Khrennikov Andrei, Watanabe Noboru
International Center for Mathematical Modeling in Physics and Cognitive Sciences, Linnaeus University, SE-351 95 Växjö, Sweden.
Department of Information Sciences, Tokyo University of Science, Noda City, Chiba 278-8510, Japan.
Entropy (Basel). 2021 Mar 16;23(3):355. doi: 10.3390/e23030355.
This paper is our attempt, on the basis of physical theory, to bring more clarification on the question "What is life?" formulated in the well-known book of Schrödinger in 1944. According to Schrödinger, the main distinguishing feature of a biosystem's functioning is the ability to preserve its order structure or, in mathematical terms, to prevent increasing of entropy. However, Schrödinger's analysis shows that the classical theory is not able to adequately describe the order-stability in a biosystem. Schrödinger also appealed to the ambiguous notion of negative entropy. We apply quantum theory. As is well-known, behaviour of the quantum von Neumann entropy crucially differs from behaviour of classical entropy. We consider a complex biosystem composed of many subsystems, say proteins, cells, or neural networks in the brain, that is, S=(Si). We study the following problem: whether the compound system can maintain "global order" in the situation of an increase of local disorder and if can preserve the low entropy while other Si increase their entropies (may be essentially). We show that the entropy of a system as a whole can be constant, while the entropies of its parts rising. For classical systems, this is impossible, because the entropy of cannot be less than the entropy of its subsystem Si. And if a subsystems's entropy increases, then a system's entropy should also increase, by at least the same amount. However, within the quantum information theory, the answer is positive. The significant role is played by the entanglement of a subsystems' states. In the absence of entanglement, the increasing of local disorder implies an increasing disorder in the compound system (as in the classical regime). In this note, we proceed within a quantum-like approach to mathematical modeling of information processing by biosystems-respecting the quantum laws need not be based on genuine quantum physical processes in biosystems. Recently, such modeling found numerous applications in molecular biology, genetics, evolution theory, cognition, psychology and decision making. The quantum-like model of order stability can be applied not only in biology, but also in .
本文是我们基于物理理论，尝试对薛定谔1944年在其著名著作中提出的“生命是什么？”这一问题进行更清晰阐释的成果。根据薛定谔的观点，生物系统功能运作的主要显著特征是保持其有序结构的能力，或者用数学术语来说，是防止熵增加的能力。然而，薛定谔的分析表明，经典理论无法充分描述生物系统中的有序稳定性。薛定谔还提及了负熵这一模糊概念。我们应用量子理论。众所周知，量子冯·诺依曼熵的行为与经典熵的行为有很大不同。我们考虑一个由许多子系统组成的复杂生物系统，比如蛋白质、细胞或大脑中的神经网络，即S = (Si)。我们研究以下问题：在局部无序增加的情况下，复合系统能否维持“全局秩序”，以及在其他Si的熵增加（可能大幅增加）时，它能否保持低熵。我们表明，系统整体的熵可以保持不变，而其各部分的熵在增加。对于经典系统而言，这是不可能的，因为S的熵不可能小于其子系统Si的熵。如果一个子系统的熵增加，那么系统的熵至少也应增加相同的量。然而，在量子信息理论中，答案是肯定的。子系统状态的纠缠起着重要作用。在没有纠缠的情况下，局部无序的增加意味着复合系统中无序的增加（如同在经典情形中）。在本笔记中，我们采用类量子方法对生物系统信息处理进行数学建模——遵循量子规律不一定基于生物系统中真正的量子物理过程。最近，这种建模在分子生物学、遗传学、进化理论、认知、心理学和决策制定等领域有了众多应用。类量子的有序稳定性模型不仅可应用于生物学，还可应用于……
