$H$-theorem for continuous- and discrete-time chemical kinetic systems and a system of nucleosynthesis equations

An $H$-theorem is proved for generalizations of continuous- and discrete-time chemical kinetic equations. A mathematical model of heavy nuclei formation based on neutron capture in astrophysical conditions is constructed. The model describes both rapid and slow processes with allowance for radiative capture and photodetachment of neutrons and $\beta$-decay. An $H$-theorem for this model is proved.