Irreversible transformation description

These assumptions are partially different from those introduced in our previous model.10 In that work, in fact, in order to simplify the kinetic description, we assumed that all the steps involved in the formation of both the chain growth monomer CH2 and water (i.e., Equations 16.3 and 16.4a to 16.4e) were a series of irreversible and consecutive steps. Under this assumption, it was possible to describe the rate of the overall CO conversion process by means of a single rate equation. Nevertheless, from a physical point of view, this hypothesis implies that the surface concentration of the molecular adsorbed CO is nil, with the rate of formation of this species equal to the rate of consumption. However, recent in situ Fourier transform infrared (FT-IR) studies carried out on the same catalyst adopted in this work, at the typical reaction temperature and in an atmosphere composed by H2 and CO, revealed the presence of a significant amount of molecular CO adsorbed on the catalysts surface.17 For these reasons, in the present work, the hypothesis of the irreversible molecular CO adsorption has been removed. 

In conclusion, we should mention that in the description of the behavior of distinct alkoxides it appears very difficult to distinguish the influence of each of the two factors — the inhomogeneity of the molecular composition and the presence of oxoderivatives. In certain cases the reversibility of transformations and reproducibility of the properties of the oligomeric forms can be used as criterion (as for Al(OPr )3) indicating the constant chemical composition and the dominance of the first factor. At the same time, an irreversible aggregation/ polymerization can result from the both factors. 

Reduction of the motion models to the rest models and determination of their role in the general model engineering. Transformation of the equations of irreversible macroscopic kinetics. Equilibrium description of explosions, hydraulic shock, short circuit, and other "supemonequilibrium" processes. 

Unlike classical quantum mechanics, the spontaneous processes of the damped oscillator are irreversible, so its quantum mechanical description needs changes to some instruments of classical quantum mechanics. To do this, we use the Heisenberg picture of quantum processes. In this picture, the observables are time-dependent linear Hermitian operators, and the state vector of the system is time independent. Using the terminology introduced in the first part, the infinitesimal time transformation of the Hermitian operator could happen in two ways ... 

Nevertheless there is a principle that makes scientifically possible the description of the state of this space-time. It is the principle of S3mimetry. Both time and space can be interpreted through the prism of this principle. Vernadsky determined the space of living matter as dissymmetrical. The space-time of living matter could be also called dissymmetrical, because Vernadsky connects the irreversibility of time with the dissymmetry of space (Vernadsky, 1988, pp. 224, 284-285 Aksenov, 1996). From the viewpoint the notions that characterise, for example, fundamental spatial properties of a natural body (e.g. symmetry) would reflect the prop>erties of the space itself and therefore the time, because, thanks to the inseparability of space and time, the characteristics of space and time must be mutually transformable. Then, the question Why is the time of living matter irreversible , can be answered Because the space of living matter is dissymmetric . 

Time-reversibility of irreversible processes sounds paradoxical and requires some explanation (Yablonsky et al., 2011b). The most direct interpretation of time-reversing is to go back in time. This means taking a solution of the dynamic equations x t) and checking whether x(—t) is also a solution. For microscopic dynamics (the Newton or Schrbdinger equations), we expect this to be the case. Nonequilibrium statistical physics combines this idea with the description of macroscopic or mesoscopic kinetics by an ensemble of elementary processes (reactions). The microscopic reversing of time at this level turns into reversing of arrows the reaction a, A, —> Eft , transforms into... 

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