath. Remarkably, both the energy functions satisfy the quantum counterpart of energy equipartition theorem, but with different probability distributions on the frequency domain of the heat bath. Moreover, the Gibbs approach to thermodynamics provides us with yet another thermally-averaged energy function. In the weak-coupling limit, all the above-mentioned energy expressions reduce to ϵ=ħω02coth(ħω02kBT), which is the familiar result. We generalize our analysis to the case of the three-dimensional dissipative charged oscillator placed in a spatially-uniform magnetic field.

Interpreting pore-scale fluctuations: Predicting transport coefficients in multiphase flow through porous media using the Green–Kubo formulation—An experimental investigation

Flow fluctuations that are commonly associated with multiphase flow in porous media are studied using concepts from non-equilibrium thermodynamic and statistical mechanics. We investigate how the Green–Kubo formulation of the fluctuation dissipation theorem can be used to predict the transport coefficient from the two-phase extension of Darcy's law. Flow rate-time series data are recorded at the millisecond timescale using a novel experimental setup that allows for the determination of flow fluctuation statistics. By using Green–Kubo relations, a transport coefficient is predicted based on the integrated autocorrelation function. Notably, this coefficient aligned closely with the total effective phase mobility computed using Darcy's equation for multiphase flow, particularly in scenarios where a linear relationship between flow rate and pressure gradient was observed. Our results open a new field of coefficient explorations where microscale fluctuations during multiphase flow are directly linked to macroscale parameters.

Introduction to dynamical mean-field theory of randomly connected neural networks with bidirectionally correlated couplings

Dynamical mean-field theory is a powerful physics tool used to analyze the typical behavior of neural networks, where neurons can be recurrently connected, or multiple layers of neurons can be stacked. However, it is not easy for beginners to access the essence of this tool and the underlying physics. Here, we give a pedagogical introduction of this method in a particular example of random neural networks, where neurons are randomly and fully connected by correlated synapses and therefore the network exhibits rich emergent collective dynamics. We also review related past and recent important works applying this tool. In addition, a physically transparent and alternative method, namely the dynamical cavity method, is also introduced to derive exactly the same results. The numerical implementation of solving the integro-differential mean-field equations is also detailed, with an illustration of exploring the fluctuation dissipation theorem.

Brownian Particle in a Poisson‐Shot‐Noise Active Bath: Exact Statistics, Effective Temperature, and Inference

AbstractThe dynamics of an overdamped Brownian particle in a thermal bath that contains a dilute solution of active particles is studied. The particle moves in a harmonic potential and experiences Poisson shot‐noise kicks with specified amplitude distribution due to moving active particles in the bath. From the Fokker–Planck equation for the particle dynamics, the stationary solution for the displacement distribution is derived along with the moments characterizing mean, variance, skewness, and kurtosis, as well as finite‐time first and second moments. An effective temperature is also computed through the fluctuation–dissipation theorem and show that equipartition theorem holds for all zero‐mean kick distributions, including those leading to non‐Gaussian stationary statistics. For the case of Gaussian‐distributed active kicks, a re‐entrant behavior from non‐Gaussian to Gaussian stationary states and a heavy‐tailed leptokurtic distribution across a wide range of parameters are found as seen in recent experimental studies. Further analysis reveals statistical signatures of the irreversible dynamics of the particle displacement in terms of the time asymmetry of cross‐correlation functions. Fruits of the work is the development of an compact inference scheme that may allow experimentalists to extract the rate and moments of underlying shot‐noise solely from the statistics the particle position.

Kinetic theory of inhomogeneous systems with long-range interactions and fluctuation–dissipation theorem

Kinetic theory of inhomogeneous systems with long-range interactions and fluctuation–dissipation theorem

Viscoelastic active diffusion governed by nonequilibrium fractional Langevin equations: Underdamped dynamics and ergodicity breaking

In this work, we investigate the active dynamics and ergodicity breaking of a nonequilibrium fractional Langevin equation (FLE) with a power-law memory kernel of the form K(t)∼t−(2−2H), where 1/2<H<1 represents the Hurst exponent. The system is subjected to two distinct noises: a thermal noise satisfying the fluctuation–dissipation theorem and an active noise characterized by an active Ornstein–Uhlenbeck process with a propulsion memory time τA. We provide analytic solutions for the underdamped active fractional Langevin equation, performing both analytical and computational investigations of dynamic observables such as velocity autocorrelation, the two-time position correlation, ensemble- and time-averaged mean-squared displacements (MSDs), and ergodicity-breaking parameters. Our results reveal that the interplay between the active noise and long-time viscoelastic memory effect leads to unusual and complex nonequilibrium dynamics in the active FLE systems. Furthermore, the active FLE displays a new type of discrepancy between ensemble- and time-averaged observables. The active component of the system exhibits ultraweak ergodicity breaking where both ensemble- and time-averaged MSDs have the same functional form with unequal amplitudes. However, the combined dynamics of the active and thermal components of the active FLE system are eventually ergodic in the infinite-time limit. Intriguingly, the system has a long-standing ergodicity-breaking state before recovering the ergodicity. This apparent ergodicity-breaking state becomes exceptionally long-lived as H→1, making it difficult to observe ergodicity within practical measurement times. Our findings provide insight into related problems, such as the transport dynamics for self-propelled particles in crowded or polymeric media.

Viscous QCD medium effects on the bottom quark transport coefficients

The bottom quark transport coefficients, i.e., drag and diffusion coefficients, have been studied for the collisional and soft gluon radiative processes within the viscous QCD medium. The thermal medium effects are incorporated using the effective fugacity quasiparticle model (EQPM). Both the shear and bulk viscous effects at leading order are embedded through the near-equilibrium distribution functions of the quark–gluon plasma (QGP) constituent quasiparticles. The transport coefficients’ dependence on the bottom quark’s initial momentum and QGP temperature have been investigated. The relative dominance of the radiative over the collisional process for the bottom quark seems to occur at a higher initial momentum compared to that of the charm quark. In contrast, the effect of the viscous corrections seems to be more for the charm quark. Furthermore, we also investigate the validity of the Einstein fluctuation–dissipation theorem for our analysis.

Differentiation of Forest Stands by Susceptibility to Folivores: A Retrospective Analysis of Time Series of Annual Tree Rings with Application of the Fluctuation-Dissipation Theorem

This study analyzed the relationship between characteristics of annual tree ring time series and the intensity of attacks on forest stands by forest insects. Using tenets of the fluctuation–dissipation theorem (which is widely used in physics), time series parameters are proposed that can help to assess the susceptibility of a forest stand to insect pests. The proposed approach was applied to evaluate differences in parameters of tree ring widths among outbreaks of the pine looper, Siberian silk moth, and spongy moth. A comparison of trees characteristics between outbreak locations and undamaged forest stands (control) showed that the tested parameters statistically significantly differed between the outbreak locations and control stands and can be used to assess the risk of pest outbreaks in forest stands.

FDT for fluctuations of a special perturbated harmonic oscillator and its application in q-deformed Harmonic Oscillator

Abstract In this paper, we will use fluctuation dissipation theorem on the harmonic oscillator with time correlation creation annihilation operator as the perturbated term and through calculation, we find that the exact value of the dissipation associated Imχ of this special perturbation harmonic oscillator is exactly equal to π. Next, we give its potential application in the q-deformed harmonic oscillator, which means connect the q-deformed harmonic oscillator with fluctuation dissipation.

Noise–dissipation relation for nonlinear electronic circuits

An extension of fluctuation–dissipation theorem is used to derive a “speed limit” theorem for nonlinear electronic devices. This speed limit provides a lower bound on the dissipation that is incurred when transferring a given amount of electric charge in a certain amount of time with a certain noise level (average variance of the current). This bound, which implies a high energy dissipation for fast, low-noise operations (such as switching a bit in a digital memory), brings together recent results of stochastic thermodynamics into a form that is usable for practical nonlinear electronic circuits, as we illustrate on a switching circuit made of an nMOS pass gate in a state-of-the-art industrial technology.

Reentry vehicle friction heat estimated by means of Boltzmann integral-differential equation of fluctuation-dissipation theory

We begin with Atmosphere Einstein Brownian motions toward Knudsen Gas Boltzmann Kinetic formulism of the fluctuation-dissipation theory and applied the formulism to space travelers reentry vehicles. Early experimental results are estimated on the worst situation upper bound when a reentry vehicle is frictionally passing through a dense atmosphere. In reality, the vehicle has spent more time in a dilute atmosphere space. Accordingly, the fluctuation and dissipation theorem, derived from the Boltzmann kinetic equation, predicted a much less friction heat than the final reentry stage.

Threshold Pressure in Non-Darcian Flow Derived from the Langevin Equation and Fluctuation Dissipation Theorem: Generalized Darcy’s Law

Threshold Pressure in Non-Darcian Flow Derived from the Langevin Equation and Fluctuation Dissipation Theorem: Generalized Darcy’s Law

First-principles study of electronic and optical properties of novel 2D TiOS monolayer and bilayer—Dimensionality reduction opens up a band gap in TiOS

The finding of advanced functional materials with superior properties to existing ones to develop cutting-edge technologies for societal advancement is indispensable. We identify a new two-dimensional (2D) TiOS, which opens up a band gap due to the lowering of the dimensionality employing first-principles computations within the framework of density functional theory (DFT) and beyond. Electronic structure estimations reveal that bulk TiOS is metal whereas the 2D-TiOS possesses a band gap of ∼4.5 eV within GW approximation, which is higher than the band gap of 2D-InOF and 2D transition metal dichalcogenides. The computed phonon dispersion curves show that the 2D-TiOS is dynamically stable. The 2D-TiOS has a very high absorption coefficient in the 0–50 eV. Third-order elastic constants (TOECs) of this 2D-TiOS are achieved using DFT and within the adiabatic-connection fluctuation–dissipation theorem in the random phase approximation. Surprisingly, we find a band overlap, indicating that TiOS/TiOS bilayer is a metal. If the incident light frequency surpasses the plasma frequency (60.00 eV), and then the bilayer turns out to be transparent. Our findings suggest that this 2D sheet is a promising alternative for nanotechnology and optoelectronic devices.

Variation of Spring Stiffness, Monomeric Friction, and Brownian Intensity in the Simulation System of Unentangled Melt under Steady Flow

Understanding the nonlinear dynamics of an unentangled polymer melt from the bead-spring chain model requires knowledge of the variation of spring stiffness, monomeric friction, and Brownian intensity. In this work, these nonequilibrium (NE) parameters are quantified in the model simulation systems of unentangled melt under steady-flow conditions. We focus on a particular version of the model with undefined NE parameters. Some expressions to relate the NE parameters with the rheological and structural properties are pointed out. The spring stiffening parameter rκ is proven to be easily accessible in the planar flows. The distribution of the stiffening effect along the polymer contour is identified. The alignment-induced reduction of monomeric friction is confirmed in the simulation systems, but the anisotropic feature of friction is also emphasized. The constraint on the cooperative variation of spring stiffness and friction is proven to be an important property of extensional flow. The variation of Brownian intensity is found to be decoupled with the variation of friction, which means the violation of the fluctuation–dissipation (FD) theorem. The NE parameters of the simulation systems are further compared with those from the experimental systems.

On the link between mechanics and thermal properties: mechanothermics

We report on the theoretical derivation of macroscopic thermal properties (specific heat, thermal conductivity) of an electrically insulating rod connected to two reservoirs, from the linear superposition of its mechanical mode Brownian motions. The calculation is performed for a weak thermal gradient, in the classical limit (high temperature). The development is kept basic as far as geometry and experimental conditions are concerned, enabling an almost fully analytic treatment. In the modeling, each of the modes is subject to a specific Langevin force, which enables to produce the required temperature profile along the rod. The theory is predictive: the temperature gradient (and therefore energy transport) is linked to motion amplitude cross-correlations between nearby mechanical modes. This arises because energy transport is actually mediated by mixing between the modal waves, and not by the modes themselves. This result can be tested on experiments, and shall extend the concepts underlying equipartition and fluctuation–dissipation theorems. The theory links intimately the macroscopic size of the clamping region where the mixing occurs to the microscopic lengthscale of the problem at hand: the phonon mean-free-path. This clamping region, which is key, has received recently a renewed attention in the field of nanomechanics with topical works on ‘phonon shields’ and ‘soft clamping’. We believe that our work should impact the domain of thermal transport in nanostructures, with future developments of the theory toward the quantum regime.