Nonequilibrium phases

For sodium palmitate, 5-phase is the thermodynamically preferred, or equiUbrium state, at room temperature and up to - 60° C P-phase contains a higher level of hydration and forms at higher temperatures and CO-phase is an anhydrous crystal that forms at temperatures comparable to P-phase. Most soap in the soHd state exists in one or a combination of these three phases. The phase diagram refers to equiUbrium states. In practice, the drying routes and other mechanical manipulation utilized in the formation of soHd soap can result in the formation of nonequilibrium phase stmcture. This point is important when dealing with the manufacturing of soap bars and their performance. 

The problems with the adiabatic Yamada-Kawasaki distribution and its thermostatted versions can be avoided by developing a nonequilibrium phase space probability distribution for the present case of mechanical work that is analogous to the one developed in Section IVA for thermodynamic fluxes due to imposed thermodynamic gradients. The odd work is required. To obtain this, one extends the work path into the future by making it even about t ... 

For nonequilibrium statistical mechanics, the present development of a phase space probability distribution that properly accounts for exchange with a reservoir, thermal or otherwise, is a significant advance. In the linear limit the probability distribution yielded the Green-Kubo theory. From the computational point of view, the nonequilibrium phase space probability distribution provided the basis for the first nonequilibrium Monte Carlo algorithm, and this proved to be not just feasible but actually efficient. Monte Carlo procedures are inherently more mathematically flexible than molecular dynamics, and the development of such a nonequilibrium algorithm opens up many, previously intractable, systems for study. The transition probabilities that form part of the theory likewise include the influence of the reservoir, and they should provide a fecund basis for future theoretical research. The application of the theory to molecular-level problems answers one of the two questions posed in the first paragraph of this conclusion the nonequilibrium Second Law does indeed provide a quantitative basis for the detailed analysis of nonequilibrium problems. 

Quantum Field Theory for Nonequilibrium Phase Transitions... 

Quantum field theory for nonequilibrium phase transitions... 

Abstract. We review the recent development of quantum dynamics for nonequilibrium phase transitions. To describe the detailed dynamical processes of nonequilibrium phase transitions, the Liouville-von Neumann method is applied to quenched second order phase transitions. Domain growth and topological defect formation is discussed in the second order phase transitions. Thermofield dynamics is extended to nonequilibrium phase transitions. Finally, we discuss the physical implications of nonequilibrium processes such as decoherence of order parameter and thermalization. 

Keywords Nonequilibrium phase transitions, Liouville-von Neumann approach, domain growth, topological defect formation. 

To describe nonequilibrium phase transitions, there have been developed many methods such as the closed-time path integral by Schwinger and Keldysh (J. Schwinger et.al., 1961), the Hartree-Fock or mean field method (A. Ringwald, 1987), and the l/lV-expansion method (F. Cooper et.al., 1997 2000). In this talk, we shall employ the so-called Liouville-von Neumann (LvN) method to describe nonequilibrium phase transitions (S.P. Kim et.al., 2000 2002 2001 S.P. Kim et.al., 2003). The LvN method is a canonical method that first finds invariant operators for the quantum LvN equation and then solves exactly the... 

As a field model for nonequilibrium phase transitions of second order, we consider a scalar field potential... 

We now turn to the potential (4) for nonequilibrium phase transition. We separate the Hamiltonian density H into a quadratic part Ho and a perturbation part Hp ... 

Now we study the effects of the dynamical processes of nonequilibrium phase transitions on domain growth and topological defects. The quench models describe such nonequilibrium processes, which can be... 

Haken, J. (1978). Synergetics. An Introduction. Nonequilibrium Phase Transitions and Self-Organization in Physics, Chemistry and Biology. Berlin Springer-Verlag. 

TNC.53. 1. Prigogine and J. W. Turner, Nonequilibrium phase transitions, Proc. Karcher Symp. Structural Aspects of Homogeneous, Heterogeneous and Biological Catalysis, University Oklahoma, American Crystallographic Association, pp. 103—141. 

TNC.54. 1. Prigogine, New aspects of chemical kinetics and nonequilibrium phase transitions. Proceedings of Symposium Structure and Dynamics in Chemistry, Uppsala, 1977, P. Ahlberg and L.-O. Sundelof, eds., pp. 172-186. 

TNC.64. M. Malek-Mansour, G. Nicolis, and I. Prigogine, Nonequilibrium phase transitions in chemical systems, in Thermodynamics and Kinetics of Biological Processes, 1. Lamprecht and A. 1. Zotin, eds., W. de Gmyter, Berlin, 1982, pp. 75-103. 

Truskinovsky, L., 1988, Nonequilibrium phase boundaries, Dokl. Akad. Nauk SSSR, 303 1337. 

Damaskin and Baturina [171] have studied unstable states during coumarin adsorption on mercury electrode. These instabilities were attributed to the nonequilibrium phase transitions in the adsorption layer, during which the orientation of coumarin molecules changed at the electrode surface. 

Three Zero-One Laws and Nonequilibrium Phase Transitions in Multiscale Systems... 

In multiscale asymptotic analysis of reaction network we found several very attractive zero-one laws. First of all, components eigenvectors are close to 0 or +1. This law together with two other zero-one laws are discussed in Section 6 "Three zero-one laws and nonequilibrium phase transitions in multiscale systems". 

THREE ZERO-ONE LAWS AND NONEQUILIBRIUM PHASE TRANSITIONS IN MULTISCALE SYSTEMS... 

The following mechanism for the formation of the final phase was proposed. At relatively low temperature, BaC03 and y-Al203 particles react to form the nonequilibrium phase BaAl204. The formation of the stable Ba-hexaaluminate phase starts at 1200°C and occurs via a very slow solid state reaction between... 

The conference was divided into four parts to each of which a full day was devoted the first one treated Equilibrium Statistical Mechanics, with special regard to The Theory of Critical Phenomena the second part regarded Nonequilibrium Statistical Mechanics. Cooperative Phenomena the third one, The Macroscopic Approach to Coherent Behavior in Far Equilibrium Conditions and the fourth and last, Fluctuation Theory and Nonequilibrium Phase Transitions. ... 

Dynamical Self-Organization. When the parameter X passes slowly through X (l),the bifurcation picture of the previous section accurateiy describes the system. However, in Fucus, and probably in many other examples, this time scale separation between the characteristic time on which X varies and the time to obtain the patterned state does not hold. Thus a dynamical theory allowing for the interplay of these two time scales is required to characterize the developmental scenario. A natural formalism to describe this process is that of time dependent Ginzburg-Landau (tdgl) equations used successfully in other contexts of nonequilibrium phase transitions (27). 

---