Binary non-Markovian theory of bulk associative–dissociative reaction $$ A + A \leftrightarrow C $$. I: many-particle aspects of the theory

It is shown that reversible reaction may be considered as irreversible one on restricted time interval. However, the time range of the applicability of the law of mass action for the case of many-particle derivation of binary kinetic equations which is valid at small density parameters also has time restrictions. If the range of binary description is narrower than that of irreversible approximation of the kinetics, then this approximation is valid over the entire time range of the applicability of the law of mass action. The necessary conditions are found for which hierarchies for reduced distribution functions (RDFs) for the reaction at hand are constructed that satisfy the required hierarchy condition, and have all the properties inherent in BBGKY hierarchies of non-equilibrium statistical mechanics. This allows one to use the advanced methods of non-equilibrium statistical mechanics in many-particle derivation of kinetic equations of chemical reactions in solutions. It is shown that such initial conditions are possible at which for complete evolution no closed kinetic equation exists. Development of RDFs for reaction systems opens the way to the employment of advanced methods of non-equilibrium statistical mechanics in many-particle derivation of kinetic equations of chemical reactions in solutions.