Chemical evolution, nonequilibrium

TNG.67.1. Prigogine, Nonequilibrium Thermodynamics and Chemical Evolution An Overview,... 

Before addressing the main topic of chemical evolution, I would like to discuss briefly the rather curious story of the Belgian school of thermodynamics, often called the Brussels school. It took shape at the end of the 1920s and during the 1930s. At a time when the great schools of thermodynamics, such as the Californian school founded by Lewis and the British school with Guggenheim, directed their efforts almost exclusively to the study of equilibrium systems, the point of view presented by the Brussels school appeared as quite unorthodox and somewhat controversial. Indeed, the Brussels school tried to approach equilibrium as a special case of nonequilibrium and concentrated its efforts on the presentation of thermodynamics in a form that would be applicable also to nonequilibrium situations. This story is rather curious from the point of view of the history of science, so let me go into a little more detail. 

Here, I would like to elaborate further on the theme of bifurcation. Section II describes the present state of bifurcation analysis of nonequilibrium systems and gives some of my personal perspectives on what I consider to be some promising lines of development. Section III reviews a number of physical, chemical, or biological problems which can be modeled by means of this theory and which provide us with illustrations of chemical evolution, the subject of the present volume. A representative case, the origin and selection of chirality, is analyzed in Section IV. Some conclusions regarding the dynamics of self-organizing systems are presented in Section V. 

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... 

The state variables are (41). The time evolution (63) does not involve any nondissipative part and consequently the operator L, in which the Hamiltonian kinematics of (41) is expressed, is absent (i.e., L = 0). Time evolution will be discussed in Section 3.1.3. We now continue to specify the dissipation potential 5. Following the classical nonequilibrium thermodynamics, we introduce first the so-called thermodynamic forces (X 1-.. X k) Jdriving the chemically reacting system to the chemical equilibrium. As argued in nonequilibrium thermodynamics, they are linear functions of (nj,..., nk,) (we recall that n = (p i = 1,2,..., k on the Gibbs-Legendre manifold) with the coefficients... 

Therefore, at equilibrium A, = 0. Equation (8.97) shows that during the time evolution, the surrogate system 2 proceeds through stable equilibrium states, and system 1 proceeds through states Xs. This condition is stated without any reference to microscopic reversibility, and applies for all values of X, which represent both the chemical equilibrium and nonequilibrium states. We can expand each of the r reactions into a Taylor series around the chemical equilibrium state at which X = 0... 

The evolution of thermodynamically nonequilibrium systems (including the systems with complex stepwise chemical transformations, among them catalytic and biological reactions) occurs with respective changes in thermo dynamic parameters of the whole system or of its parts. Hence, nonequilib rium states are inherent in the nonequilibrium systems (both open and closed), while the relevant parameters and features of those states can be functions of time and/or space. For example, when a system is temperature and pressure isotropic, the Gibbs potential, G, of the entire system may be a function of not only temperature (T) and pressure (p) but also of time (t) ... 

This specific feature of the stationary state of chemical systems that undergo their evolution via an arbitrary combination of only monomolec ular (or reduced to monomolecular) transformations, as well as transforma tions that are linear in respect to the intermediates, is of practical importance to simplify the analysis of complex stepwise chemical processes with the use of methods of nonequilibrium thermodynamics. 

There are two interesting regimes of time evolution in the probing/detection of dynamical nonequilibrium structures. In the regime of dynamics, the time evolution of atomic positions is detected on its intrinsic timescale, i.e., femtoseconds. Short X-ray pulses - on the timescale of atomic motion - are required in order to follow the dynamics of the chemical bond. In the regime of kinetics, which has to do with the time evolution of populations - and in the context of time-resolved X-ray diffraction -the time evolution in an ensemble average of different interatomic distances or the structural determination of short-lived chemical species is considered. 

The preparation of nonequilibrium level or species populations is the first step in any kinetic experiment. The introduction of lasers to chemical research has opened up new possibilities for preparing, often state-selectively, the initial nonequilibrium states. However, the subsequent time evolution of the molecular populations occurs almost invariably along several relaxation pathways. Some of which, like intra- and intermolecular vibrational energy transfer in infrared multiphoton absorption experiments, may interfere with the exciting laser pulse and/or with the specific process investigated. In such cases, as in chemical laser research, one has to interpret the behavior of complex nonequilibrium molecular systems in which the laser radiation plays of course a major role. This establishes the link between the present article and the general subject of this volume. 

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