Phase space theory microscopic reversibility

To invoke microscopic reversibility and obtain a rate expression for a unimolecular reaction through considering the association of its products is an idea with a long history [706] and has been taken up in recent years in mass spectrometry [486, 489]. There are a number of treatments [165, 166, 486, 489], which are similar to each other and all of which can be considered to be, in essence, reformulations of QET. There is a tendency to refer to these reformulations, either individually of collectively, as phase space theory [165, 166, 452, 485] and this term is used in a collective sense here. 

The essential nature of this relationship is clear statistical theories are based on a number of simplifying assumptions consistent with chaotic behavior. Specifically,2 any such theory must satisfy microscopic reversibility and the condition of zero relevance. The latter condition requires that the final state be independent of all initial conditions other than conserved quantities, that is, from the viewpoint of classical mechanics, that the system display the relaxation characteristic of chaotic motion. We note, for reference, that this minimal set of requirements allows for the construction of a large number of theories,3 the most prominant of which are the RRK.M theory of uni-molecular dissociation4 and the phase space theory of bimolecular reactions.5 Such theories have analogues, and in some cases their origins are in other areas such as nuclear physics.6... 

Although radiative association has been occasionally studied in the laboratory (e.g., in ion traps ), most experiments are imdertaken at densities high enough that ternary association, in which collision with the background gas stabihses the complex, dominates. A variety of statistical treatments, such as the phase-space theory, have been used to study both radiative and ternary association. These approximate theories are often quite reliable in their estimation of the rate coefficients of association reactions. In the more detailed treatments, microscopic reversibility has been applied to the formation and re-dissociation of the complex. Enough experimental and theoretical studies have been undertaken on radiative association reactions to know that rate coefficients range downward from a collisional value to one lower than lO cm s and depend strongly on the lifetime of the complex and the frequency of photon emitted. The... 

The plan of this chapter is the following. Section II gives a summary of the phenomenology of irreversible processes and set up the stage for the results of nonequilibrium statistical mechanics to follow. In Section III, it is explained that time asymmetry is compatible with microreversibility. In Section IV, the concept of Pollicott-Ruelle resonance is presented and shown to break the time-reversal symmetry in the statistical description of the time evolution of nonequilibrium relaxation toward the state of thermodynamic equilibrium. This concept is applied in Section V to the construction of the hydrodynamic modes of diffusion at the microscopic level of description in the phase space of Newton s equations. This framework allows us to derive ab initio entropy production as shown in Section VI. In Section VII, the concept of Pollicott-Ruelle resonance is also used to obtain the different transport coefficients, as well as the rates of various kinetic processes in the framework of the escape-rate theory. The time asymmetry in the dynamical randomness of nonequilibrium systems and the fluctuation theorem for the currents are presented in Section VIII. Conclusions and perspectives in biology are discussed in Section IX. 

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