Order-Stability in Complex Biological, Social, and AI-Systems from Quantum Information Theory

Abstract

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 S 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 S can maintain “global order” in the situation of an increase of local disorder and if S 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 S 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 S (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 social science and artificial intelligence.

Open Systems, Quantum Probability, and Logic for Quantum-like Modeling in Biology, Cognition, and Decision-Making

“…Once again, the theory of open quantum systems is used (see [198]) in attempting to bring more clarification to the question "What is life?" We consider a complex biosystem S composed of many subsystems, such as proteins, cells, or neural networks in the brain, i.e., S = (S i ).…”

Uncertainty and information causality in opportunity-as-artefact driving entrepreneurial actions

“…The increase of entropy implies a decrease in information, diminishing orderliness; on the contrary, the reduction of entropy means an increase in information and orderliness. The level of information access improves the degree of self-organisation (Khrennikov & Watanabe, 2021).…”

“…In fact, entropy can be regarded as a measure of ignorance. “Entropy is the basic measure of disorder in physics and information theory” (Khrennikov & Watanabe, 2021, p. 18).Given the opposite relationship between information and entropy, the diversity of socioeconomic structure (information in its aggregate way: H) reduces internal socioeconomic entropy to promote economic development by means of non-equilibrium market exchanges in which every price is a mix of information and entropy. Their respective proportions depend on disparities between supply (s p ) and demand (d m ) that fluctuate over space and time: a higher proportion of superfluously valued entropy is included in price formation when d m > s p , and vice versa (Rodríguez & Cáceres-Hernández, 2018, p. 74)…”

Quantum Probability for Modeling Cognition, Decision Making, and Artificial Intelligence

“…Once again theory of open quantum systems is used (see paper [178]) in attempting to bring more clarification on the question "What is life?" We consider a complex biosystem S composed of many subsystems, say proteins, or cells, or neural networks in the brain, i.e., S = (S i ).…”

“…It is shown that within quantum information theory the answer is positive [178]. Entanglement of the subsystems states plays the crucial role.…”