At present, the world is witnessing the historic convergence of a new round of scientific and technological revolution and industrial change with the transformation of the development mode, and it is strategically important and far-reaching to rapidly enhance new qualitative productivity kinetic energy (NQPKE) on the basis of the lessons learning from the experience of the pioneering countries for all countries, so as to expand the room for manoeuvre of the economic development, obtain the initiative of international competition, and realise the benign interaction of high-quality development and high-level of security. On the basis of analysing the formation mechanism of NQPKE, we characterize NQPKE by the coupling and coordination degree of digital productivity and green productivity, we analyse NQPKE by using the entropy weight TOPSIS method and the coupling and synergistic model, and analyse the spatial-temporal characteristics, steady state development and constraints of NQPKE by using the method of kernel density estimation, the Markov chain, the spatial Markov chain, and the obstacle degree model based on data from 21 European countries from 2009 to 2022. The study finds that: (1) The NQPKE shows a wave-like development trend, and the polarization or multi-polarization state of the whole and the four major regions has been slowly weakened, with a certain degree of "club convergence" and "spatial spillover"; (2) The overall situation of barriers to NQPKE is relatively stable, the insufficient investment in scientific and technological development and weak technological innovation capacity are the most critical factors constraining the NQPKE in various countries. Based on the above conclusions, the article proposes to hold high the banner of peaceful development and win-win cooperation, give full play to the "club convergence" and "spatial spillover" effects of NQPKE, accelerate the development of NQPKE adapt to local conditions, and the "digital + green" double base will stimulate technological innovation, and the construction of a digital and green synergistic management system stimulates the potential of the new quality productivity of enterprises, ultimately unleash the surging kinetic energy of new quality productivity development.
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