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 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.
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 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.
The aim of this review is to highlight the possibility of applying the mathematical formalism and methodology of quantum theory to model behavior of complex biosystems, from genomes and proteins to animals, humans, and ecological and social systems. Such models are known as quantum-like, and they should be distinguished from genuine quantum physical modeling of biological phenomena. One of the distinguishing features of quantum-like models is their applicability to macroscopic biosystems or, to be more precise, to information processing in them. Quantum-like modeling has its basis in quantum information theory, and it can be considered one of the fruits of the quantum information revolution. Since any isolated biosystem is dead, modeling of biological as well as mental processes should be based on the theory of open systems in its most general form-the theory of open quantum systems. In this review, we explain its applications to biology and cognition, especially theory of quantum instruments and the quantum master equation. We mention the possible interpretations of the basic entities of quantum-like models with special interest given to QBism, as it may be the most useful interpretation.
The aim of this chapter is to highlight the possibility of applying the mathematicalformalism and methodology of quantum theory to model behaviourof complex biosystems, from genomes and proteins to animals, humans, ecologicaland social systems. Such models are known as quantum-like and theyshould be distinguished from genuine quantum physical modeling of biologicalphenomena. One of the distinguishing features of quantum-like models istheir applicability to macroscopic biosystems, or to be more precise, to informationprocessing in them. Quantum-like modeling has the base in quantuminformation theory and it can be considered as one of the fruits of the quantuminformation revolution. Since any isolated biosystem is dead, modelingof biological as well as mental processes should be based on theory of opensystems in its most general form – theory of open quantum systems. In thischapter we advertise its applications to biology and cognition, especiallytheory of quantum instruments and quantum master equation. We mentionthe possible interpretations of the basic entities of quantum-like models withspecial interest to QBism as maybe the most useful interpretation.
Abstract Recently the quantum formalism and methodology started to be applied to modeling of information processing in biosystems, mainly to the process of decision making and psychological behavior (but some applications to microbiology and genetics are considered as well). Since a living system is fundamentally open (an isolated biosystem is dead), the theory of open quantum systems is the most powerful tool for life-modeling. In this paper, we turn to the famous Schrödinger book “What is life?” and reformulate his speculations in terms of this theory. Schrödinger pointed toorder preservation as one of the main distinguishing features of biosystems. Entropy is the basic quantitative measure of order. In physical systems, entropy has the tendency to increase (Second Law of Thermodynamics for isolated classical systems and dissipation in open classical and quantum systems). Schrödinger emphasized the ability of biosystems to beat this tendency. We demonstrate that systems processing information in the quantum-like way can preservethe order-structure expressed by the quantum (von Neumann or linear) entropy. We emphasize the role of the special class of quantum dynamics and initial states generating the camel-like graphs for entropy-evolution in the process of interaction with a new environment ℰ: 1) entropy (disorder) increasing in the process of adaptation to the specific features of ℰ; 2) entropy decreasing (order increasing) resulting from adaptation; 3) the restoration of order or even its increase for limiting steady state. In the latter case the steady state entropy can be even lower than the entropy of the initial state.
Recently, the quantum formalism and methodology have been used in application to the modelling of information processing in biosystems, mainly to the process of decision making and psychological behaviour (but some applications in microbiology and genetics are considered as well). Since a living system is fundamentally open (an isolated biosystem is dead), the theory of open quantum systems is the most powerful tool for life-modelling. In this paper, we turn to the famous Schrödinger’s book “What is life?” and reformulate his speculations in terms of this theory. Schrödinger pointed to order preservation as one of the main distinguishing features of biosystems. Entropy is the basic quantitative measure of order. In physical systems, entropy has the tendency to increase (Second Law of Thermodynamics for isolated classical systems and dissipation in open classical and quantum systems). Schrödinger emphasized the ability of biosystems to beat this tendency. We demonstrate that systems processing information in the quantum-like way can preserve the order-structure expressed by the quantum (von Neumann or linear) entropy. We emphasize the role of the special class of quantum dynamics and initial states generating the camel-like graphs for entropy-evolution in the process of interaction with a new environment [Formula: see text]: 1) entropy (disorder) increasing in the process of adaptation to the specific features of [Formula: see text]; 2) entropy decreasing (order increasing) resulting from adaptation; 3) the restoration of order or even its increase for limiting steady state. In the latter case the steady state entropy can be even lower than the entropy of the initial state.
The textbook conceptualization of phenotype creation, "genotype (G) + environment (E) + genotype & environment interactions (GE) ↦ phenotype (Ph)", is modeled with open quantum systems theory (OQST) or more generally with adaptive dynamics theory (ADT). The model is quantum-like, i.e., it is not about quantum physical processes in biosystems. Generally such modeling is about applications of the quantum formalism and methodology outside of physics. Macroscopic biosystems, in our case genotypes and phenotypes, are treated as information processors which functioning matches the laws of quantum information theory. Phenotypes are the outputs of the E-adaptation processes described by the quantum master equation, Gorini-Kossakowski-Sudarshan-Lindblad equation (GKSL). Its stationary states correspond to phenotypes. We highlight the class of GKSL dynamics characterized by the camel-like graphs of (von Neumann) entropy: in the process of E-adaptation phenotype's state entropy (disorder) first increases and then falls down - a stable and well-ordered phenotype is created. Traits, an organism's phenotypic characteristics, are modeled within the quantum measurement theory, as generally unsharp observables given by positive operator valued measures (POVMs. This paper is also a review on the methods and mathematical apparatus of quantum information biology.
Quantum biology, as introduced in the previous chapter, mainly studies the dynamical influence of quantum effects in biological systems. In processes such as exciton transport in photosynthetic complexes, radical pair spin dynamics in magnetoreception, and photo-induced retinal isomerization in the rhodopsin protein, a quantum description is a necessity rather than an option. The quantum modelling of biological processes is not limited to solving the Schrödinger equation for an isolated molecular structure. Natural systems are open to the exchange of particles, energy or information with their surrounding environments that often have complex structures. Therefore the theory of open quantum systems plays a key role in dynamical modelling of quantum-biological systems. Research in quantum biology and open quantum system theory have found a bilateral relationship. Quantum biology employs open quantum system methods to a great extent while serving as a new paradigm for development of advanced formalisms for non-equilibrium biological processes. In this chapter, we overview the basic concepts of quantum mechanics and approaches to open quantum system (or decoherence ) dynamics. Here, we do not intend to discuss all aspects of about a century-old theory of open quantum systems that dates back to the original work of Paul Dirac on atomic radiative emission and absorption (Dirac, 1927). Instead, we mainly focus on the integro-differential equations that are commonly used for modelling quantum-biological systems. Interested readers can learn more about open quantum systems in various books and review articles in both physics and chemistry literature, including the references (Kraus, 1983; Breuer and Petruccione, 2002; Kubo et al. , 2003; Weiss, 2008; May and Kühn, 2011).