Editor, Editors, USER, admin, Bureaucrats, Check users, dev, editor, founder, Interface administrators, oversight, Suppressors, Administrators, translator
10,784
edits
Difference between revisions of "Store:QLMen02"
no edit summary
| Line 18: | Line 18: | ||
}}</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) | }}</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=": | 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=":Khrennikov12">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>). | ||
''Quantum-like models'' (Khrennikov, 2004b<ref name=": | ''Quantum-like models'' (Khrennikov, 2004b<ref name=":Khrennikov13">Khrennikov A. On quantum-like probabilistic structure of mental information Open Syst. Inf. Dyn., 11 (3) (2004), pp. 267-275</ref>) | ||
reflect the features of biological processes that naturally match the quantum formalism. In such modeling, it is useful to explore ''quantum information theory,'' which can be applied not just to the micro-world of quantum systems. Generally, systems processing information in the quantum-like manner need not be quantum physical systems; in particular, they can be macroscopic biosystems. Surprisingly, the same mathematical theory can be applied at all biological scales: from proteins, cells and brains to humans and ecosystems; we can speak about ''quantum information biology'' (Asano et al., 2015a<ref name=":1">Asano M., Basieva I., Khrennikov A., Ohya M., Tanaka Y., Yamato I. Quantum information biology: from information interpretation of quantum mechanics to applications in molecular biology and cognitive psychology Found. Phys., 45 (10) (2015), pp. 1362-1378</ref>). | reflect the features of biological processes that naturally match the quantum formalism. In such modeling, it is useful to explore ''quantum information theory,'' which can be applied not just to the micro-world of quantum systems. Generally, systems processing information in the quantum-like manner need not be quantum physical systems; in particular, they can be macroscopic biosystems. Surprisingly, the same mathematical theory can be applied at all biological scales: from proteins, cells and brains to humans and ecosystems; we can speak about ''quantum information biology'' (Asano et al., 2015a<ref name=":1">Asano M., Basieva I., Khrennikov A., Ohya M., Tanaka Y., Yamato I. Quantum information biology: from information interpretation of quantum mechanics to applications in molecular biology and cognitive psychology Found. Phys., 45 (10) (2015), pp. 1362-1378</ref>). | ||