Nonequilibrium transient state

Nonequilibrium Transient State (NETS). The system is initially... 

Nonequilibrium Transient State (NETS). Initially the bead is in equilibrium and the trap is at rest in a given position x (0). Suddenly the trap is set in motion. In this case b x) = and the boundary... 

The nonequilibrium aging state (NBAS, see Section III.A) is a nonstationary state characterized by slow relaxation and a very low rate of energy dissipation to the surroundings. Aging systems fail to reach equilibrium unless one waits an exceedingly large amount of time. For this reason, the NEAS is very different from either the nonequilibrium transient state (NETS) or the nonequilibrium steady state (NESS). 

There are still other categories of NESS. For example, in nonequilibrium transient steady states the system starts in a nonequilibrium steady state but is driven out of that steady state by an external perturbation to finally settle in a new steady state. 

The fluctuating variables aie thereby projected onto pair-density fluctuations, whose time-dependence follows from that of the transient density correlators q(,)(z), defined in (12). Tliese describe the relaxation (caused by shear, interactions and Brownian motion) of density fluctuations with equilibrium amplitudes. Higher order density averages are factorized into products of these correlators, and the reduced dynamics containing the projector Q is replaced by the full dynamics. The entire procedure is written in terms of equilibrium averages, which can then be used to compute nonequilibrium steady states via the ITT procedure. The normalization in (10a) is given by the equilibrium structure factors such that the pair density correlator with reduced dynamics, which does not couple linearly to density fluctuations, becomes approximated to ... 

F(, is reduced to the ordinary phase rule if we put S = R = 0. Langmuir pointed out that nonequilibrium states are of two kinds steady states, in which the intrinsic properties of all phases and the relative amounts of the phases do not vary with time, and transient states in which at least one of these variables change with time. 

The fluctuation theorem deals with fluctuations. Since the statistics of fluctuations will be different in different statistical ensembles, the fluctuation theorem is a set of closely related theorems. Also some theorems consider nonequilibrium steady-state fluctuations, while others consider transient fluctuations. One of the fluctuation theorems state that in a time-reversible dynamic system in contact with constant temperature heat bath, the fluctuations in the time-averaged irreversible entropy productions in a nonequilibrium steady state satisfy Eqn (15.49) (Evans and Searles, 2002). 

The approximate solution of the evolution equation for P (x, y t) based on the hypothesis of low coupling between cells shows that the transition between two homogeneous stationary states occurs via an inhomogeneous transient state. Transient inhomogeneous structures may be also responsible for the stabilisation of an unstable state. Such kinds of phenomena are reminiscent of nucleation processes (Blanche, 1981 Frankowicz, 1984) and might be considered as a nonequilibrium analogue of an equilibrium phenomenon. 

GK = Green-Kubo LIT = linear irreversible thermodynamics LRT = linear response theory NEMD = nonequilibrium molecular dynamics NESS = nonequilibrium steady state TTC = thermal transport coefficient TTCF = transient time correlation function. 

Of course, depending on the system, the optimum state identified by the second entropy may be the state with zero net transitions, which is just the equilibrium state. So in this sense the nonequilibrium Second Law encompasses Clausius Second Law. The real novelty of the nonequilibrium Second Law is not so much that it deals with the steady state but rather that it invokes the speed of time quantitatively. In this sense it is not restricted to steady-state problems, but can in principle be formulated to include transient and harmonic effects, where the thermodynamic or mechanical driving forces change with time. The concept of transitions in the present law is readily generalized to, for example, transitions between velocity macrostates, which would be called an acceleration, and spontaneous changes in such accelerations would be accompanied by an increase in the corresponding entropy. Even more generally it can be applied to a path of macrostates in time. 

The FT in Eq. (27) finds application in several nonequilibrium contexts. Here we describe specific results for transient and steady states. 

We will assume a system initially in thermal equilibrium that is transiently brought to a nonequilibrium state. We are going to show that, under such conditions, the entropy production in Eq. (22) is equal to the heat delivered by the system to the sources. We rewrite Eq. (22) by introducing the potential energy function Gx C),... 

Assuming further that linear response theory for the solute/solvent system applies, the dependence of the nonequilibrium free energies of the system (in the ground Fg and excited Fe states) are portrayed in Figure 1 as a function of the electrical polarization of the solvent (see below). In a transient fluores-... 

An aspect of the ES FR that has not been fully exploited as yet is the fact that the dissipation function is sensitive to the choice of the distribution function. Therefore, if a system is presumed to have a particular equilibrium distribution function, with an associated dissipation function, then a field is applied, the transient ES FR should be satisfied for all time. This provides a way of testing if a system is equilibrated, for example. If the FR is not satisfied for the presumed Q, then it indicates that the equilibrium state is not what was expected. This fact has recently been used to establish that domains of the nondissipative, nonequilibrium distributions of glassy systems can be described by Boltzmann weights. Apart from the reversibility of the dynamics, the other key assumption in the derivation of the transient ES FR is that the initial distribution and the dynamics are ergodically consistent. In the same paper, Williams and Evans demonstrated that away from the actual glass... 

Figure 6. Dynamics ofprimary electron-transfer processes triggered hy the femtosecond UV excitation of an aqueous sodium chloride solution ([H20]/[NaCl] = 55). The different steps of an electron photodetachment from the halide ion (Cl ) involve charge transfer to the solvent state (1,2), transient electron-atom couplings (4, 5), and the nonequilibrium state of excess electrons (3). The final steps of the multiple electron photodetachment trajectories (6, 7) are also reported. These data are obtained from time-resolved UV-IR femtosecond spectroscopic data published in references 85 and 86.

Distinguishing between interface-dominated currents and bulk-dominated (ohmic) currents often requires a self-consistent interpretation of a variety of electrical conductivity measurements. These may be steady-state and transient, equilibrium and nonequilibrium, and can use a variety of electrode materials and sample geometries. 

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