有限温度下一维Gaudin-Yang模型的热力学性质

本文通过数值求解有限温度下一维均匀费米Gaudin-Yang模型的热力学Bethe-ansatz方程, 研究了此模型的基本性质,得到了在给定的温度或给定的相互作用下, 化学势、相互作用、粒子密度和熵的相互变化图像. 对结果分析发现, 在给定温度和相互作用下, 熵随着化学势的变化有一个量子临界区域.     

Study of thermal fluctuations in five-dimensional rotating regular black hole

In this paper, we discuss the effects of thermal fluctuations on thermodynamics of rotating regular black hole in five-dimensional spacetime. We first evaluate thermodynamic quantities such as Hawking temperature, entropy, angular velocity and electric potential of the considered model. To discuss the effects of thermal fluctuations, we compute the logarithmic correction terms to entropy around the equilibrium state. We also check the validity of the first law of thermodynamics in the presence of these correction terms. Finally, we determine stability of the system through specific heat and Hessian matrix. It is concluded that logarithmic corrections originated from thermal fluctuations yield a stable model.     

Phase transition and thermodynamics of thorium from first-principles calculations

We report on the first-principles study of the phase transition and thermodynamic properties of the thorium metal (Th) within the framework of quasiharmonic approximation. The structural properties of Th under pressure are well reproduced. It is found that the fcc–bct phase transition occurs at 70 GPa. Based on our calculated phonon dispersion curve that is in good agreement with experiment, the thermal equation of state and thermodynamic properties, such as thermal pressure, heat capacity and entropy are obtained. All the properties of Th under high pressure and high temperature are predicted successfully.     

Thermodynamic properties of electron gas in complex-shaped quantum well

Thermodynamic properties of degenerate two-dimensional electron gas in complex-shaped quantum well are studied. We determine the equation of state, chemical potential, entropy and heat capacity of the electron gas. An influence of profile and parameters of the quantum well on thermodynamic characteristics are investigated.     

Impact of Thermal Fluctuations on Logarithmic Corrected Massive Gravity Charged Black Hole

We investigate the influence of the first-order correction of entropy caused by thermal quantum fluctuations on the thermodynamics of a logarithmic corrected charged black hole in massive gravity. For this black hole, we explore the thermodynamic quantities, such as entropy, Helmholtz free energy, internal energy, enthalpy, Gibbs free energy and specific heat. We discuss the influence of the topology of the event horizon, dimensions and nonlinearity parameter on the local and global stability of the black hole. As a result, it is found that the holographic dual parameter vanishes. This means that the thermal corrections have no significant role to disturb the holographic duality of the logarithmic charged black hole in massive gravity, although the thermal corrections have a substantial impact on the thermodynamic quantities in the high-energy limit and the stability conditions of black holes.     

A Thermodynamic Approach to Measuring Entropy in a Few-Electron Nanodevice

The entropy of a system gives a powerful insight into its microscopic degrees of freedom; however, standard experimental ways of measuring entropy through heat capacity are hard to apply to nanoscale systems, as they require the measurement of increasingly small amounts of heat. Two alternative entropy measurement methods have been recently proposed for nanodevices: through charge balance measurements and transport properties. We describe a self-consistent thermodynamic framework for applying thermodynamic relations to few-electron nanodevices—small systems, where fluctuations in particle number are significant, whilst highlighting several ongoing misconceptions. We derive a relation (a consequence of a Maxwell relation for small systems), which describes both existing entropy measurement methods as special cases, while also allowing the experimentalist to probe the intermediate regime between them. Finally, we independently prove the applicability of our framework in systems with complex microscopic dynamics—those with many excited states of various degeneracies—from microscopic considerations.     

Band structure and thermodynamic potentials

The behavior of different thermodynamic functions of a system of delocalized electrons in a crystal is considered in the single-band strong coupling approximation depending on the degree of energy band filling and temperature. The chemical potential, grand thermodynamic potential, internal energy, free energy, entropy, and heat capacity are numerically calculated. Dependences of these quantities on the electron concentration at high temperatures are investigated. Their limited energy spectrum leads to the special features in the behavior of these quantities in comparison with the free electron gas.     

Thermodynamics of electron-hole liquids in graphene

The impact of Coulomb interactions on the chemical potential, heat capacity, and oscillating magnetic moment is studied. The cases of low and high temperatures are considered. At low temperatures, doped graphene behaves as the common Fermi liquids with the power temperature laws for thermodynamic properties. However, at high temperatures and relatively low carrier concentrations, it exhibits the collective electron-hole behavior: the chemical potential tends to its value in the undoped case going with the temperature to the charge neutrality point. Simultaneously, the electron contribution into the heat capacity tends to the constant value as in the case of the Boltzmann statistics.     

常压下固态KNO2热力学性质的密度泛函理论研究

采用密度泛函理论结合准谐德拜模型研究常压下300~725 K间KNO₂立方结构的热力学性质,重点分析常压下定压热容、定容热容、熵、德拜温度、体膨胀系数、平衡体积和体弹模量随温度的变化.结果显示,常压下计算的定压热容随温度的变化与实验数据符合较好,而计算的熵与实验数据相差较大.计算得到KNO₂的平均体膨胀系数约为1.837 8×10^-5K^-1,常温下(300 K)KNO₂的德拜温度约为667.13K.     

Partitioning Entropy with Action Mechanics: Predicting Chemical Reaction Rates and Gaseous Equilibria of Reactions of Hydrogen from Molecular Properties

Our intention is to provide easy methods for estimating entropy and chemical potentials for gas phase reactions. Clausius’ virial theorem set a basis for relating kinetic energy in a body of independent material particles to its potential energy, pointing to their complementary role with respect to the second law of maximum entropy. Based on this partitioning of thermal energy as sensible heat and also as a latent heat or field potential energy, in action mechanics we express the entropy of ideal gases as a capacity factor for enthalpy plus the configurational work to sustain the relative translational, rotational, and vibrational action. This yields algorithms for estimating chemical reaction rates and positions of equilibrium. All properties of state including entropy, work potential as Helmholtz and Gibbs energies, and activated transition state reaction rates can be estimated, using easily accessible molecular properties, such as atomic weights, bond lengths, moments of inertia, and vibrational frequencies. We conclude that the large molecular size of many enzymes may catalyze reaction rates because of their large radial inertia as colloidal particles, maximising action states by impulsive collisions. Understanding how Clausius’ virial theorem justifies partitioning between thermal and statistical properties of entropy, yielding a more complete view of the second law’s evolutionary nature and the principle of maximum entropy. The ease of performing these operations is illustrated with three important chemical gas phase reactions: the reversible dissociation of hydrogen molecules, lysis of water to hydrogen and oxygen, and the reversible formation of ammonia from nitrogen and hydrogen. Employing the ergal also introduced by Clausius to define the reversible internal work overcoming molecular interactions plus the configurational work of change in Gibbs energy, often neglected; this may provide a practical guide for managing industrial processes and risk in climate change at the global scale. The concepts developed should also have value as novel methods for the instruction of senior students.     

Thermodynamic effects of Bardeen black hole surrounded by perfect fluid dark matter under general uncertainty principle

The thermodynamics of Bardeen black hole surrounded by perfect fluid dark matter is investigated. We calculate the analytical expresses of corresponding thermodynamic variables, e.g., the Hawking temperature, entropy of the black hole. In addition, we derive the heat capacity to analyze the thermal stability of the black hole. We also compute the rate of emission in terms of photons through tunneling. By numerical method, an obvious phase transition behavior is found. Furthermore, according to the general uncertainty principle, we study the quantum corrections to these thermodynamic quantities and obtain the quantum-corrected entropy containing the logarithmic term. Lastly, we investigate the effects of the magnetic charge g, the dark matter parameter k and the generalized uncertainty principle parameter α on the thermodynamics of Bardeen black hole surrounded by perfect fluid dark matter under general uncertainty principle.     

Transport Properties of a Modified Lorentz Gas

We present a detailed study of the first simple mechanical system that shows fully realistic transport behavior while still being exactly solvable at the level of equilibrium statistical mechanics. The system under consideration is a Lorentz gas with fixed freely-rotating circular scatterers interacting with point particles via perfectly rough collisions. Upon imposing a temperature and/or a chemical potential gradient, a stationary state is attained for which local thermal equilibrium holds for low values of the imposed gradients. Transport in this system is normal, in the sense that the transport coefficients which characterize the flow of heat and matter are finite in the thermodynamic limit. Moreover, the two flows are non-trivially coupled, satisfying Onsager's reciprocity relations to within numerical accuracy as well as the Green–Kubo relations. We further show numerically that an applied electric field causes the same currents as the corresponding chemical potential gradient in first order of the applied field. Puzzling discrepancies in higher order effects (Joule heating) are also observed. Finally, the role of entropy production in this purely Hamiltonian system is shortly discussed.     

Negative heat capacity of Ar55 cluster

The solid–liquid phase transitions of Ar₅₅ cluster was simulated by the microcanonical molecular dynamics and microcanonical parallel tempering methods using Lennard–Jones potential, and thermodynamic quantities were calculated. The caloric curve of cluster has S-bend. To understand this behaviour, configurational and total entropies were evaluated, and the dents on the entropy curves were noticed as the sign of negative heat capacity. The heat capacities were evaluated by using configurational entropy data. The potential energy distributions have bimodal behaviour in the given range at the melting temperature. At the same time by using configurational entropy canonical caloric curve and canonical heat capacity were calculated. To obtain entropy change upon melting, total entropy were calculated from the caloric curve. The microcanonical results melting temperature, latent heat and entropy change upon melting values were reported and compared with the values reported in the literature and the values calculated from the thermodynamic relations offered for bulk matter, consistent values were found.     

Gel–liquid crystal phase transition in dry and hydrated SOPC phospholipid studied by differential scanning calorimetry

We study the thermodynamic properties of pure and hydrated samples of SOPC (stearoyl-2-oleoyl-sn-glycero-3-phosphocholine) membrane via Differential Scanning Calorimetry. We estimate the fundamental thermodynamic quantities, such as enthalpy and entropy, of the bilayer phosphatidylcholine. It is found that the gel-liquid crystal phase transition is driven by the van’t Hoff enthalpy, revealing the occurrence of an intermediate phase transition. We discuss the influence of the heating rate on the enthalpy and on the gel ? liquid crystal phase transition temperature by introducing the adequate thermodynamic Gibbs potential. The effect of hydrogen bonding of the water molecules with the polar head and polar-apolar interface on the energetics of the bilayer membrane matrix is analysed. The obtained transition temperature was found to vary between 3 and 4°C depending on the hydration level. A result corroborated by the behaviour of the heat capacity of SOPC computed via Molecular dynamics simulation.     

高温高压下闪锌矿相GaN结构和热力学特性的分子动力学研究

利用分子动力学方法和Buckingham经验势模型对重要半导体材料GaN立方闪锌矿相的晶格常数、相变压力(从闪锌矿到岩盐结构)、热膨胀、等温体模量、定压热容等结构和热力学特性在300—3000K的温度范围和0—65GPa的压力范围内进行了研究.研究表明，闪锌矿相GaN常态下的结构和热力学参数的模拟结果与实验数据及其他理论结果相符.同时在所选作用势模型可靠性检验的基础上，对等温体模量、定压热容诸非谐性参量在高温高压下的热力学行为进行了预测.所得结果在材料科学等领域的研究中具有一定的应用背景和参考价值. 关键词： GaN Buckingham势 分子动力学模拟 高温高压     

A core-softened fluid model in disordered porous media. Grand canonical Monte Carlo simulation and integral equations

We have studied the microscopic structure and thermodynamic properties of a core-softened fluid model in disordered matrices of Lennard-Jones particles by using grand canonical Monte Carlo simulation. The dependence of density on the applied chemical potential (adsorption isotherms), pair distribution functions, as well as the heat capacity in different matrices are discussed. The microscopic structure of the model in matrices changes with density similar to the bulk model. Thus one should expect that the structural anomaly persists at least in dilute matrices. The region of densities for the heat capacity anomaly shrinks with increasing matrix density. This behavior is also observed for the diffusion coefficient on density from independent molecular dynamics simulation. Theoretical results for the model have been obtained by using replica Ornstein-Zernike integral equations with hypernetted chain closure. Predictions of the theory generally are in good agreement with simulation data, except for the heat capacity on fluid density. However, possible anomalies of thermodynamic properties for the model in disordered matrices are not captured adequately by the present theory. It seems necessary to develop and apply more elaborated, thermodynamically self-consistent closures to capture these features.     

First-principles calculation of structural stability,lattice dynamic and thermodynamic properties of BeX (X = S,Se and Te) compounds under high pressure

The phase transitions, lattice dynamical and thermodynamic properties of BeS, BsSe and BeTe at high pressure have been investigated with the density functional theory. The calculated equilibrium structural parameters agree well with the available experimental and theoretical values. The phase transition pressures from the zinc-blende (ZB) to the nickel arsenide (NiAs) phase of these compounds are determined. The calculated phonon dispersion curves of these compounds in ZB phase at zero pressure do not show any anomaly or instability. Dynamically, the ZB phase of BeS, BeSe and BeTe is found to be stable near transition pressures P_T. Within the quasiharmonic approximation, the thermodynamic properties including the thermal expansion coefficient, heat capacity at constant volume, heat capacity at constant pressure and entropy are predicted.     

磁场中非广延相对论费米系统的统计性质

基于广义外势中的非广延统计理论,运用理论解析与数值模拟方法,研究磁场中非广延极端相对论费米气体的热力学性质,给出总能、热容量、化学势的解析式,分析非广延参数、极端相对论效应、磁场及温度对系统热力学性质的影响机理.研究显示,非广延参数不仅对热力学性质有直接的影响,而且也影响着磁场的物理效应. 随温度的升高,非广延参数及磁场对热力学性质的影响均被放大.极端相对论效应对化学势及热容量有特别显著的影响.     

强磁场中弱相互作用费米气体的热力学性质

基于赝势法和局域密度近似研究了强磁场中弱相互作用费米气体的热力学性质,得出化学势、总能和热容量的解析式,同时分析了磁场及相互作用对系统热力学性质的影响.研究表明,无论是高温情况还是低温情况下,磁场都能调节相互作用的影响.低温下,与无磁场的系统相比,磁场降低系统的化学势、总能和热容量;与无相互作用系统相比,排斥作用增加化学势而降低总能及热容量.高温下,磁场和排斥作用均可降低系统的总能而增加热容量,强磁场可以改变相互作用对总能及热容量的影响. 关键词： 强磁场 弱相互作用 费米气体 热力学性质     

Thermodynamics of phonon-stabilized Fermi distributions with application to uranium

Since phonons are built on the free energy of electrons, their frequencies can be altered by thermal electronic excitations, implying that thermal electronic excitations can alter the phonon entropy. The effect of this extra phonon entropy on electronic distribution functions and thermodynamic properties is calculated in the limit of classical vibrations. The phonon entropy stabilizes electrons above the Fermi level by more than the usual k _B T. The thermodynamic coupling of electron and phonon degrees of freedom allows far more heat capacity than in equivalent independent systems. The method developed is used to explain uranium data from the literature.