Nonequilibrium state, evolution from

When tryptophan is excited to the La state, the local equilibrium is shifted and the system is in a nonequilibrium state. Our observed hydration dynamics, with two distinct time scales, reflect the temporal evolution of two types of motions from the initial nonequilibrium configuration to new equilibrated state... 

From the perspective of the fluctuation-dissipation approach, Dewey (1996) proposed that the time evolution of a protein depends on the shared information entropy. S between sequence and structure, which can be described with a nonequilibrium thermodynamics theory of sequence-structure evolution. The sequence complexity follows the minimal entropy production resulting from a steady nonequilibrium state... 

Let us consider now the nonequilibrium state of a fractal-like medium assuming that this nonequilibrium state is characterized by many events such that a subsequent event is separated by a certain time interval r, from a previous event. In this case, some intervals will be eliminated from a continuous process of system evolution by a definite law. Assume that such a process is caused by a temporal fractal state of dimensionality df the corresponding relaxation equation can be written as... 

For a many-spin system, the solution of Equation (4.6) becomes very complicated and the individual coupling frequencies d cannot always be extracted from experimental data. Nevertheless, the sum polarization 2, S,j. remains time invariant and is called a constant of the motion. In principle, we must describe the time evolution of an initial nonequilibrium state tr(0) = 2, c,(0)S, as a series of rotations of the density operator in the Hilbert space of the entire spin system. At times t > 0 not only populations but also many-spin terms of the form riA S jnmSmri S appear in the density operator. Of course, this time evolution is fully deterministic and reversible. The reversibility was in fact demonstrated in the polarization-echo experiments [10] (Fig. 4.2) where two sequential time evolutions with a scaling factor of s =1 and s = -1/2 follow each other (see Equation (4.5)). If the second period has twice the length of the first period, the time evolution under the dipolar interaction is refocused and the density operator returns to the initial density operator. 

This interplay between the action of the electric field and the elastic and inelastic collision processes causes the electron component to generally reach a state far from the thermodynamic equilibrium. This nonequilibrium behavior of the electron component cannot be described using the well-developed methods of thermodynamics for equilibrium conditions. Thus, the requirement arises that the state of the electron component established in anisothermal plasmas or its temporal and spatial evolution can be described only on an appropriate microphysical basis. 

Studied the time evolution of the interfacial tension when polyisobutylene (PIB)-b-PDMS was introduced to PIB/PDMS blend, with the copolymer added to the PIB phase in that study both homopolymers were poly disperse. The time dependence of the interfacial tension was fitted with an expression that allowed the evaluation of the characteristic times of the three components. The characteristic time of the copolymer was the longest, whereas the presence of the additive was found to delay the characteristic times of the blend components from their values in the binary system. The possible complications of slow diffusivities on the attainment of a stationary state of local equilibrium at the interface were thoroughly discussed by Chang et al. [58] within a theoretical model proposed by Morse [279]. Actually, Morse [279] suggested that the optimal system for measuring the equilibrium interfacial tension in the presence of a nearly symmetric diblock copolymer would be one in which the copolymer tracer diffusivity is much higher in the phase to which the copolymer is initially added than in the other phase because of the possibility of a quasi-steady nonequilibrium state in which the interfacial coverage is depleted below its equilibrium value by a continued diffusion into the other phase. 

In their subsequent works, the authors treated directly the nonlinear equations of evolution (e.g., the equations of chemical kinetics). Even though these equations cannot be solved explicitly, some powerful mathematical methods can be used to determine the nature of their solutions (rather than their analytical form). In these equations, one can generally identify a certain parameter k, which measures the strength of the external constraints that prevent the system from reaching thermodynamic equilibrium. The system then tends to a nonequilibrium stationary state. Near equilibrium, the latter state is unique and close to the former its characteristics, plotted against k, lie on a continuous curve (the thermodynamic branch). It may happen, however, that on increasing k, one reaches a critical bifurcation value k, beyond which the appearance of the... 

Thus it becomes clear that C( ) in fact measures the evolution of the solvent coordinate as it evolves from its initial (Franck-Condon) nonequilibrium displacement in the excited state, to its final equilibrium value, i.e., C(oo) = 0 = 1— z(oo). 

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