Mathematical formalism of physics of systems with motivation

The paper discusses fundamental problems in mathematical description of social systems based on physical concepts, with so-called statistical social systems being the main subject of consideration. Basic properties of human beings and human societies that distinguish social and natural systems from each other are listed to make it clear that individual mathematical formalism and physical notions should be developed to describe such objects rather then can be directly inherited from classical mechanics and statistical physics. As a particular example systems with motivation are considered. Their characteristic features are analyzed individually and the appropriate mathematical description is proposed. Finally the paper concludes that the basic elements necessary for describing statistical social systems or, more rigorously, systems with motivation are available or partly developed in modern physics and applied mathematics.