We have applied the term "entrepreneurship" to the development of non-profit organizations working in the field of social and innovation activity, as a movement through the development of ideas towards creating new enterprises. We reviewed the promotion of social innovations on a methodological basis of sociosynergetics using cross-disciplinary and fractal-evolutionary approaches. The introduction of innovations is accompanied by the irreversibility expressed by the violation of symmetry

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... the past and the future (according to I. Prigozhin), and the research of innovations requires the introduction of the concept of an "event". Some events should have the ability to change the course of evolution. The criterion for evaluating the advancement of social innovation is the degree of its influence on the social system: the local nature of the impact -Auto-Poesies models; the emergence of a new parameter of order -Synergyintegrating models; the allocation of a new sub-system in the modernized old social system -Openness entrepreneurship models; the birth of a new social system. In managing innovation processes, it is important to choose such innovations that are in line with the trends in the development of the social system.