Thermodynamic stability of equilibrium system and critical state

On the basis of general Gibbs conditions of stability, the requirements of critical state stability that are applied to adiabatic coefficient of stability (ACS) and their derivatives are obtained. The examination of these conditions with critical state definition establishes the existence of four alternative types of critical behaviour of the thermodynamic system. These types are classified by the critical behaviour of ACS and K_C, which is connected with ACS. Analysis of the asymptotic behaviour of adiabatic quantity (AQ), which is consistent with stability requirements, demonstrates that both analytic and nonanalytic behaviours are possible.     

Non-isothermal adiabatic critical state stability of a hard superconductor

A basic feature of a hard superconductor is that dissipative processes occur in them because of a thermally activated motion of vortices. The resulting dissipation of the energy stored may be accompanied by a disruption of the critical state. This instability leads to an increase in the temperature of the superconductor. Most of the carried out investigations have been based on a study of the initial stage of the magnetic flux penetration and ignore permissible heating of the superconductor. The main purpose of this work is to analyze the conditions for the onset of the thermomagnetic instability in a hard superconductor with allowance for a non-zero initial temperature heating. Conditions for adiabatic stability of the screening currents induced by an external magnetic field are formulated. It is shown that the adiabatic criteria for stability of the critical state depend strongly on the initial temperature of the superconductor.     

Restriction of the values of the critical indices by the condition of thermodynamic stability

A phase transition is of second order if the adjacent phases are both stable up to and on the phase limit. The stability condition together with the assumption that the scaling laws should hold restrict the critical indices to two sets of numbers for those second order phase transitions which exhibit a logarithmic singularity and a jump of the specific heat.     

Dynamical stability and pure thermodynamic phases

A notion of stability of dynamics under distant perturbations is introduced. It is demonstrated, for quasi-local systems, that the stability of an equilibrium state under the same perturbations implies the state is factorial, i.e. strongly clustering in space. We also characterize the set of perturbations necessary to ensure the equivalence of stability and factorialness.     

Stellar stability by thermodynamic instability

For gravity-dominated systems the three features shrinking <=> energy decrease <=> temperature increase are dynamically linked together. So are their inverses: expansion <=> energy increase <=> temperature decrease. We exhibit these features by one classical particle in a suitable environment, and by many particles with purely attractive interactions. We then show how the ensuing negative heat capacity tames an explosive energy input.     

On the stability of the critical state with inhomogeneous temperature in composite superconductors

The problem of the thermal and magnetic destruction of the critical state in composite superconductors is investigated. The initial distributions of temperature and electromagnetic field are assumed to be essentially inhomogeneous. The limit of the thermomagnetic instability in quasi-stationary approximation is determined. The obtained integral criterion, unlike the analogous criterion for a homogeneous temperature profile, is shown to take into account the influence of any part of the superconductor on the threshold for critical-state instability. Received 11 October 2001 / Received in final form 30 November 2002 Published online 14 February 2003 RID="a" ID="a"e-mail: taylanov@iaph.tkt.uz     

固体物理学中平衡态的热力学条件分析

在具体分析和讨论肖特基缺陷热平衡浓度的热力学平衡条件的基础上,指出其热力学平衡条件是自由焓Φ最小的态;对于固体物理学中采用自由能F最小作为热力学平衡态的条件进行了分析和讨论,在压强为大气压或压强足够低的条件下,自由焓Φ最小近似为自由能F最小。     

A scaling equation of state near the critical point and the stability boundary of a liquid

A new scaling equation of state is proposed to describe the equilibrium thermodynamic properties of liquids near the critical point. In distinction from the existing scaling equations, which are parametric, the new equation is nonparametric and is expressed directly in terms of the physical quantities (pressure, temperature, and so on). It creates a number of advantages for the traditional representation and data processing. The equation gives rise to a binodal, spinodal, and a curve of thermal capacity divergence (pseudospinodal). The equation is expressed in terms of reduced variables (the ratio of the deviation of a thermodynamic variable from its critical value to the critical value) and contains 3 system-dependent adjustable constants. With the help of this equation, we conducted an approximation of the experimental PVT data in the critical region of ⁴He, C₂H₄, and H₂O with a pressure error of 0.4% and carried out a calculation of the C _v ⁴He thermal capacity with no more than 4% error using a three-system constant determined from the PVT data.     

A Riemannian geometry for thermodynamic state space

We consider a class of thermodynamic systems in which the dynamics of the spontaneous approach to equilibrium is governed by the gradient of negentropy, where the gradient is taken with respect to a Riemannian metric. In open systems (dissipative structures) this gradient field is superposed with a vector field of interactions with environment. We consider three characteristics of the economy of dissipative structures: negentropy inflow (income), negentropy consumption (i.e. entropy production), and negentropy surplus (reserves). We derive explicit formulas for these characteristics and for the relations between them.     

On the thermodynamic stability of odd-frequency superconductors

The thermodynamic stability of odd-frequency pairing states is investigated within an Eliashberg-type framework. We find the rigorous result that in the weak coupling limit a continuous transition from the normal state to a spatially homogeneous odd-in-ω superconducting state is forbidden, irrespective of details of the pairing interaction and of the spin symmetry of the gap function. For isotropic systems, it is shown that the inclusion of strong coupling corrections does not invalidate this result. We discuss a few scenarios that might escape these thermodynamic constraints and permit stable odd-frequency pairing states.     

能量公设与热力学系统独立状态参量的选取

论述了能量公设,并得到能量状态的一般表达式由各种能位形式组成,每一种能位形式可表示为一个强度量和一个广延量的乘积．由此,提出了热力学系统独立状态参量的数目由能位数目来决定,并且每一个独立状态参量只能是组成同一能位的强度量ξi和广延量ξi中的一个．     

On the stability of the critical state in hard superconductors with a heterogeneous temperature profile

The problem of the thermal and magnetic destruction of the critical state in hard superconductors is investigated. The initial distributions of temperature and electromagnetic field are assumed to be essentially inhomogeneous. The limit of the thermomagnetic instability in quasi-stationary approximation is determined. The obtained integral criterion, unlike the analogous criterion for a homogeneous temperature profile, is shown to take into account the influence of any part of the superconductor on the threshold for critical-state instability.     

Generalized thermodynamic stability of systems under shear

Starting from the extended irreversible thermodynamics (EIT) theory, some corrections to the specific heat and to the thermal compressibility of a nonequilibrium system are obtained. We study the subsequent modifications of the static stability conditions of a system under shear. In some situations, a shear-induced melting transition can be present.     

高温高压气体的状态方程与热力学性质

本文根据高温高压下气体分子要压缩的观点出发,提出了一个简单实用的高温高压气体状态方程,并用以研究和计算气体在高温高压下的热力学函数与性质.     

n维经典非理想气体的物态方程与热力学函数

求出了n维经典非理想气体的物态方程和热力学函数.由London理论得出了维数n(n<6)不同时的经典非理想气体的物态方程形式基本一样,且与能谱关系无关的结论;当维数n≥6时,如果仍用London理论,巨配分函数发散,此时物态方程及热力学函数将无意义.事实上只要使用刚性球模型,无论是否使用London理论,总存在一个维数n,当维数大于n时巨配分函数发散.     

Thermodynamics of the critical state

We discuss the asymptotic behavior of thermodynamic functions in the vicinity of critical points on the basis of the theory of thermodynamic equilibrium stability. We obtain two types of relations between critical exponents in the critical state. The general thermodynamic results are illustrated using classic self-consistent Van der Waals and Curie-Weiss field models.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 58–63, October, 1987.     

Statistical theory of thermodynamic stability of crystalline phases

The equation of state of a face-centered cubic phase has been quantitatively analyzed in terms of the statistical theory of crystals. It has been shown that, for xenon at room temperature, the pressure equal to 1.5 GPa determines the instability point where the condition of the positive bulk modulus of a face-centered cubic crystal is violated. A “universal line” bounding the thermodynamic stability region of the face-centered cubic phase of van der Waals crystals has been constructed. An analysis of the data available in the literature allows the conclusion that the revealed transition of face-centered cubic xenon to the martensitic phase at a pressure of 1.5 GPa and a temperature of 300 K can be considered a manifestation of the predicted instability. In this respect, it is important to perform detailed experiments on polymorphic transformations of real xenon (and also krypton). Another aspect of the proposed theory is that it provides a means for quantitatively predicting the characteristics of the so-called “cold” (at negative pressures) melting, which recently has become accessible for experimental observation.     

Mechanical stability and thermodynamic properties of OsC from first-principles calculations

The elastic and thermodynamic characteristics of OsC crystal have been predicted through a method of density functional theory within the generalized gradient approximation (GGA). Compared with WC-type OsC, NaCl-type OsC is not only energy unfavorable but also mechanics unstable. The five independent elastic constants (C_ij), bulk modulus (B₀), the dependence of bulk modulus on temperature and pressure as well as the thermal expansion coefficient (α_V) at various temperatures for WC-type OsC are discussed. According to our calculations, WC-type OsC should be an ultra-incompressible material with high bulk modulus about 381 GPa. In addition, the bulk modulus will increase with increasing pressure while decrease with increasing temperature. The researches on the thermal expansion coefficient indicate that there will be a knee point during the process of thermal expansion coefficient variation versus increasing temperature. Our results may provide useful information for theoretical and experimental investigation of OsC.