Stochastic and Deterministic Formulation of Chemical Rate Equations

It is shown, on the basis of some examples, that the commonly used stochastic theory of gas‐phase chemical rate equations reduces to the deterministic formulation in the thermodynamic limit, $\mathrm{N\hspace{0.17em}\to \hspace{0.17em}\infty }$ , $\mathrm{V\hspace{0.17em}\to \hspace{0.17em}\infty }$ , $\mathrm{N\hspace{0.17em}/\hspace{0.17em}V}$ fixed. Since the commonly used deterministic collision theory of chemical kinetics is derivable from the Boltzmann equation with reactive scattering terms, the stochastic formulation of chemical kinetics is thus shown to be equivalent to the results of the Boltzmann equation in the thermodynamic limit. However, since the stochastic theory has not been derived from the Liouville equation for finite systems, the validity of the calculations of the deviation of the stochastic mean from the deterministric results and the fluctuations about that mean for finite $N$ has not been established.