Chapter 18 - Application of the H function in vibrational relaxation

Abstract

Classical dynamics is symmetric with respect to time reversal. Newtonian function f = ma or Hamilton's equations are symmetric under t ->-t transformation. However, our world seems irreversible. Everything always moves toward the future. It is never in reverse. In physics, the quantity for irreversibility is entropy, S. Entropy is a macroscopic idea. How to relate micro-reversible process to the macro-irreversible process, or how to derive macro-irreversible phenomena from a micro-reversible process is a fundamental physical problem. Boltzmann has derived a distribution function for a many-particle system to construct the so-called H function which decreases as time elapses till the system reaches equilibrium. In other words, the H function is the foundation for entropy. The relation is: Here, kB is Boltzmann's constant. The significance of Boltzmann's work is the derivation of an irreversible process from time-reversal dynamics. Using examples, the author shows in analogy with the H function, we will construct a function that increases with time in the coset dynamics. This analogous H function can be used to characterize the relaxation of molecular vibration. The construction of the H function for vibrational relaxation is studied here. Resonances in H2O and DCN vibration are also covered in the chapter. From cases of H2O and DCN by employing the algebraic coset algorithm, we have constructed an H function in analogy with the H function in thermodynamics. Through this H function, resonances in high vibrational excitation can be studied in a convenient way. Though only the cases of H2O and DCN are considered, the potential application of this algorithm deserves attention, especially in IVR for highly excited vibration.