On the weighted interactions in the discrete thermostatted kinetic theory
The mathematical modeling of the interactions among the active particles of a complex system is an important issue in the discrete thermostatted kinetic theory. In particular a weight function needs to be introduced in order to differentiate the multiple interactions. This paper is devoted to the definition of a weighted framework of the discrete thermostatted kinetic theory of the active particles. Specifically the weight function is assumed to be solution of an inverse problem based on the weighted global density of the system. The existence and uniqueness of the weight function is in general proved by employing the maximum entropy principle of Shannon. Moreover the analytical expression of the weight function is derived. Finally application to complex systems and research perspectives are discussed in the last section of the paper.