Quantum-like modeling in biology with open quantum systems and
instruments
- URL: http://arxiv.org/abs/2010.15573v1
- Date: Tue, 27 Oct 2020 18:38:16 GMT
- Title: Quantum-like modeling in biology with open quantum systems and
instruments
- Authors: Irina Basieva, Andrei Khrennikov, and Masanao Ozawa
- Abstract summary: We present the novel approach to mathematical modeling of information processes in biosystems.
It is based on quantum information representation of biosystem's state and modeling its dynamics in the framework of theory of open quantum systems.
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- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We present the novel approach to mathematical modeling of information
processes in biosystems. It explores the mathematical formalism and methodology
of quantum theory, especially quantum measurement theory. This approach is
known as {\it quantum-like} and it should be distinguished from study of
genuine quantum physical processes in biosystems (quantum biophysics, quantum
cognition). It is based on quantum information representation of biosystem's
state and modeling its dynamics in the framework of theory of open quantum
systems. This paper starts with the non-physicist friendly presentation of
quantum measurement theory, from the original von Neumann formulation to modern
theory of quantum instruments. Then, latter is applied to model combinations of
cognitive effects and gene regulation of glucose/lactose metabolism in
Escherichia coli bacterium. The most general construction of quantum
instruments is based on the scheme of indirect measurement, in that measurement
apparatus plays the role of the environment for a biosystem. The biological
essence of this scheme is illustrated by quantum formalization of Helmholtz
sensation-perception theory. Then we move to open systems dynamics and consider
quantum master equation, with concentrating on quantum Markov processes. In
this framework, we model functioning of biological functions such as
psychological functions and epigenetic mutation.
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