Nonequilibrium decays

The concept was developed further by Narayanaswamy (1971) and Moynihan et al. (1976) who treated the kinetics of the aging processes by describing the relaxation toward an equilibrium state in terms of a nonequilibrium decay function. As this depended on the departure from equilibrium, the kinetics are also nonlinear. To allow for this, the average relaxation time, t, was made a function of both temperature and structure and expressed as... 

Markov decay time, Monte Carlo heat flow simulation, nonequilibrium molecular dynamics, 80-81... 

The oil-water dynamic interfacial tensions are measured by the pulsed drop (4) technique. The experimental equipment consists of a syringe pump to pump oil, with the demulsifier dissolved in it, through a capillary tip in a thermostated glass cell containing brine or water. The interfacial tension is calculated by measuring the pressure inside a small oil drop formed at the tip of the capillary. In this technique, the syringe pump is stopped at the maximum bubble pressure and the oil-water interface is allowed to expand rapidly till the oil comes out to form a small drop at the capillary tip. Because of the sudden expansion, the interface is initially at a nonequilibrium state. As it approaches equilibrium, the pressure, AP(t), inside the drop decays. The excess pressure is continuously measured by a sensitive pressure transducer. The dynamic tension at time t, is calculated from the Young-Laplace equation... 

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] ... 

The Kolmogorov-Sinai entropy per unit time is defined in Eq. (89) as the supremum of h over all the possible partitions V. Since we expect that the probability of the nonequilibrium steady state is not time-reversal symmetric, the probability of the time-reversed paths should decay at a different rate, which can be called a time-reversed entropy per unit time [3]... 

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. 

Sharp and Lohr proposed recently a somewhat different point of view on the relation between the electron spin relaxation and the PRE (126). They pointed out that the electron spin relaxation phenomena taking a nonequilibrium ensemble of electron spins (or a perturbed electron spin density operator) back to equilibrium, described in Eqs. (53) and (59) in terms of relaxation superoperators of the Redfield theory, are not really relevant for the PRE. In an NMR experiment, the electron spin density operator remains at, or very close to, thermal equilibrium. The pertinent electron spin relaxation involves instead the thermal decay of time correlation functions such as those given in Eq. (56). The authors show that the decay of the Gr(T) (r denotes the electron spin vector components) is composed of a sum of contributions... 

We can now distinguish three general cases, depending on whether the first decaying species has a longer, a much longer, or a shorter half-hfe than that of the daughter nuclide. These three cases are transient equilibrium, secular equilibrium, and nonequilibrium. 

Figure 11,8 Composite decay curves for (A) mixtures of independently decaying species, (B) transient equilibrium, (C) secular equilibrium, and (D) nonequilibrium, a composite decay curve b decay curve of longer-lived component (A) and parent radio nuclide (B, C, D) c decay curve of short-lived radionuclide (A) and daughter radionuclide (B, C, D) d daughter radioativity in a pure parent fraction (B, C, D) e total daughter radioactivity in a parent-plus-daughter fraction (B). In all cases, the detection coefficients of the various species are assumed to be identical. From Nuclear and Radiochemistry, G. Friedlander and J. W. Kennedy, Copyright 1956 by John Wiley and Sons. Reprinted by permission of John Wiley and Sons Ltd.

Nonequilibrium Aging State (NEAS). The system is initially prepared in a nonequilibrium state and put in contact with the sources. The system is then allowed to evolve alone but fails to reach thermal equilibrium in observable or laboratory time scales. In this case the system is in a nonstationary slowly relaxing nonequilibrium state called aging state and is characterized by a very small entropy production of the sources. In the aging state two-times correlations decay slower as the system becomes older. Two-time correlation functions depend on both times and not just on their difference. 

Time-resolved laser flash ESR spectroscopy generates radicals with nonequilibrium spin populations and causes spectra with unusual signal directions and intensities. The signals may show absorption, emission, or both and be enhanced as much as 100-fold. Deviations from Boltzmann intensities, first noted in 1963, are known as chemically induced dynamic electron polarization (CIDEP). Because the splitting pattern of the intermediate remains unaffected, the CIDEP enhancement facilitates the detection of short-lived radicals. A related technique, fluorescence detected magnetic resonance (FDMR) offers improved time resolution and its sensitivity exceeds that of ESR. The FDMR experiment probes short-lived radical ion pairs, which form reaction products in electronically excited states that decay radiatively. ... 

Atmospheric pressure plasmas, just like most other plasmas, are generated by a high electric field in a gas volume. The few free electrons which are always present in the gas, due to, for example, cosmic radiation or radioactive decay of certain isotopes, will, after a critical electric field strength has been exceeded, develop an avalanche with ionization and excitation of species. Energy gained by the hot electrons is efficiently transferred and used in the excitation and dissociation of gas molecules. In a nonequilibrium atmospheric pressure plasma, collisions and radiative processes are dominated by energy transfer by stepwise processes and three-body collisions. The dominance of these processes has allowed many... 

Khandelwal A, Rabideau AJ. Transport of sequentially decaying reaction products influenced by linear nonequilibrium sorption. Water Resour Res 1999 35 1939-1945. 

However, in all the papers mentioned above the authors analyzed only three-dimensional (3D) systems, while a two-dimensional (2D) case is also experimentally observed surfaces of various absorbers, heterogeneous catalysts, photocatalysts, etc. In [137], Fel dman and Lacelle examined the quenched disorder average of nonequilibrium magnetization, i.e., a free induction decay G(t) and its relative fluctuations for dipolar coupled homonuclear spins in dilute substitutionally disordered lattices. The studies of NMR free induction decays and their relative fluctuations revealed that the functional form of the disorder average (G(t))c depends on the space-filling dimentionality D of the lattice. Explicit evaluations of these averages for dilute spin networks with D = 1, 2, 3 were presented in [137] ... 

Some serious discrepancies however exist, as follows (1) The total Stokes shifts from nonequilibrium calculations, 17.7 kJ/mole for isomer 1 and 22.5 kJ/mol for isomer 2, are significantly larger than the experimental result, 9.5 kJ/mol (2) no ultrafast decay (or inertial motion) in less than 1 ps in the experiments... 

The kinetic equations serve as a bridge between the microscopic domain and the behavior of macroscopic irreversible processes through the description of hydrodynamics in terms of intermolecular collisions. Hydrodynamics can specify a large number of nonequilibrium states by a small number of reproducible properties such as the mass, density, velocity, and energy density of a fluid conserved during the collision of molecules. Therefore, the hydrodynamic equations can describe a wide range of relaxation processes of nonequilibrium states to equilibrium state. We call such processes decay processes represented by phenomenological equations, such as Fourier s law of heat conduction. The decay rates are determined by the transport coefficients. Reliable transport coefficients provide microscopic and macroscopic information, and validate the results of molecular dynamics. 

In nonequilibrium systems, spontaneous decaying phenomena toward equilibrium take place. When systems are in the vicinity of global equilibrium, linear relations exist between flows Jt and thermodynamic driving forces A). 

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