Prigogine–Defay ratio for systems with more than one order parameter

Restricted Phase Space Thermodynamics of Einstein-Power-Yang-Mills AdS Black Hole

We consider the thermodynamics of the Einstein-power-Yang-Mills AdS black holes in the context of the gauge-gravity duality. Under this framework, Newton's gravitational constant and the cosmological constant are varied in the system. We rewrite the thermodynamic first law in a more extended form containing both the pressure and the central charge of the dual conformal field theory, i.e., the restricted phase transition formula. A novel phenomena arises: the dual quantity of pressure is the effective volume, not the geometric one. That leads to a new behavior of the Van de Waals-like phase transition for this system with the fixed central charge: the supercritical phase transition. From the Ehrenfest's scheme perspective, we check out the second-order phase transition of the EPYM AdS black hole. Furthermore the effect of the non-linear Yang-Mills parameter on these thermodynamic properties is also investigated.

Configurational Entropy Effects on Glass Transition in Metallic Glasses

Configurational entropy (S_conf) is known to be a key thermodynamic factor governing a glass transition process. However, this significance remains speculative because S_conf is not directly measurable. In this work, we demonstrate the role of S_conf theoretically and experimentally by a comparative study of a Zr-Ti-Cu-Ni-Be high-entropy metallic glass (HE-MG) with one of its conventional MG counterparts. It is revealed that the higher S_conf leads to a glass that is energetically more stable and structurally more ordered. This is manifested by ab initio molecular dynamics simulations, showing that ∼60% fewer atoms are agitated above T_g, and experimental results of smaller heat capacity jump, inconspicuous stiffness loss, insignificant structural change during glass transition, and a more depressed boson peak in the HE-MG than its counterpart. We accordingly propose a model to explain that a higher S_conf promotes a faster degeneracy-dependent kinetics for exploration of the potential energy landscape upon glass transition.

Theory of structural relaxation in glass from the thermodynamics of irreversible processes

This work proposes a fundamental thermodynamic description of structural relaxation in glasses by establishing a link between the Prony series solution to volume relaxation derived from the principles of irreversible thermodynamics and asymmetric Lévy stable distribution of relaxation rates. Additionally, it is shown that the bulk viscosity of glass, and not the shear viscosity, is the transport coefficient governing structural relaxation. We also report the distribution of relaxation times and energy barrier heights underpinning stretched exponential relaxation. It is proposed that this framework may be used for qualitative and quantitative descriptions of the relaxation kinetics in glass.

Integro-Differential Equation for the Non-Equilibrium Thermal Response of Glass-Forming Materials: Analytical Solutions

An integro-differential equation describes the non-equilibrium thermal response of glass-forming substances with a dynamic (time-dependent) heat capacity to fast thermal perturbations. We found that this heat transfer problem could be solved analytically for a heat source with an arbitrary time dependence and different geometries. The method can be used to analyze the response to local thermal perturbations in glass-forming materials, as well as temperature fluctuations during subcritical crystal nucleation and decay. The results obtained can be useful for applications and a better understanding of the thermal properties of glass-forming materials, polymers, and nanocomposites.

Nanoscale Heat Conduction in CNT-POLYMER Nanocomposites at Fast Thermal Perturbations

Nanometer scale heat conduction in a polymer/carbon nanotube (CNT) composite under fast thermal perturbations is described by linear integrodifferential equations with dynamic heat capacity. The heat transfer problem for local fast thermal perturbations around CNT is considered. An analytical solution for the nonequilibrium thermal response of the polymer matrix around CNT under local pulse heating is obtained. The dynamics of the temperature distribution around CNT depends significantly on the CNT parameters and the thermal contact conductance of the polymer/CNT interface. The effect of dynamic heat capacity on the local overheating of the polymer matrix around CNT is considered. This local overheating can be enhanced by very fast (about 1 ns) components of the dynamic heat capacity of the polymer matrix. The results can be used to analyze the heat transfer process at the early stages of “shish-kebab” crystal structure formation in CNT/polymer composites.

Nanometer scale thermal response of polymers to fast thermal perturbations

Nanometer scale thermal response of polymers to fast thermal perturbations is described by linear integro-differential equations with dynamic heat capacity. The exact analytical solution for the non-equilibrium thermal response of polymers in plane and spherical geometry is obtained in the absence of numerical (finite element) calculations. The solution is different from the iterative method presented in a previous publication. The solution provides analytical relationships for fast thermal response of polymers even at the limit t → 0, when the application of the iterative process is very problematic. However, both methods give the same result. It was found that even fast (ca. 1 ns) components of dynamic heat capacity greatly enhance the thermal response to local thermal perturbations. Non-equilibrium and non-linear thermal response of typical polymers under pulse heating with relaxation parameters corresponding to polystyrene and poly(methyl methacrylate) is determined. The obtained results can be used to analyze the heat transfer process at the early stages of crystallization with fast formation of nanometer scale crystals.

Nonequilibrium thermodynamics. III. Generalization of Maxwell, Clausius-Clapeyron, and response-function relations, and the Prigogine-Defay ratio for systems in internal equilibrium

We follow the consequences of internal equilibrium in nonequilibrium systems that has been introduced recently [Gujrati, Phys. Rev. E 81, 051130 (2010) and Gujrati, Phys. Rev. E 85, 041128 (2012).] to obtain the generalization of the Maxwell relation and the Clausius-Clapeyron relation that are normally given for equilibrium systems. The use of Jacobians allows for a more compact way to address the generalized Maxwell relations in the presence of internal variables. The Clausius-Clapeyron relation in the subspace of observables shows not only the nonequilibrium modification but also the modification due to internal variables that play a dominant role in glasses to which we apply the above relations. Real systems do not directly turn into glasses (GL) that are frozen structures from the supercooled liquid state L; there is an intermediate state (gL) where the internal variables are not frozen. A system possesses several kinds of glass transitions, some conventional (L→gL; gL→GL) in which the state changes continuously and the transition mimics a continuous or second-order transition, and some apparent (L→gL; L→GL) in which the free energies are discontinuous so that the transition appears as a zeroth-order transition, as discussed in the text. We evaluate the Prigogine-Defay ratio Π in the subspace of the observables at these transitions. We find that it is normally different from 1, except at the conventional transition L→gL, where Π=1.

On the theoretical determination of the Prigogine-Defay ratio in glass transition

In a recent analysis [J. W. P. Schmelzer and I. Gutzow, J. Chem. Phys. 125, 184511 (2006)] it was shown for the first time that--in contrast to earlier belief arising from the works of Prigogine and Defay [Chemical Thermodynamics (Longman, London, 1954), Chap. 19; The first French edition of this book was published in 1950] and Davies and Jones [Adv. Phys. 2, 370 (1953); and Proc. R. Soc. London, Ser. A 217, 26 (1953)]--a satisfactory theoretical interpretation of the experimentally observed values of the so-called Prigogine-Defay ratio Π, being a combination of jumps of thermodynamic coefficients at glass transition, can be given employing only one structural order parameter. According to this analysis, this ratio has to be, in full agreement with experimental findings, larger than one (Π > 1). Its particular value depends both on the thermodynamic properties of the system under consideration and on cooling and heating rates. Based on above-mentioned analysis, latter dependence on cooling rates has been studied in detail in another own preceding paper [T. V. Tropin, J. W. P. Schmelzer, and C. Schick, J. Non-Cryst. Solids 357, 1303 (2011)]. In the present analysis, an alternative general method of determination of the Prigogine-Defay ratio is outlined, allowing one to determine this ratio having at ones disposal the generalized equation of state of the glass-forming melts under consideration and, in particular, the knowledge of the equilibrium properties of the melts in the glass transformation range. Employing, as an illustration of the method, a particular model for the description of glass-forming melts, theoretical estimates are given for this ratio being, again, in good agreement with experimental data.

Two Species/Nonideal Solution Model for Amorphous/Amorphous Phase Transitions

A simple macroscopic thermodynamic model for first order transitions between two amorphous phases in a one component liquid is reviewed, augmented and evaluated. The model presumes the existence in the liquid of two species, whose concentrations are temperature and pressure dependent and which form a solution with large, positive deviations from ideality. Application of the model to recent data indicates that water can undergo an amorphous/amorphous phase transition below a critical temperature Tc of 217K and above a critical pressure Pc of 380 atm.

Solution of the spherically symmetric linear thermoviscoelastic problem in the inertia-free limit

The coupling between mechanical and thermal properties due to thermal expansion complicates the problem of measuring frequency-dependent thermoviscoelastic properties, in particular for highly viscous liquids. A simplification arises if there is spherical symmetry where--as detailed in the present paper--the thermoviscoelastic problem may be solved analytically in the inertia-free limit, i.e., the limit where the sample is much smaller than the wavelength of sound waves at the frequencies of interest. As for the one-dimensional thermoviscoelastic problem [Christensen et al., Phys. Rev. E 75, 041502 (2007)], the solution is conveniently formulated in terms of the so-called transfer matrix, which directly links to the boundary conditions that can be experimentally controlled. Once the transfer matrix has been calculated, it is fairly easy to deduce the equations describing various experimentally relevant special cases (boundary conditions that are adiabatic, isothermal, isochoric, etc.). In most situations the relevant frequency-dependent specific heat is the longitudinal specific heat, a quantity that is in between the isochoric and isobaric frequency-dependent specific heats.

The laboratory glass transition

The phenomenology of the laboratory glass transition is examined in the enthalpy landscape framework. It is shown that a generic description of the glassy state based on partitioning of the phase space caused by the finiteness of the time of observation explains all universal features of glass transition. Using this description of glass, which is referred to as the extrinsically constrained liquid, expressions are derived for properties of glass and for property changes at the laboratory glass transition. A model enthalpy landscape is used to illustrate the basic concepts of this description. Additional new consequences of this description, such as the role of complexity in glass transition and the zero residual entropy of a glass, are discussed.

Single-order-parameter description of glass-forming liquids: A one-frequency test

Thermoviscoelastic linear-response functions are calculated from the master equation describing viscous liquid inherent dynamics. From the imaginary parts of the frequency-dependent isobaric specific heat, isothermal compressibility, and isobaric thermal expansion coefficient, we define a "linear dynamic Prigogine-Defay ratio" LambdaTp(omega) with the property that if LambdaTp(omega)=1 at one frequency, then LambdaTp(omega) is unity at all frequencies. This happens if and only if there is a single-order-parameter description of the thermoviscoelastic linear responses via an order parameter (which may be nonexponential in time). Generalizations to other cases of thermodynamic control parameters than temperature and pressure are also presented.

A free-energy landscape picture and Landau theory for the dynamics of disordered materials

Landau's theory of phase transitions [Nature (London) 138, 840 (1936); Statistical Physics (Pergamon, London, 1959)] is adapted to treat independently relaxing regions in complex systems using nanothermodynamics. The order parameter we use governs the thermal fluctuations, not a specific static structure. We find that the entropy term dominates the thermal behavior, as is reasonable for disordered systems. Consequently, the thermal equilibrium occurs at the internal-energy maximum, so that the potential-energy minima have negligible influence on the dynamics. The dynamics involves normal thermal fluctuations about the free-energy minimum, with a time scale that is governed by the curvature of the internal-energy maximum. The temperature dependence of the fluctuations yields Vogel-Tamman-Fulcher-type [Phys. Z. 22, 645 (1921); J. Am. Ceram. Soc. 8, 339 (1925); Z. Anorg. Allg. Chem. 156, 245 (1926)] relaxation rates and approximate time-temperature superposition, consistent with the Williams-Landell-Ferry [J. Am. Chem. Soc. 77, 3701 (1955)] procedure for analyzing the dynamics of complex fluids, while the size dependence of the fluctuations provides an explanation for the distribution of relaxation times and heterogeneity that are found in glass-forming liquids, thus providing a unified picture for several features in the dynamics of disordered materials.