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Difference between revisions of "Quantum-like modeling in biology with open quantum systems and instruments"
Quantum-like modeling in biology with open quantum systems and instruments (view source)
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| Pdfcopy = https://reader.elsevier.com/reader/sd/pii/S0303264720301994?token=9E6F7237289217F8D6A21294818E5F9111D7628180E899826FA16E10EA3210006062A7EDB9291235E0B72F1C40845360&originRegion=eu-west-1&originCreation=20220619134918<!-- eventual polished PDF document --> | | Pdfcopy = https://reader.elsevier.com/reader/sd/pii/S0303264720301994?token=9E6F7237289217F8D6A21294818E5F9111D7628180E899826FA16E10EA3210006062A7EDB9291235E0B72F1C40845360&originRegion=eu-west-1&originCreation=20220619134918<!-- eventual polished PDF document --> | ||
| License = CC BY | | License = CC BY | ||
}} | }} | ||
Irina Basieva<sup>a</sup>, Andrei Khrennikov<sup>a</sup>, Masanao Ozawa<sup>b,c</sup> | |||
<sup>a</sup>Linnaeus University, International Center for Mathematical Modeling in Physics and Cognitive Sciences Växjö, SE-351 95, Sweden | <sup>a</sup>Linnaeus University, International Center for Mathematical Modeling in Physics and Cognitive Sciences Växjö, SE-351 95, Sweden | ||
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== Introduction == | == Introduction == | ||
The standard mathematical methods were originally developed to serve classical physics. The real analysis served as the mathematical basis of Newtonian mechanics (Newton, 1687)<ref>Newton | The standard mathematical methods were originally developed to serve classical physics. The real analysis served as the mathematical basis of Newtonian mechanics (Newton, 1687)<ref>{{cita libro | ||
| autore = Newton Isaac | |||
| titolo = Philosophiae naturalis principia mathematica | |||
| url = https://archive.org/details/bub_gb_6EqxPav3vIsC | |||
| volume = | |||
| opera = | |||
| anno = 1687 | |||
| editore = Benjamin Motte | |||
| città = London UK | |||
| ISBN = | |||
| DOI = | |||
| PMID = | |||
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| oaf = <!-- qualsiasi valore --> | |||
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}}</ref> (and later Hamiltonian formalism); classical statistical mechanics stimulated the measure-theoretic approach to probability theory, formalized in Kolmogorov’s axiomatics (Kolmogorov, 1933)<ref>Kolmogorov A.N.Grundbegriffe Der Wahrscheinlichkeitsrechnung. Springer-Verlag, Berlin (1933)</ref>. However, behavior of biological systems differ essentially from behavior of mechanical systems, say rigid bodies, gas molecules, or fluids. Therefore, although the “classical mathematics” still plays the crucial role in biological modeling, it seems that it cannot fully describe the rich complexity of biosystems and peculiarities of their behavior — as compared with mechanical systems. New mathematical methods for modeling biosystems are on demand.(a,b) | |||
In this paper, we present the applications of the mathematical formalism of quantum mechanics and its methodology to modeling biosystems’ behavior.(c) The recent years were characterized by explosion of interest to applications of quantum theory outside of physics, especially in cognitive psychology, decision making, information processing in the brain, molecular biology, genetics and epigenetics, and evolution theory.4 We call the corresponding models ''quantum-like''. They are not directed to micro-level modeling of real quantum physical processes in biosystems, say in cells or brains (cf. with biological applications of genuine quantum physical theory Penrose 1989,<ref>Penrose R. The Emperor’S New Mind Oxford Univ. Press, New-York (1989)</ref> Umezawa 1993,<ref>Umezawa H. Advanced Field Theory: Micro, Macro and Thermal Concepts AIP, New York (1993)</ref> Hameroff 1994,<ref>Hameroff S. Quantum coherence in microtubules. a neural basis for emergent con- sciousness? J. Cons. Stud., 1 (1994)</ref> Vitiello 1995,<ref>Vitiello G. Dissipation and memory capacity in the quantum brain model Internat. J. Modern Phys. B, 9 (1995), p. 973</ref> Vitiello 2001,<ref>Vitiello G. My Double Unveiled: The Dissipative Quantum Model of Brain, Advances in Consciousness Research, John Benjamins Publishing Company(2001)</ref> Arndt et al., 2009,<ref>Arndt M., Juffmann T., Vedral V. Quantum physics meets biology HFSP J., 3 (6) (2009), pp. 386-400, 10.2976/1.3244985</ref> Bernroider and Summhammer 2012,<ref>Bernroider G., Summhammer J. Can quantum entanglement between ion transition states effect action potential initiation? Cogn. Comput., 4 (2012), pp. 29-37</ref> Bernroider 2017<ref>Bernroider G. Neuroecology: Modeling neural systems and environments, from the quantum to the classical level and the question of consciousness J. Adv. Neurosci. Res., 4 (2017), pp. 1-9</ref>). Quantum-like modeling works from the viewpoint to quantum theory as a measurement theory. This is the original Bohr’s viewpoint that led to ''the Copenhagen interpretation of quantum mechanics'' (see Plotnitsky, 2009<ref>Plotnitsky A. Epistemology and Probability: Bohr, Heisenberg, SchrÖdinger and the Nature of Quantum-Theoretical Thinking Springer, Berlin, Germany; New York, NY, USA (2009</ref> for detailed and clear presentation of Bohr’s views). One of the main bio-specialties is consideration of ''self-measurements that biosystems perform on themselves.'' In our modeling, the ability to perform self-measurements is considered as the basic feature of biological functions (see Section 8.2 and paper Khrennikov et al., 2018<ref name=":0">Khrennikov A., Basieva I., PothosE.M., Yamato I. Quantum Probability in Decision Making from Quantum Information Representation of Neuronal States, Sci. Rep., 8 (2018), Article 16225</ref>). | In this paper, we present the applications of the mathematical formalism of quantum mechanics and its methodology to modeling biosystems’ behavior.(c) The recent years were characterized by explosion of interest to applications of quantum theory outside of physics, especially in cognitive psychology, decision making, information processing in the brain, molecular biology, genetics and epigenetics, and evolution theory.4 We call the corresponding models ''quantum-like''. They are not directed to micro-level modeling of real quantum physical processes in biosystems, say in cells or brains (cf. with biological applications of genuine quantum physical theory Penrose 1989,<ref>Penrose R. The Emperor’S New Mind Oxford Univ. Press, New-York (1989)</ref> Umezawa 1993,<ref>Umezawa H. Advanced Field Theory: Micro, Macro and Thermal Concepts AIP, New York (1993)</ref> Hameroff 1994,<ref>Hameroff S. Quantum coherence in microtubules. a neural basis for emergent con- sciousness? J. Cons. Stud., 1 (1994)</ref> Vitiello 1995,<ref>Vitiello G. Dissipation and memory capacity in the quantum brain model Internat. J. Modern Phys. B, 9 (1995), p. 973</ref> Vitiello 2001,<ref>Vitiello G. My Double Unveiled: The Dissipative Quantum Model of Brain, Advances in Consciousness Research, John Benjamins Publishing Company(2001)</ref> Arndt et al., 2009,<ref>Arndt M., Juffmann T., Vedral V. Quantum physics meets biology HFSP J., 3 (6) (2009), pp. 386-400, 10.2976/1.3244985</ref> Bernroider and Summhammer 2012,<ref>Bernroider G., Summhammer J. Can quantum entanglement between ion transition states effect action potential initiation? Cogn. Comput., 4 (2012), pp. 29-37</ref> Bernroider 2017<ref>Bernroider G. Neuroecology: Modeling neural systems and environments, from the quantum to the classical level and the question of consciousness J. Adv. Neurosci. Res., 4 (2017), pp. 1-9</ref>). Quantum-like modeling works from the viewpoint to quantum theory as a measurement theory. This is the original Bohr’s viewpoint that led to ''the Copenhagen interpretation of quantum mechanics'' (see Plotnitsky, 2009<ref>Plotnitsky A. Epistemology and Probability: Bohr, Heisenberg, SchrÖdinger and the Nature of Quantum-Theoretical Thinking Springer, Berlin, Germany; New York, NY, USA (2009</ref> for detailed and clear presentation of Bohr’s views). One of the main bio-specialties is consideration of ''self-measurements that biosystems perform on themselves.'' In our modeling, the ability to perform self-measurements is considered as the basic feature of biological functions (see Section 8.2 and paper Khrennikov et al., 2018<ref name=":0">Khrennikov A., Basieva I., PothosE.M., Yamato I. Quantum Probability in Decision Making from Quantum Information Representation of Neuronal States, Sci. Rep., 8 (2018), Article 16225</ref>). | ||