Thermodynamics of quantum dissipative many-body systems

We consider quantum nonlinear many-body systems with dissipation described within the Caldeira-Leggett model, i.e., by a nonlocal action in the path integral for the density matrix. Approximate classical-like formulas for thermodynamic quantities are derived for the case of many degrees of freedom, with general kinetic and dissipative quadratic forms. The underlying scheme is the pure-quantum self-consistent harmonic approximation (PQSCHA), equivalent to the variational approach by the Feynman-Jensen inequality with a suitable quadratic nonlocal trial action. A low-coupling approximation permits us to get manageable PQSCHA expressions for quantum thermal averages with a classical Boltzmann factor involving an effective potential and an inner Gaussian average that describes the fluctuations originating from the interplay of quanticity and dissipation. The application of the PQSCHA to a quantum phi(4) chain with Drude-like dissipation shows nontrivial effects of dissipation, depending upon its strength and bandwidth.     

Thermodynamics and phase transitions in dissipative and active Morse chains

We study the evolution of a simple one-dimensional chain of N=4 particles with Morse interactions and periodic boundary conditions which are imbedded into a heat bath creating dissipation and noise. The investigation is concentrated on thermodynamic properties for equilibrium, near-equilibrium and far-equilibrium conditions. For the thermodynamic equilibrium, created by white noise and passive friction obeying Einsteins fluctuation dissipation relation, we find a standard phase diagram. By applying active friction forces the system is driven to stationary non-equilibrium states, creating conditions where various self-sustained oscillations are excited. Thermodynamic quantities like energy, pressure and entropy are calculated near equilibrium, around a critical distance from equilibrium and far from equilibrium. We observe maximal order (minimum entropy) in certain region of the noise temperature, a phenomenon which is reminiscent of stochastic resonance. With increasing distance from equilibrium new phases corresponding to the existence of several attractors of the dynamical stem appear.     

Non-equilibrium thermodynamics and dissipative fluid theories

Summary Some of the available, phenomenological studies on the dissipative fluid theories have involved extending the set of independent dynamical variables. In the favourite case of a chemically inert fluid, one can propose to enlarge the usual hydrodynamic space both by introducing eight components of the stress deviator and the heat flux and by treating them as the fundamental variables on the same footing as the mass density and the specific internal energy. A candidate theory of this kind is based upon the quasi-linear, first-order partial differential equations for the evaluation of all variables. In this paper, the differential field equations are studied with a view to a deeper understanding of non-equilibrium thermodynamics for dissipative fluids. A characteristic feature of the endeavour is that not only it is now possible to have the differential field equations consistent with a supplementary balance law, interpreted as the equation of balance of entropy, but also possible to clarify the meaning of temperature and pressure beyond local equilibrium and to obtain the theory of thermodynamic potentials for systems ?not infinitesimally near to equilibrium?. These results are achieved via the use of the critical-point theory, as formulated by Morse, in the context of the well-known extremum property of entropy. Mathematically, the supplementary balance law is derived by exploiting the calculus of ?vertical? differential forms, and the differential field equations are defined intrinsically,i.e. without making any explicit reference to a particular coordinate system. Finally, the paper discusses some problems concerning the structure of an expression for the entropy flux.     

Thermodynamics of a quantum dissipative charged magneto‐oscillator

Quantum dissipative effect on the thermodynamics of an electron in the combined presence of a parabolic potential and a uniform (and homogeneous) magnetic field, is investigated here. Starting from the microscopic system plus bath model, we explicitly derive the thermodynamic properties using the reduced partition function of the system which is calculated using the imaginary time path integral method. The quantum heat bath we consider here is a structured heat bath whose spectral density corresponds to a structured thermal harmonic noise. All the statistical thermodynamic functions calculated do reconcile with the requirements of the fundamental axioms of physics. In particular, the specific heat and the entropy vanishes as the temperature approaches its absolute zero value, a necessity of the third law of thermodynamics. Moreover the specific heat satisfies classical equipartition theorem at high temperatures. The coefficients of the leading temperature dependent terms of the thermodynamic quantities depend only on the damping constant but not on other parameters of the bath spectral density, which is similar to the analysis based on the Drude bath spectral density. Our study facilitates the physics of small quantum systems, which are always in contact with some environments, at very low temperatures.

     

The stability of cosmic string loops

A general perturbation analysis is performed on closed string loops to investigate whether small perturbations cause the known class of non-self-intersecting loops to self-intersect. This leads to the conclusion that most of this class of loops are stable to small perturbations.     

Bracket formulation of dissipative fluid mechanics equations

The bracket formulation of the Euler fluid mechanics equations is extended to the fluid mechanics equations corresponding to the Navier-Stokes-Fourier and the Edelen constitutive relations.     

Thermodynamics of an interfacial fluid membrane

We discuss a closed system of field equations for a semipermeable membrane which has particle and heat exchange with its surroundings. In this case we consider a surface with an arbitrary shape for specific quantities and mechanical properties. A representation of the constitutive equations follows from the principle of material objectivity in space as well as on surfaces. The constitutive equations can be restricted by an entropy principle. We present both the Gibbs equation and the entropy flux. Furthermore, we obtain the surface stress and the chemical potential in terms of the specific free energy of the membrane. Both the heat flux and the particle flux normal to the membrane depend on the mean curvature and the friction between the particle across the membrane. The interaction tangential to the interface is dependent up on gradients of the surface stress as well as the chemical potential of the interface.     

Thermodynamics of a long-range triangle-well fluid

The long-range triangle-well fluid has been studied using three different approaches: firstly, by an analytical equation of state obtained by a perturbation theory, secondly via a self-consistent integral equation theory, the so-called self-consistent Ornstein–Zernike approach (SCOZA) which is presently one of the most accurate liquid-state theories, and finally by Monte Carlo simulations. We present vapour–liquid phase diagrams and thermodynamic properties such as the internal energy and the pressure as a function of the density at different temperatures and for several values of the potential range. We assess the accuracy of the theoretical approaches by comparison with Monte Carlo simulations: the SCOZA method accurately predicts the thermodynamics of these systems and the first-order perturbation theory reproduces the overall thermodynamic behaviour for ranges greater than two molecular diameters except that it overestimates the critical point. The simplicity of the equation of state and the fact that it is analytical in the potential range makes it a good candidate to be used for calculating other thermodynamic properties and as an ingredient in more complex theoretical approaches.     

Spinodal phase decomposition with dissipative fluid dynamics

The spinodal amplification of density fluctuations is treated perturbatively within dissipative fluid dynamics including not only shear and bulk viscosity but also heat conduction, as well as a gradient term in the local pressure. The degree of spinodal amplification is calculated along specific dynamical phase trajectories and the results suggest that the effect can be greatly enhanced by tuning the collision energy so that maximum compression occurs inside the region of spinodal instability.     

From kinetic theory to dissipative fluid dynamics

We present the results of deriving the Israel-Stewart equations of relativistic dissipative fluid dynamics from kinetic theory via Grad’s 14-moment expansion. Working consistently to second order in the Knudsen number, these equations contain several new terms which are absent in previous treatments.     

Numerical tests of causal relativistic dissipative fluid dynamics

We present numerical methods to solve the Israel–Stewart (IS) equations of causal relativistic dissipative fluid dynamics with bulk and shear viscosities. We then test these methods studying the Riemann problem in (1+1)- and (2+1)-dimensional geometry. The numerical schemes investigated here are applicable to realistic (3+1)-dimensional modeling of a relativistic dissipative fluid.     

Thermodynamics of the λ line in binary fluid mixtures

Thermodynamics of the λ line, variations on a theme by Wheeler and Griffiths, have been presented.     

Thermodynamics of the Stockmayer fluid in an applied field

The thermodynamic properties of the Stockmayer fluid in an applied field are studied using theory and computer simulation. Theoretical expressions for the second and third virial coefficients are obtained in terms of the dipolar coupling constant (λ, measuring the strength of dipolar interactions as compared to thermal energy) and dipole–field interaction energy (α, being proportional to the applied field strength). These expressions are tested against numerical results obtained by Mayer sampling calculations. The expression for the second virial coefficient contains terms up to λ⁴, and is found to be accurate over realistic ranges of dipole moment and temperature, and over the entire range of the applied field strength (from zero to infinity). The corresponding expression for the third virial coefficient is truncated at λ³, and is not very accurate: higher order terms are very difficult to calculate. The virial coefficients are incorporated in to a thermodynamic theory based on a logarithmic representation of the Helmholtz free energy. This theory is designed to retain the input virial coefficients, and account for some higher order terms in the sense of a resummation. The compressibility factor is obtained from the theory and compared to results from molecular dynamics simulations with a typical value λ = 1. Despite the mathematical approximations of the virial coefficients, the theory captures the effects of the applied field very well. Finally, the vapour–liquid critical parameters are determined from the theory, and compared to published simulation results; the agreement between the theory and simulations is good.     

CUO基态分子热力学稳定性研究

根据热力学原理、Debye固体理论和量子力学从头计算的分子结构，运用统计热力学方法计算得到物质的热力学函数值.由算得的CUO(g)分子在不同温度下的标准生成自由能变，表明了在高温下可能有CUO(g)分子的稳定存在. 关键词： CUO 热力学函数 稳定性     

The thermoelectric working fluid: Thermodynamics and transport

Thermoelectric devices are heat engines, which operate as generators or refrigerators using the conduction electrons as a working fluid. The thermoelectric heat-to-work conversion efficiency has always been typically quite low, but much effort continues to be devoted to the design of new materials boasting improved transport properties that would make them of the electron crystal–phonon glass type of systems. On the other hand, there are comparatively few studies where a proper thermodynamic treatment of the electronic working fluid is proposed. The present article aims at contributing to bridge this gap by addressing both the thermodynamic and transport properties of the thermoelectric working fluid covering a variety of models, including interacting systems.     

Second-order dissipative fluid dynamics for ultrarelativistic nuclear collisions

The Müller-Israel-Stewart second-order theory of relativistic imperfect fluids based on Grad's moment method is used to study the expansion of hot matter produced in ultrarelativistic heavy-ion collisions. The temperature evolution is investigated in the framework of the Bjorken boost-invariant scaling limit. The results of these second-order theories are compared to those of first-order theories due to Eckart and to Landau and Lifshitz and those of zeroth order (perfect fluid) due to Euler.     

Thermodynamics and weak cosmic censorship conjecture of BTZ black holes in extended phase space

As a charged fermion drops into a BTZ black hole, the laws of thermodynamics and the weak cosmic censorship conjecture are investigated in both the normal and extended phase space, where the cosmological parameter and renormalization length are regarded as extensive quantities. In the normal phase space, the first and second law of thermodynamics, and the weak cosmic censorship are found to be valid. In the extended phase space, although the first law and weak cosmic censorship conjecture remain valid, the second law is dependent on the variation of the renormalization energy d K. Moreover, in the extended phase space, the configurations of extremal and near-extremal black holes are not changed, as they are stable, while in the normal phase space, the extremal and near-extremal black holes evolve into non-extremal black holes.