This paper constitutes the first attempt to bridge the evolutionary theory in economics and the theory of active particles in mathematics. It seeks to present a kinetic model for an evolutionary formalization of economic dynamics. The new derived mathematical representation intends to formalize the processes of learning and selection as the two fundamental drivers of evolutionary environments [G. Dosi, M.-C. Pereira and M.-E. Virgillito, The footprint of evolutionary processes of learning and selection upon the statistical properties of industrial dynamics, Ind. Corp. Change, 26 (2017) 187–210]. To coherently represent the aforementioned properties, the kinetic theory of active particles [N. Bellomo, A. Bellouquid, L. Gibelli and N. Outada, A Quest Towards a Mathematical Theory of Living Systems (Birkhäuser-Springer, 2017)] is here further developed, including the complex interaction of two hierarchical functional subsystems. Modeling and simulations enlighten the predictive ability of the approach. Finally, we outline the potential avenues for future research.

中文翻译：

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从粒子到公司：关于攀登进化景观的动力学理论

本文首次尝试将经济学中的进化理论与数学中的活性粒子理论联系起来。它试图为经济动态的演化形式化提出一个动力学模型。新派生的数学表示旨在将学习和选择过程形式化为进化环境的两个基本驱动因素[G. 多西，M.-C。佩雷拉和 M.-E。Virgillito，学习和选择的进化过程对工业动态统计特性的影响，Ind. Corp. Change, 26 (2017) 187–210]。为了连贯地表示上述性质，活性粒子的动力学理论 [N. Bellomo、A. Bellouquid、L. Gibelli 和 N. Outada，对生命系统数学理论的探索（Birkhäuser-Springer，2017)]在这里得到进一步发展，包括两个分层功能子系统的复杂交互。建模和模拟启发了该方法的预测能力。最后，我们概述了未来研究的潜在途径。