Chemical Kinetics and Dynamics

TLDR

Chemical reactions are irreversible processes that generate entropy, belong to nonintegrable Poincaré systems, involve quantum resonances, and exhibit multiple time scales. Λ is defined by the interactions among all species, including the solvent, in the system. By analyzing simple decay processes, the authors derived a nonunitary, invertible operator Λ that reduces to the unitary operator U for integrable systems, yielding kinetic equations with broken time symmetry that explicitly demonstrate irreversible behavior and entropy production.

Abstract

A bstract : Chemical reactions correspond to irreversible processes creating entropy. Chemistry belongs to the class of nonintegrable Poincare systems. In general, chemistry is associated with resonances—transitions of quantum states. We have studied some very simple examples of such processes, like decay of an unstable state, in detail. (In such cases, there are always multiple time scales.) We obtain a nonunitary (‘star unitary’), invertible, nondistributive operator Λ (which reduces to the unitary transformation operator U for integrable systems). The explicit form of Λ depends on the interaction of each species with all other types of molecules in the system including the solvent. The basic property that results from Λ is that the fundamental description of nonintegrable systems is no longer in terms of Hamiltonian equations, but in terms of kinetic equations with broken time symmetry. Once we have the kinetic equations, it is easy to show that we have irreversible processes and entropy production.