The H-theorem for the chemical kinetic equations with discrete time and for their generalizations

Abstract

Abstract. In this paper the generalizations of equations of chemical kinetics, including classical and quantum chemical kinetics, is considered. We make time discrete in these equations and prove the H-theorem.

Approaches to determining the kinetics for the formation of a nano-dispersed substance from the experimental distribution functions of its nanoparticle properties

“…In the linear case, the transition from continuous time to discrete gives the transition from a Markov process to a Markov chain and the H-theorem is valid and studied (see [54] and references in it, [55]). In the nonlinear case, for explicit time discretization it is fulfilled in rare cases [19,20] and for the implicit one, it is investigated in [20,21]. The diffuse approximation is widely used for the modeling of crystallization processes of a dispersed substance [5][6][7][8].…”

“…For the system of equation (21)-(2.3) the H-theorem is fulfilled, but for the system with the explicit time discretization the H-theorem is not valid: it is proved in [19,20] that the H-theorem is not fulfilled for the case of this system when only single molecules and dimers are considered. Also, it is valid for the implicit time discretization: when ∆N (n, t) ≡ N (n, t) − N (n, t − ∆t) [20,21], and thus, we can't use the explicit time discretization for the computer simulations. Instead the equation (2.1) one can write the conservation law of the number of all molecules of the forming the phase substance in the system N 0 :…”