Nonequilibrium phenomenon

McCourt F R, Beenakker J, Kohler W E and Kijscer I 1990 Nonequilibrium Phenomena In Polyatomic Gases. 1. Dilute Gases (Oxford Clarendon)... 

The general problem of finding nonequilibrium solutions to Boltzman s equation is, as already mentioned above, an exceedingly difficult problem. Two tools that have proven invaluable in providing insight into nonequilibrium phenomena,... 

Introduction.—Statistical physics deals with the relation between the macroscopic laws that describe the internal state of a system and the dynamics of the interactions of its microscopic constituents. The derivation of the nonequilibrium macroscopic laws, such as those of hydrodynamics, from the microscopic laws has not been developed as generally as in the equilibrium case (the derivation of thermodynamic relations by equilibrium statistical mechanics). The microscopic analysis of nonequilibrium phenomena, however, has achieved a considerable degree of success for the particular case of dilute gases. In this case, the kinetic theory, or transport theory, allows one to relate the transport of matter or of energy, for example (as in diffusion, or heat flow, respectively), to the mechanics of the molecules that make up the system. 

In this way, nonequilibrium phenomena in steady or quasi-steady state can be taken into account. 

Finally, a relatively new area in the computer simulation of confined polymers is the simulation of nonequilibrium phenomena [72,79-87]. An example is the behavior of fluids undergoing shear flow, which is studied by moving the confining surfaces parallel to each other. There have been some controversies regarding the use of thermostats and other technical issues in the simulations. If only the walls are maintained at a constant temperature and the fluid is allowed to heat up under shear [79-82], the results from these simulations can be analyzed using continuum mechanics, and excellent results can be obtained for the transport properties from molecular simulations of confined liquids. This avenue of research is interesting and could prove to be important in the future. 

To summarize, in this article we have discussed some aspects of a semiclassical electron-transfer model (13) in which quantum-mechanical effects associated with the inner-sphere are allowed for through a nuclear tunneling factor, and electronic factors are incorporated through an electronic transmission coefficient or adiabaticity factor. We focussed on the various time scales that characterize the electron transfer process and we presented one example to indicate how considerations of the time scales can be used in understanding nonequilibrium phenomena. 

Ngai KL, Riande E, Ingram MD (eds) (1998) Proceedings of the third international discussion meeting on relaxations in complex systems. J Non-Cryst Solids vols 235-237 Giordano M, Leporini D, Tosi M (eds) (1999) Special issne Second workshop on nonequilibrium phenomena in snpercooled flnids, glasses and amorphons materials. J Phys Condens Matter ll(lOA)... 

This nanoparticle sample exhibits strong anisotropy, due to the uniaxial anisotropy of the individual particles and the anisotropic dipolar interaction. The relative timescales (f/xm) of the experiments on nanoparticle systems are shorter than for conventional spin glasses, due to the larger microscopic flip time. The nonequilibrium phenomena observed here are indeed rather similar to those observed in numerical simulations on the Ising EA model [125,126], which are made on much shorter time (length) scales than experiments on ordinary spin glasses [127]. 

F. R. McCourt, J. Beenakker, W. E. Kohler, and I. Kuscer Nonequilibrium phenomena in polyatomic gases, Volume I... 

In this paper we present a brief discussion and comparison of the probabilistic and dynamic approaches to the treatment of nonequilibrium phenomena in physical systems. The discussion is not intended to be complete but only illustrative. Details of many of the derivations appear elsewhere and only the results will be discussed here. We shall focus our attention on the probabilistic approach and shall emphasize its advantages and drawbacks. The main body of the paper deals with the properties of the master equation and, more cursorily, with the properties of the Langevin equation. 

In 1977. Professor Ilya Prigogine of the Free University of Brussels. Belgium, was awarded Ihe Nobel Prize in chemistry for his central role in the advances made in irreversible thermodynamics over the last ihrec decades. Prigogine and his associates investigated Ihe properties of systems far from equilibrium where a variety of phenomena exist that are not possible near or al equilibrium. These include chemical systems with multiple stationary states, chemical hysteresis, nucleation processes which give rise to transitions between multiple stationary states, oscillatory systems, the formation of stable and oscillatory macroscopic spatial structures, chemical waves, and Lhe critical behavior of fluctuations. As pointed out by I. Procaccia and J. Ross (Science. 198, 716—717, 1977). the central question concerns Ihe conditions of instability of the thermodynamic branch. The theory of stability of ordinary differential equations is well established. The problem that confronted Prigogine and his collaborators was to develop a thermodynamic theory of stability that spans the whole range of equilibrium and nonequilibrium phenomena. 

Important questions about equilibrium situations remain to be answered, and a strong continuing research effort in this direction is essential. Nevertheless, enough is now known about equilibrium to justify a strong parallel effort toward understanding nonequilibrium phenomena— an effort much greater than exists at present. 

Luettmer-Strathmann J (2002) In Kohler W, Wiegand S (eds) Thermal nonequilibrium phenomena in fluid mixtures. Springer, Heidelberg, p 24... 

Chang, S. S.-H. (1975). Nonequilibrium Phenomena in Dusty Supersonic Flow Past Blunt Bodies of Revolution. Phys. Fluids, 18,446. 

Ionic Nonequilibrium Phenomena in Tissue Interactions with Electromagnetic Fields... 

Models of Nonequilibrium Phenomena in Bioeffects of Weak EM Fields... 

McCourt FRW, Kohler WE, Beenakker JJM, Kuscer I (1990) Nonequilibrium phenomena in gases Dilute gases. Clarendon Press, Oxford... 

William Russel May I follow up on that and sharpen the issue a bit In the complex fluids that we have talked about, three types of nonequilibrium phenomena are important. First, phase transitions may have dynamics on the time scale of the process, as mentioned by Matt Tirrell. Second, a fluid may be at equilibrium at rest but is displaced from equilibrium by flow, which is the origin of non-Newtonian behavior in polymeric and colloidal fluids. And third, the resting state itself may be far from equilibrium, as for a glass or a gel. At present, computer simulations can address all three, but only partially. Statistical mechanical or kinetic theories have something to say about the first two, but the dynamics and the structure and transport properties of the nonequilibrium states remain poorly understood, except for the polymeric fluids. 

E. W. Montroll and F. Shlesinger, in Nonequilibrium Phenomena II From Stochastics to Hydrodynamics, J. L. Lebowitz, E. W. Montroll, eds., North-Holland, Amsterdam, 1984. 

This equation describes the pressure difference because of the mass fraction difference when there is no temperature difference. This is called the osmotic pressure. This effect is reversible because AT - 0,, /2 = 0. and at stationary state J = 0. Therefore, Eq. (7.244) yields Jq = 0, and the rate of entropy production is zero. The stationary state under these conditions represents an equilibrium state. Equation (7.263) does not contain heats of transport, which is a characteristic quantity for describing nonequilibrium phenomena. 

One needs to describe nonequilibrium phenomena by the simultaneous consideration of mass, temperature, and time of the local states while accounting for the given time and energy dissipation due to temperature changes. The time scale over which microscopic changes occm is much smaller than the time scale associated with macroscopic changes. Temperature fluctuations in a microstate will be different from those in a macroscopic state in which the properties are the averages of many microstate values. 

Laggner P. Nonequilibrium phenomena in lipid-membrane phase-transitions. J. Phys. IV 1993 3 259-269. 

Any nonequilibrium phenomena necessarily involve states in which different portions of a given system display different physical characteristics. To handle this situation we subdivide the system into tiny subunits and allow all variables of interest to become functions of their position within the sample, and also, to become functions of time. Thus, each thermodynamic variable (pi of interest must be specified in terms of its position r at time t (pi = (pi r,t). 

As our first illustration of nonequilibrium phenomena we consider the case of shock effects in conjunction with Fig. 6.2.1. 

B. Hafskjold, in Thermal Nonequilibrium Phenomena in Fluid Mechanics, W. Kohler and S. Wiegand (eds). Springer, Berlin, 2002. 

When a surfactant-water or surfactant-brine mixture is carefully contacted with oil in the absence of flow, bulk diffusion and, in some cases, adsorption-desorption or phase transformation kinetics dictate the way in which the equilibrium state is approached and the time required to reach it. Nonequilibrium behavior in such systems is of interest in connection with certain enhanced oil recovery processes where surfactant-brine mixtures are injected into underground formations to diplace globules of oil trapped in the porous rock structure. Indications exist that recovery efficiency can be affected by the extent of equilibration between phases and by the type of nonequilibrium phenomena which occur (J ). In detergency also, the rate and manner of oily soil removal by solubilization and "complexing" or "emulsification" mechanisms are controlled by diffusion and phase transformation kinetics (2-2). 

The diffusion path method has been used to interpret nonequilibrium phenomena in metallurgical and ceramic systems (10-11) and to explain diffusion-related spontaneous emulsification in simple ternary fluid systems having no surfactants (12). It has recently been applied to surfactant systems such as those studied here including the necessary extension to incorporate initial mixtures which are stable dispersions instead of single thermodynamic phases (13). The details of these calculations will be reported elsewhere. Here we simply present a series of phase diagrams to show that the observed number and type of intermediate phases formed and the occurrence of spontaneous emulsification in these systems can be predicted by the use of diffusion paths. 

---