H-THEOREM FOR LIFETIME DISTRIBUTIONS OF ACTIVE INTERMEDIATES IN NONEQUILIBRIUM CHEMICAL-SYSTEMS WITH STABLE LIMIT-CYCLES

The large time behavior of the lifetime distributions of active interm ediates is investigated for nonequilibrium chemical systems with stabl e limit cycles. The lifetime distributions are the solutions of a syst em of partial differential equations which can be integrated by using the method of characteristics. A generalized H-function is defined in terms of two sets of solutions of these partial differential equations corresponding to two different initial solutions. An H-theorem is pro ven which shows that for a system with a stable limit cycle ail transi ent lifetime distributions evolve toward the same normal form which is a periodic function of time and which, up to a constant phase factor, is independent of the initial conditions. A frequency response tracer experiment is suggested for the evaluation of the probability distrib ution of the lifetime of an intermediate. A special experiment makes p ossible the direct measurement of the Fourier transform of the probabi lity distribution with respect to the lifetime of a molecule. This Fou rier transform. is a generalized susceptibility function which depends both on time and frequency. The real and imaginary parts for the susc eptibility function are related to each other by means of a set of gen eralized Kramers-Kronig relationships, which are a consequence of caus ality. The theory is used for generalizing the kinetic spectrum analys is of time-dependent normal processes. An alternative approach to spec tral kinetic analysis determines the influence of environmental fluctu ations on the lifetime distributions. It is shown that the average lif etimes of active intermediates in the system increase with the strengt h of environmental fluctuations and in the limit of random processes w ith long memory, even though the concentrations remain finite, the ave rage lifetimes tend to infinity. A numerical computation of the large time behavior of active intermediates is carried out in the particular case of the Selkov model with a stable limit cycle. The numerical ana lysis confirms the theoretical predictions presented in the article.