Chemical evolution, nonequilibrium thermodynamics

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. 

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... 

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. 

Modeling of spatiotemporal evolution may serve as a powerful complementary tool for studying experimental nonisothermal reaction-diffusion systems within a porous catalyst particle and a membrane. The linear nonequilibrium thermodynamics approach may be used in modeling coupled nonisothermal reaction-diffusion systems when the system is in the vicinity of global equilibrium. In the modeling, the information on coupling mechanisms among transport processes and chemical reactions is not needed. 

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... 

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