Heat Bath Temperature Research Articles

The intrinsic switching field of single domain ferromagnetic particles

The intrinsic switching field defined as the minimum field to induce spontaneous magnetic reversal is calculated at finite temperatures for a uniaxially anisotropic single domain particle using a formalism based on the generalized free energy function of the system. For a fine ferromagnetic particle coupled to a constant temperature heat bath, the switching field is smaller than the field predicted by the Stoner-Wohlfarth (SW) theory and the difference is dependent on the direction of the applied field resulting in breaking of the symmetry of the SW astroid.

Demonstration of a Full-Scale Brassboard TES Microcalorimeter Array for the Athena X-IFU

We have characterized a full-scale transition-edge sensor (TES) microcalorimeter array as a milestone towards the demonstration of technology readiness level (TRL) 5 for the detector array for the X-ray Integral Field Unit (X-IFU) instrument on ESA's future flagship X-Ray Observatory called Athena. We fabricated a 90 mm full-scale prototype TES array and measured the properties and the performance in a newly developed platform in which up to 960 out of ∼3,200 pixels can be read out. In this paper, we report on measurements of the uniformity of the transition temperature and shape, the uniformity of the spectral energy resolutions at 7 keV and 10 keV, the thermal crosstalk for the first, the diagonal, and the second nearest neighbors, and the energy sensitivities to environment perturbations for the magnetic field, the TES bias voltage, and the heat bath temperature.

Quantum advantage in variational Bayes inference

Variational Bayes (VB) inference algorithm is used widely to estimate both the parameters and the unobserved hidden variables in generative statistical models. The algorithm-inspired by variational methods used in computational physics-is iterative and can get easily stuck in local minima, even when classical techniques, such as deterministic annealing (DA), are used. We study a VB inference algorithm based on a nontraditional quantum annealing approach-referred to as quantum annealing variational Bayes (QAVB) inference-and show that there is indeed a quantum advantage to QAVB over its classical counterparts. In particular, we show that such better performance is rooted in key quantum mechanics concepts: i) The ground state of the Hamiltonian of a quantum system-defined from the given data-corresponds to an optimal solution for the minimization problem of the variational free energy at very low temperatures; ii) such a ground state can be achieved by a technique paralleling the quantum annealing process; and iii) starting from this ground state, the optimal solution to the VB problem can be achieved by increasing the heat bath temperature to unity, and thereby avoiding local minima introduced by spontaneous symmetry breaking observed in classical physics based VB algorithms. We also show that the update equations of QAVB can be potentially implemented using ⌈logK⌉ qubits and 𝒪(K) operations per step, where K is the number of values hidden categorical variables can take. Thus, QAVB can match the time complexity of existing VB algorithms, while delivering higher performance.

Characterization of local non-equilibrium phonons in bulk MoS2 probed by temperature-dependent Raman scattering

This study presents an experimental implementation to determine the temperature dependence of Raman spectra of bulk 2H-MoS2 in the temperature range of 300–650 K. In addition, we have measured according to the anti-Stokes to Stokes integrated intensity ratio (). The results indicate that Raman shift of both the vibration modes and exhibits a linear temperature-dependent behavior in the heating and cooling processes. It is confirmed that the sample did not deteriorate by oxidization and decomposition at high temperatures. However, above 500 K, the measured phonon temperature deviated from the heat bath temperature. It is suggested that the does not correspond to the equilibrium population of optical phonons, thus indicating that the measurement was not in thermal equilibrium but in a thermal steady state under laser irradiation. We conclude that this is caused by the difference in relaxation times in the thermal steady state.

Modeling heat bath and probing environmental temperature effect in gene expression

Modeling heat bath and probing environmental temperature effect in gene expression

Non-Additive Entropy Composition Rules Connected with Finite Heat-Bath Effects.

Mathematical generalizations of the additive Boltzmann-Gibbs-Shannon entropy formula have been numerous since the 1960s. In this paper we seek an interpretation of the Rényi and Tsallis q-entropy formulas single parameter in terms of physical properties of a finite capacity heat-bath and fluctuations of temperature. Ideal gases of non-interacting particles are used as a demonstrating example.

Numerical Simulation to Predict the Effect of Process Parameters on Hardness during Martempering of AISI4140 Steel

Martempering is a widely practiced industrial heat treatment process to harden steel parts with minimum distortion. A numerical experiment to predict hardness distribution in AISI 4140 steel cylinders of various diameters during martempering is presented in this work. Apart from the diameter (D), the effect of other process variables such as heat transfer coefficient (h), bath temperature (Tb), and residence time (tr) was also studied. The relationship between hardness distribution and the aforementioned process variables was highly nonlinear. An artificial neural network (ANN) model with a single hidden layer and 30 hidden layer neurons was thus developed to predict the hardness distribution in martempered AISI 4140 steel cylinders. The increase in bath temperature, diameter, and residence time decreased the average hardness, and an increase in the heat transfer coefficient increased the average hardness of martempered AISI 4140 cylinders. The weights of the ANN model were used to calculate the relative importance of all input variables and they followed a decreasing order of Tb>D>tr>h.

Quantum state transmission through a spin chain in finite-temperature heat baths

Transmission of a quantum state is essential for performing quantum information processing tasks. The communication channel will be inevitably immersed in its surrounding environment under realistic conditions. In this paper, we investigate the influence of environment noise on the transmission fidelity when transferring a quantum state through a spin chain. The non-Markovian open system dynamics is systematically analyzed by using the quantum state diffusion equation method. With each spin immersed in its own finite temperature and non-Markovian heat bath, we consider three types of system–bath interaction: dephasing, dissipation and spin-boson. The transmission fidelity is found to decrease with the increasing bath temperature and system–bath coupling strength. Interestingly, we find that the bath non-Markovianity can help enhancing the transmission fidelity.

Numerically “exact” simulations of entropy production in the fully quantum regime: Boltzmann entropy vs von Neumann entropy

We present a scheme to evaluate thermodynamic variables for a system coupled to a heat bath under a time-dependent external force using the quasi-static Helmholtz energy from the numerically "exact" hierarchical equations of motion (HEOM). We computed the entropy produced by a spin system strongly coupled to a non-Markovian heat bath for various temperatures. We showed that when changes to the external perturbation occurred sufficiently slowly, the system always reached thermal equilibrium. Thus, we calculated the Boltzmann entropy and the von Neumann entropy for an isothermal process, as well as various thermodynamic variables, such as changes in internal energies, heat, and work, for a system in quasi-static equilibrium based on the HEOM. We found that although the characteristic features of the system entropies in the Boltzmann and von Neumann cases as a function of the system-bath coupling strength are similar, those for the total entropy production are completely different. The total entropy production in the Boltzmann case is always positive, whereas that in the von Neumann case becomes negative if we chose a thermal equilibrium state of the total system (an unfactorized thermal equilibrium state) as the initial state. This is because the total entropy production in the von Neumann case does not properly take into account the contribution of the entropy from the system-bath interaction. Thus, the Boltzmann entropy must be used to investigate entropy production in the fully quantum regime. Finally, we examined the applicability of the Jarzynski equality.

Fokker-Planck equation for Coulomb relaxation and wave-particle diffusion: Spectral solution and the stability of the Kappa distribution to Coulomb collisions.

The present paper considers the time evolution of a charged test particle of mass m in a constant temperature heat bath of a second charged particle of mass M. The time dependence of the distribution function of the test particles is given by a Fokker-Planck equation with a diffusion coefficient for Coulomb collisions as well as a diffusion coefficient for wave-particle interactions. For the mass ratio m/M→0, the steady distribution is a Kappa distribution which has been employed in space physics to fit observed particle energy spectra. The time dependence of the distribution functions with some initial value is expressed in terms of the eigenvalues and eigenfunctions of the linear Fokker-Planck operator and also interpreted with the transformation to a Schrödinger equation. We also consider the explicit time dependence of the distribution function with a discretization of the Fokker-Planck equation. We study the stability of the Kappa distribution to Coulomb collisions.

Temperature–energy-space sampling molecular dynamics: deterministic and single-replica method utilizing continuous temperature system

For enhanced sampling of physical system (PS) states, we utilized the coupled Nosé–Hoover (NH) molecular dynamics equations of motion (EOM), wherein the heat-bath temperature for the PS fluctuates according to an arbitrary predetermined weight. The coupled NH is defined by suitably combining the NH EOM of the PS and the NH EOM of the temperature system (TS), where the inverse heat-bath temperature β is a dynamical variable. In this study, we developed a method to determine the effective weight for β for enhanced sampling of PS states. The method, based on ergodic theory, is reliable, and eliminates the need for time-consuming iterative procedures and resource-consuming replica systems. The resulting TS potential in a two dimensional (β, ϵ)-space makes a valley-shape, where the potential minimum path provides a route for β and ϵ and guides their motions. β oscillates around the potential minima for each energy ϵ, and the motion of β derives a motion of ϵ and receives the ϵ’s feedback, which leads to a mutual boost effect. Thus, it also provides a specific dynamical mechanism to explain the features of enhanced sampling such that the temperature-space ‘random walk’ enhances the energy-space ‘random walk.’ These mutual dynamics between β and ϵ naturally arise from the static probability theory formalism of double density dynamics that was previously developed, where the Liouville equation with an arbitrarily given probability density function is the fundamental polestar. Numerical examples using a model system and explicitly solvated protein system verify the reliability and simplicity of the method.

Probing the dynamics of an open quantum system via a single qubit

We investigate strategies to monitor the dynamics and determine the characteristics of a dissipative harmonic oscillator coupled to a finite temperature heat bath. For this purpose we use a single qubit coupled via dephasing to the oscillator. The whole system is described by a quantum master equation, which can be solved analytically. The solution is surprisingly simple and allows one to read off all relevant parameters from the behavior of the qubit coherence as a function of time. Analyzing the qubit coherence for a short time, turns out to be sufficient to predict the complete dynamics of the oscillator, including its asymptotic state at thermal equilibrium.

Optimal Control of an Endoreversible Solar Power Plant

AbstractWhile in the classic Curzon–Ahlborn and Novikov engines the temperatures of the heat baths are kept fixed or follow a deterministic time function, it is the aim of this work to study the impact of fluctuating heat bath temperatures. As an example serves a solar power plant, where the stochastically varying cloud cover leads to fluctuations in the temperature of the hot heat bath. This solar thermal power plant is modeled as a stochastic endoreversible system. On the basis of this model the maximum expected work output of the power plant and the corresponding optimal control policy is derived. For the considered system it is found that the maximum expected work output changes with the reversion speed of the hot temperature depending on the relation of the starting hot temperature and the temperature of the power plant’s receiver. Additionally, it is found that the maximum expected work output increases with the hot temperature’s fluctuation strength.

Stochastic Novikov engine with time dependent temperature fluctuations

In this article a Stochastic Novikov engine is used to model a solar power plant. This heat engine is characterized by a fluctuating hot heat bath temperature. The distribution function of these fluctuations is derived based on a stochastic solar irradiation model. Using this distribution the control problem of determining the maximum of the expected work output is solved. This work output as well as the corresponding efficiency is deduced in dependence of the chosen control type. Considering this work output and this efficiency, which can be considered as performance measures of the solar power plant, the influence of the system parameters is discussed. It turns out that these performance measures increase monotonously with the parameter of the hot temperature’s distribution function and that more control leads to higher efficiencies.

Influencing factors of viscosity measurement by rotational method

Rotational rheometer was used to measure the shear viscosity of a liquid reference material of viscosity named GBW13604. The influences of heat balance time, bath temperature, environment temperature and sampling volume on results of measurements were investigated. Furthermore, a comparison of accuracy and repeatability of shear viscosity results between two commonly used systems with cone–plate and coaxial cylinder geometry was performed. Rheological tests indicate that the coaxial cylinder method is applicable to tests requiring high accuracy, while the cone-plate method is suitable for measurements that demand low sampling volume and fast speed.

Kappa and other nonequilibrium distributions from the Fokker-Planck equation and the relationship to Tsallis entropy.

This paper considers two nonequilibrium model systems described by linear Fokker-Planck equations for the time-dependent velocity distribution functions that yield steady state Kappa distributions for specific system parameters. The first system describes the time evolution of a charged test particle in a constant temperature heat bath of a second charged particle. The time dependence of the distribution function of the test particle is given by a Fokker-Planck equation with drift and diffusion coefficients for Coulomb collisions as well as a diffusion coefficient for wave-particle interactions. A second system involves the Fokker-Planck equation for electrons dilutely dispersed in a constant temperature heat bath of atoms or ions and subject to an external time-independent uniform electric field. The momentum transfer cross section for collisions between the two components is assumed to be a power law in reduced speed. The time-dependent Fokker-Planck equations for both model systems are solved with a numerical finite difference method and the approach to equilibrium is rationalized with the Kullback-Leibler relative entropy. For particular choices of the system parameters for both models, the steady distribution is found to be a Kappa distribution. Kappa distributions were introduced as an empirical fitting function that well describe the nonequilibrium features of the distribution functions of electrons and ions in space science as measured by satellite instruments. The calculation of the Kappa distribution from the Fokker-Planck equations provides a direct physically based dynamical approach in contrast to the nonextensive entropy formalism by Tsallis [J. Stat. Phys. 53, 479 (1988)JSTPBS0022-471510.1007/BF01016429].

Calibration and energy measurement of optically levitated nanoparticle sensors.

Optically levitated nanoparticles offer enormous potential for precision sensing. However, as for any other metrology device, the absolute measurement performance of a levitated-particle sensor is limited by the accuracy of the calibration relating the measured signal to an absolute displacement of the particle. Here, we suggest and demonstrate calibration protocols for levitated-nanoparticle sensors. Our calibration procedures include the treatment of anharmonicities in the trapping potential, as well as a protocol using a harmonic driving force, which is applicable if the sensor is coupled to a heat bath of unknown temperature. Finally, using the calibration, we determine the center-of-mass temperature of an optically levitated particle in thermal equilibrium from its motion and discuss the optimal measurement time required to determine the said temperature.

Novikov Engine with Fluctuating Heat Bath Temperature

Abstract The Novikov engine is a model for heat engines that takes the irreversible character of heat fluxes into account. Using this model, the maximum power output as well as the corresponding efficiency of the heat engine can be deduced, leading to the well-known Curzon–Ahlborn efficiency. The classical model assumes constant heat bath temperatures, which is not a reasonable assumption in the case of fluctuating heat sources. Therefore, in this article the influence of stochastic fluctuations of the hot heat bath’s temperature on the optimal performance measures is investigated. For this purpose, a Novikov engine with fluctuating heat bath temperature is considered. Doing so, a generalization of the Curzon–Ahlborn efficiency is found. The results can help to quantify how the distribution of fluctuating quantities affects the performance measures of power plants.

Uncertainty contribution on the density of liquids due to unknown sinker temperature in hydrostatic weighing apparatus

In this study, the influence of the unknown sinker temperature on the measured density of liquids is evaluated. Generally, due to the intrinsic temperature instability of the heat bath temperature controller, the system will never reach thermal equilibrium but instead will oscillate around a mean temperature. The sinker temperature follows this temperature oscillation with a certain time lag. Since the sinker temperature is not measured directly in a hydrostatic weighing apparatus, the temperature of the sinker, and thus in turn the volume of the sinker, is not known exactly. As a consequence, this leads to uncertainty in the value of the density of the liquid. From an analysis of the volume relaxation of the sinker immersed into a heat bath with time-dependent temperature characteristics, the heat transfer coefficient can be estimated, and thus a characteristic time constant for achieving quasi thermal equilibrium for a hydrostatic weighing apparatus is proposed. Additionally, from a theoretical analysis of the transient behavior of the sinker volume, the systematic deviation of the theoretical to the actual measured liquid density is calculated.

Performance Features of a Stationary Stochastic Novikov Engine.

In this article a Novikov engine with fluctuating hot heat bath temperature is presented. Based on this model, the performance measure maximum expected power as well as the corresponding efficiency and entropy production rate is investigated for four different stationary distributions: continuous uniform, normal, triangle, quadratic, and Pareto. It is found that the performance measures increase monotonously with increasing expectation value and increasing standard deviation of the distributions. Additionally, we show that the distribution has only little influence on the performance measures for small standard deviations. For larger values of the standard deviation, the performance measures in the case of the Pareto distribution are significantly different compared to the other distributions. These observations are explained by a comparison of the Taylor expansions in terms of the distributions’ standard deviations. For the considered symmetric distributions, an extension of the well known Curzon–Ahlborn efficiency to a stochastic Novikov engine is given.