Processes, nonequilibrium

We now add the effects of light excitation. Suppose a flux of I0 photons/cm2 s is incident upon the sample, and the cross section for photon 

For SI GaAs it is almost always true that ni0 (unless center i is a longlifetime trap). If this inequality is sufficiently strong, then the first term on the left-hand side of Eq. (33) can be ignored, and 

A similar relationship for holes, to be used later, can easily be derived  

Each o-vni is a strong function of monochromatic light energy hv as a threshold hv = Et is approached. This phenomenon will be discussed in the next section. However, for completeness we should relate Eq. (34a) to a common expression involving the absorption coefficient a and electron lifetime x 

A more detailed analysis of extrinsic (below band gap) light excitation (Look, 1977b) gives 

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Keizer J 1987 Statistical Thermodynamics of Nonequilibrium Processes (New York Springer)... 

A cross-linked product with unsaturation at the chain ends does, indeed, have a higher modulus. This could be of commercial importance and indicates that industrial products might be formed by a nonequilibrium process precisely for this sort of reason. 

Adib, A. B., Entropy and density of states from isoenergetic nonequilibrium processes, Phys. Rev. E 2005, 71, 056128... 

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. 

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... 

In certain regions of the density-temperature plane, a significant fraction of nuclear matter is bound into clusters. The EOS and the region of phase instability are modified. In the case of /3 equilibrium, the proton fraction and the occurrence of inhomogeneous density distribution are influenced in an essential way. Important consequences are also expected for nonequilibrium processes. 

The dynamical randomness of the nonequilibrium process can be characterized by the decay of the path probabilities as defined by the entropy per unit time [12-14] ... 

For Markov chains with two states 0,1, it turns out that we always have the equality = h so that they are not appropriate to model nonequilibrium processes. 

We notice that the generating and decay functions characterize the nonequilibrium process in the steady state and, consequently, have a general dependence on the affinities which play the role of nonequilibrium parameters. 

In nonequilibrium steady states, the mean currents crossing the system depend on the nonequilibrium constraints given by the affinities or thermodynamic forces which vanish at equihbrium. Accordingly, the mean currents can be expanded in powers of the affinities around the equilibrium state. Many nonequilibrium processes are in the linear regime studied since Onsager classical work [7]. However, chemical reactions are known to involve the nonlinear regime. This is also the case for nanosystems such as the molecular motors as recently shown [66]. In the nonlinear regime, the mean currents depend on powers of the affinities so that it is necessary to consider the full Taylor expansion of the currents on the affinities ... 

In this chapter, we have described recent advances in nonequilibrium statistical mechanics and have shown that they constitute a breakthrough which opens very new perspectives in our understanding of nonequilibrium processes and the second law of thermodynamics. 

It is most remarkable that the entropy production in a nonequilibrium steady state is directly related to the time asymmetry in the dynamical randomness of nonequilibrium fluctuations. The entropy production turns out to be the difference in the amounts of temporal disorder between the backward and forward paths or histories. In nonequilibrium steady states, the temporal disorder of the time reversals is larger than the temporal disorder h of the paths themselves. This is expressed by the principle of temporal ordering, according to which the typical paths are more ordered than their corresponding time reversals in nonequilibrium steady states. This principle is proved with nonequilibrium statistical mechanics and is a corollary of the second law of thermodynamics. Temporal ordering is possible out of equilibrium because of the increase of spatial disorder. There is thus no contradiction with Boltzmann s interpretation of the second law. Contrary to Boltzmann s interpretation, which deals with disorder in space at a fixed time, the principle of temporal ordering is concerned by order or disorder along the time axis, in the sequence of pictures of the nonequilibrium process filmed as a movie. The emphasis of the dynamical aspects is a recent trend that finds its roots in Shannon s information theory and modem dynamical systems theory. This can explain why we had to wait the last decade before these dynamical aspects of the second law were discovered. 

Alternatively, for nonequilibrium process streams, where a pumped reactor sample recycle line is available, in-line fiber-optic transmission cells or probes (Figures 5.26 and 5.27) can be used to minimize sample transport. It is highly desirable that some form of pumped sample bypass loop is available for installation of the cell or probe, so that isolation and cleaning can take place periodically for background reference measurement. 

Nonequilibrium Steady State (NESS). The system is driven by external forces (either time dependent or nonconservative) in a stationary nonequilibrium state, where its properties do not change with time. The steady state is an irreversible nonequilibrium process that cannot be described by the Boltzmann-Gibbs distribution, where the average heat that is dissipated by the system (equal to the entropy production of the bath) is positive. 

We tend to identify 5p(F) as the entropy production in a nonequilibrium system, whereas B(F) is a term that contributes just at the beginning and end of the nonequilibrium process. Note that the entropy production 5p(F) is antisymmetric under time reversal, 5p(F ) = -5p(F), expressing the fact that the entropy production is a quantity related to irreversible motion. According to Eq. (21) paths that produce a given amount of entropy are much more probable than those... 

A number of assumptions are involved in the derivation of the mathematical expressions for nucleation. First, the change of one phase into another is really a nonequilibrium process. There is no guarantee that equations derived for thermodynamic equilibrium will be valid when applied to nonequilibrium. For example, the relationship between surface tension and radius applies for a static bubble, but does it apply to a bubble which is changing in size Second, it is imagined that any cluster which grows to a nucleus is bodily removed from the liquid. Thus nuclei cannot accumulate. This idea leads to a chopped distri-... 

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