Khrennikov Andrei
International Center for Mathematical Modeling in Physics and Cognitive Sciences, Linnaeus University, SE-351 95 Växjö, Sweden.
Entropy (Basel). 2023 Jun 1;25(6):886. doi: 10.3390/e25060886.
The aim of this review is to highlight the possibility of applying the mathematical formalism and methodology of quantum theory to model behavior of complex biosystems, from genomes and proteins to animals, humans, and ecological and social systems. Such models are known as quantum-like, and they should be distinguished from genuine quantum physical modeling of biological phenomena. One of the distinguishing features of quantum-like models is their applicability to macroscopic biosystems or, to be more precise, to information processing in them. Quantum-like modeling has its basis in quantum information theory, and it can be considered one of the fruits of the quantum information revolution. Since any isolated biosystem is dead, modeling of biological as well as mental processes should be based on the theory of open systems in its most general form-the theory of open quantum systems. In this review, we explain its applications to biology and cognition, especially theory of quantum instruments and the quantum master equation. We mention the possible interpretations of the basic entities of quantum-like models with special interest given to QBism, as it may be the most useful interpretation.
本综述的目的是强调将量子理论的数学形式和方法应用于对复杂生物系统行为进行建模的可能性，这些系统涵盖从基因组、蛋白质到动物、人类以及生态和社会系统。此类模型被称为类量子模型，应将它们与对生物现象的真正量子物理建模区分开来。类量子模型的一个显著特征是它们适用于宏观生物系统，或者更确切地说，适用于其中的信息处理。类量子建模基于量子信息理论，可以被视为量子信息革命的成果之一。由于任何孤立的生物系统都是无生命的，对生物过程以及心理过程的建模都应以最一般形式的开放系统理论——开放量子系统理论为基础。在本综述中，我们解释其在生物学和认知方面的应用，特别是量子仪器理论和量子主方程。我们提及类量子模型基本实体的可能解释，并对量子贝叶斯主义（QBism）给予特别关注，因为它可能是最有用的解释。
