Order-Stability in Complex Biological, Social, and AI-Systems from Quantum Information Theory
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 orde...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2021-03-01
|
| Series: | Entropy |
| Subjects: | |
| Online Access: | https://www.mdpi.com/1099-4300/23/3/355 |
| _version_ | 1797541094963019776 |
|---|---|
| author | Andrei Khrennikov Noboru Watanabe |
| author_facet | Andrei Khrennikov Noboru Watanabe |
| author_sort | Andrei Khrennikov |
| collection | DOAJ |
| description | 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 <i>S</i> composed of many subsystems, say proteins, cells, or neural networks in the brain, that is, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mo>=</mo><mo>(</mo><msub><mi>S</mi><mi>i</mi></msub><mo>)</mo><mo>.</mo></mrow></semantics></math></inline-formula> We study the following problem: whether the compound system <i>S</i> can maintain “global order” in the situation of an increase of local disorder and if <i>S</i> can preserve the low entropy while other <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>S</mi><mi>i</mi></msub></semantics></math></inline-formula> 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 <i>S</i> cannot be less than the entropy of its subsystem <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>S</mi><mi>i</mi></msub></semantics></math></inline-formula>. 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 <i>S</i> (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 <i>social science and artificial intelligence</i>. |
| first_indexed | 2024-03-10T13:10:46Z |
| format | Article |
| id | doaj.art-1d105e794c354c5d87025795937ee2b9 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-10T13:10:46Z |
| publishDate | 2021-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-1d105e794c354c5d87025795937ee2b92023-11-21T10:47:01ZengMDPI AGEntropy1099-43002021-03-0123335510.3390/e23030355Order-Stability in Complex Biological, Social, and AI-Systems from Quantum Information TheoryAndrei Khrennikov0Noboru Watanabe1International Center for Mathematical Modeling in Physics and Cognitive Sciences, Linnaeus University, SE-351 95 Växjö, SwedenDepartment of Information Sciences, Tokyo University of Science, Noda City, Chiba 278-8510, JapanThis 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 <i>S</i> composed of many subsystems, say proteins, cells, or neural networks in the brain, that is, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mo>=</mo><mo>(</mo><msub><mi>S</mi><mi>i</mi></msub><mo>)</mo><mo>.</mo></mrow></semantics></math></inline-formula> We study the following problem: whether the compound system <i>S</i> can maintain “global order” in the situation of an increase of local disorder and if <i>S</i> can preserve the low entropy while other <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>S</mi><mi>i</mi></msub></semantics></math></inline-formula> 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 <i>S</i> cannot be less than the entropy of its subsystem <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>S</mi><mi>i</mi></msub></semantics></math></inline-formula>. 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 <i>S</i> (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 <i>social science and artificial intelligence</i>.https://www.mdpi.com/1099-4300/23/3/355biological, social, and AI systemsorder-stabilityclassical vs. quantum entropyquantum channelentanglementquantum-like models |
| spellingShingle | Andrei Khrennikov Noboru Watanabe Order-Stability in Complex Biological, Social, and AI-Systems from Quantum Information Theory Entropy biological, social, and AI systems order-stability classical vs. quantum entropy quantum channel entanglement quantum-like models |
| title | Order-Stability in Complex Biological, Social, and AI-Systems from Quantum Information Theory |
| title_full | Order-Stability in Complex Biological, Social, and AI-Systems from Quantum Information Theory |
| title_fullStr | Order-Stability in Complex Biological, Social, and AI-Systems from Quantum Information Theory |
| title_full_unstemmed | Order-Stability in Complex Biological, Social, and AI-Systems from Quantum Information Theory |
| title_short | Order-Stability in Complex Biological, Social, and AI-Systems from Quantum Information Theory |
| title_sort | order stability in complex biological social and ai systems from quantum information theory |
| topic | biological, social, and AI systems order-stability classical vs. quantum entropy quantum channel entanglement quantum-like models |
| url | https://www.mdpi.com/1099-4300/23/3/355 |
| work_keys_str_mv | AT andreikhrennikov orderstabilityincomplexbiologicalsocialandaisystemsfromquantuminformationtheory AT noboruwatanabe orderstabilityincomplexbiologicalsocialandaisystemsfromquantuminformationtheory |