The best way to model, understand, and quantify the information contained in complex systems is an open question in physics, mathematics, and computer science. The uncertain relationship between entropy and complexity further complicates this question. With ideas drawn from the object-relations theory of psychology, this paper develops an object-relations model of complex systems which generalizes to systems of all types, including mathematical operations, machines, biological organisms, and social structures. The resulting Complex Information Entropy (CIE) equation is a robust method to quantify complexity across various contexts. The paper also describes algorithms to iteratively update and improve approximate solutions to the CIE equation, to recursively infer the composition of complex systems, and to discover the connections among objects across different lengthscales and timescales. Applications are discussed in the fields of engineering design, atomic and molecular physics, chemistry, materials science, neuroscience, psychology, sociology, ecology, economics, and medicine.
翻译:模拟、理解和量化复杂系统所含信息的最佳方式是物理学、数学和计算机科学方面的一个未决问题。昆虫和复杂程度之间的不确定关系使这一问题更加复杂。随着从心理学的物体关系理论中产生的想法,本文件开发了一个综合系统的目标关系模型,该模型将所有类型的系统,包括数学操作、机器、生物生物机体和社会结构加以概括。由此形成的复杂信息英特罗比(CIE)方程式是在不同情况下量化复杂程度的可靠方法。本文还描述了反复更新和改进CIE方程式的近似解决方案的算法,反复推断复杂系统的构成,并发现不同尺度和时间尺度的物体之间的联系。在工程设计、原子和分子物理学、化学、材料科学、神经科学、心理学、社会学、生态学、经济学和医学等领域都讨论了应用问题。