Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

# Order-Stability in Complex Biosystems from the Viewpoint of the Theory of Open Quantum Systems

Version 1 : Received: 31 December 2020 / Approved: 31 December 2020 / Online: 31 December 2020 (13:39:08 CET)
Version 2 : Received: 5 February 2021 / Approved: 5 February 2021 / Online: 5 February 2021 (22:04:17 CET)

How to cite: Khrennikov, A.; Watanabe, N. Order-Stability in Complex Biosystems from the Viewpoint of the Theory of Open Quantum Systems. Preprints 2020, 2020120814 (doi: 10.20944/preprints202012.0814.v1). Khrennikov, A.; Watanabe, N. Order-Stability in Complex Biosystems from the Viewpoint of the Theory of Open Quantum Systems. Preprints 2020, 2020120814 (doi: 10.20944/preprints202012.0814.v1).

## 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 Schr\"odinger in 1944. According to Schr\"odinger, the main distinguishing feature of biosystem's functioning is the ability to preserve its order structure or, in the mathematical terms, to prevent increasing of entropy. Since any biosystem is fundamentally open, it is natural to use open system's theory. However, Schr\"odinger's analysis shows that the classical theory is not able to adequately describe the order-stability in a biosystem. Schr\"odinger should also appeal to the ambiguous notion of negative entropy. We suggest to apply the quantum theory. As is well-known, behaviour of the quantum von Neumann entropy crucially differs from behaviour of the classical entropy. We consider a complex biosystem $S$ composed of many subsystems, say proteins, or cells, or neural networks in the brain, i.e., $S=(S_i).$ We study the following problem: if the composed system $S$ can preserve the global order'' in the situation of increase of local disorder and if $S$ can preserve its entropy while some of $S_i$ increase their entropies We show that within quantum information theory the answer is positive. The significant role plays entanglement of the subsystems states. In the absence of entanglement, increasing of local disorder generates disorder increasing in the compound system $S$ (as in the classical regime).

## Subject Areas

biosystems; order-stability; classical versus quantum entropy; open quantum systems; quantum channel; entanglement

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