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Radical pair mechanism in magnetobiology: state of the art

 
Federal Research & Clinic Center of Space Medicine and Biology of the Federal Biomedical Agency, Sushchevskii Val str. 24, Moscow, 127018, Russian Federation

We discuss the biological effects of weak magnetic fields, a problem that has gone unresolved for nearly half a century. We consider the spin—chemical mechanism of radical pairs, which is prevalent in the literature aiming to explain the observed phenomena. The effectiveness of this mechanism is limited by spin relaxation. The relaxation rate is estimated for a radical in a protein via the Zeeman, hyperfine, spin—orbit, and exchange interactions. Taking the relaxation and chemical kinetics into account, we present an analytic solution of the Liouville—von Neumann equation for two electrons and a nucleus, which relates the magnitude of the effects to the relaxation rate. Various aspects of the solution are discussed: the influence of the radiofrequency and hypomagnetic fields, the role of quantum entanglement, theoretical challenges and prospects, and others.

Fulltext pdf (1.2 MB)
Fulltext is also available at DOI: 10.3367/UFNe.2025.09.040032
Keywords: magnetic biological effects, animal magnetic navigation, spin decoherence, spin relaxation, spin chemistry, radical pair mechanism, Liouville—von Neumann equation, open quantum system, chemical compass, hypomagnetic fields
PACS: 82.39.−k, 87.10.−e, 87.50.−a, 87.50.C− (all)
DOI: 10.3367/UFNe.2025.09.040032
URL: https://ufn.ru/en/articles/2025/12/f/
2025PhyU...68.1242B
Citation: Binhi V N "Radical pair mechanism in magnetobiology: state of the art" Phys. Usp. 68 1242–1267 (2025)
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Received: 5th, October 2024, revised: 15th, September 2025, 17th, September 2025

Оригинал: Бинги В Н «Механизм радикальных пар в магнитобиологии: состояние дел» УФН 195 1312–1339 (2025); DOI: 10.3367/UFNr.2025.09.040032

References (231) ↓ Cited by (1) Similar articles (20)

  1. Fleming G R, Scholes G D Quantum Effects In Biology (Eds M Mohseni et al) (Cambridge: Cambridge Univ. Press, 2014) p. 3
  2. Fraikin G Ya, Rubin A B Gorizonty Biofiziki (Horizons Of Biophysics) Vol. 1 (Ed. A B Rubin) (Izhevsk: Inst. Komp’yut. Issled., 2022) p. 426
  3. Asano M et al Quantum Adaptivity In Biology: From Genetics To Cognition (Dordrecht: Springer, 2015)
  4. Menskii M B Phys. Usp. 48 389 (2005); Menskii M B Usp. Fiz. Nauk 175 413 (2005)
  5. Ivanitskii G R Phys. Usp. 53 327 (2010); Ivanitskii G R Usp. Fiz. Nauk 180 337 (2010)
  6. Binhi V N Fizicheskie Effekty Soznaniya: Zakon Vosproizvodimosti (Physical Effects Of Consciousness: The Law Of Reproducibility) (Moscow: INFRA-M, 2021)
  7. Khrennikov A Y Open Quantum Systems In Biology, Cognitive And Social Sciences (Cham: Springer, 2023)
  8. Ball P Nature 474 272 (2011)
  9. McFadden J, Al-Khalili J Proc. R. Soc. London A 474 20180674 (2018)
  10. Marais A et al J. R. Soc. Interface 15 20180640 (2018)
  11. Syurakshin A V, Saleev V A, Yushankhai V Yu Vestn. Samarskogo Univ. Estestvennonauchn. Ser. 28 (1-2) 74 (2022)
  12. Barnothy M F (Ed.) Biological Effects Of Magnetic Fields (New York: Plenum Press, 1964)
  13. Grissom C B Chem. Rev. 95 (1) 3 (1995)
  14. Binhi V N Printsipy Elektromagnitnoi Biofiziki (Principles Of Electromagnetic Biophysics) (Moscow: Fizmatlit, 2011)
  15. Buchachenko A L Russ. Chem. Rev. 83 (1) 1 (2014); Buchachenko A L Usp. Khim. 83 (1) 1 (2014)
  16. Greenebaum B, Barnes F (Eds) Biological And Medical Aspects Of Electromagnetic Fields Vol. 1, 2 4th ed. (Boca Raton, FL: CRC Press, 2019)
  17. Ghodbane S et al BioMed Res. Int. 2013 602987 (2013)
  18. Ghodbane S et al Non-Ionizing Radiation Pt. 1 Static And Extremely Low-Frequency (ELF) Electric And Magnetic Fields (IARC Monographs On The Evaluation Of Carcinogenic Risks To Humans, Vol. 80) (Lyon: IARC Press, 2002)
  19. Sarimov R M, Binhi V Bioelectromagnetics 41 360 (2020)
  20. Buchachenko A L, Kuznetsov D A Russ. J. Phys. Chem. B 15 1 (2021)
  21. Kirschvink J L, Jones D S, MacFadden B J (Eds) Magnetite Biomineralization And Magnetoreception In Organisms. A New Biomagnetism (Topics In Geobiology, Vol. 5) (New York: Plenum Press, 1985)
  22. Binhi V N, Chernavsky D S Biophysics 50 599 (2005); Binhi V N, Chernavsky D S Biofizika 50 684 (2005)
  23. Sokolik I A, Frankevich E L Sov. Phys. Usp. 16 687 (1974); Sokolik I A, Frankevich E L Usp. Fiz. Nauk 111 261 (1973)
  24. Brocklehurst B Nature 221 921 (1969)
  25. Buchachenko A L, Sagdeev R Z, Salikhov K M Magnitnye I Spinovye Effekty V Khimicheskikh Reaktsiyakh (Magnetic And Spin Effects In Chemical Reactions, Exec. Ed. Yu N Molin) (Novosibirsk: Nauka, 1978); see also, Salikhov K M, Molin Yu N, Sagdeev R Z, Buchachenko A L Spin Polarization And Magnetic Effects In Radical Reactions (Studies In Physical And Theoretical Chemistry, Vol. 22, Ed. Yu N Molin) (Amsterdam: Elsevier, 1984)
  26. Zel’dovich Ya B, Buchachenko A L, Frankevich E L Sov. Phys. Usp. 31 385 (1988); Zel’dovich Ya B, Buchachenko A L, Frankevich E L Usp. Fiz. Nauk 155 3 (1988)
  27. Steiner U E, Ulrich T Chem. Rev. 89 (1) 51 (1989)
  28. Bagryansky V A, Borovkov V I, Molin Yu N Russ. Chem. Rev. 76 493 (2007); Bagryansky V A, Borovkov V I, Molin Yu N Usp. Khim. 76 535 (2007)
  29. Hoff A J et al Biochim. Biophys. Acta BBA Bioenergetics 460 547 (1977)
  30. Schulten K, Swenberg C E, Weller A Z. Phys. Chem. Neue Folge 111 (1) 1 (1978)
  31. Wiltschko R, Wiltschko W BioEssays 28 157 (2006)
  32. Maeda K et al Nature 453 387 (2008)
  33. Cai J, Guerreschi G G, Briegel H J Phys. Rev. Lett. 104 220502 (2010)
  34. Kominis I K Chem. Phys. Lett. 542 143 (2012)
  35. Tiersch M et al J. Phys. Chem. A 118 (1) 13 (2014)
  36. Ritz T, Adem S, Schulten K Biophys. J. 78 707 (2000)
  37. Lin C, Todo T Genome Biol. 6 220 (2005)
  38. Astakhova L A et al Zh. Obshchei Biologii 80 (2) 83 (2019)
  39. Wong S Y et al J. R. Soc. Interface 18 20210601 (2021)
  40. Xu J et al Nature 594 535 (2021)
  41. Fedele G et al PLoS Genet. 10 e1004804 (2014)
  42. Lohmann K J et al Nature 428 909 (2004)
  43. Wu H et al Sci. Rep. 10 7364 (2020)
  44. Wan G et al Nature Commun. 12 771 (2021)
  45. Kattnig D R et al Nature Chem. 8 384 (2016)
  46. Rodgers C T, Hore P J Proc. Natl. Acad. Sci. USA 106 353 (2009)
  47. Kerpal C et al Nature Commun. 10 3707 (2019)
  48. Bradlaugh A A et al Nature 615 111 (2023)
  49. Hore P J ELife 8 e44179 (2019)
  50. Hiscock H G et al Biophys. J. 113 1475 (2017)
  51. Binhi V N Magnetobiology: Underlying Physical Problems (San Diego, CA: Academic Press, 2002)
  52. Cremer-Bartels G, Krause K, Küchle H J Graefe’s Arch. Clin. Exp. Ophthalmol. 220 (5) 248 (1983)
  53. Dhiman S K, Galland P J. Plant Physiol. 231 9 (2018)
  54. Fu J-P et al Protein 7 624 (2016)
  55. Binhi V N, Prato F S PLoS ONE 12 e0179340 (2017)
  56. Magin I M et al J. Phys. Chem. A 109 7396 (2005)
  57. Stovbun S V et al Sci. Rep. 13 465 (2023)
  58. Boxer S G, Chidsey C E D, Roelofs M G Annu. Rev. Phys. Chem. 34 389 (1983)
  59. Maeda K et al Proc. Natl. Acad. Sci. USA 109 4774 (2012)
  60. Henbest K B et al Proc. Natl. Acad. Sci. USA 105 14395 (2008)
  61. Beardmore J P, Antill L M, Woodward J R Angew. Chem. Int. Ed. 127 8614 (2015)
  62. Golesworthy M J et al J. Chem. Phys. 159 105102 (2023)
  63. Höytö A et al Int. J. Rad. Biol. 93 646 (2017)
  64. Agliassa C et al J. Photochem. Photobiol. B 185 32 (2018)
  65. Pooam M et al Planta 249 319 (2019)
  66. Ren J et al Front. Phys. 10 995860 (2022)
  67. Lambinet V et al J. Comp. Physiol. A 203 1029 (2017)
  68. Wang C X et al ENeuro 6 (2) e0483 (2019)
  69. Mandelstam L I, Tamm I E Izv. Akad. Nauk SSSR Ser. Fiz. 9 (1-2) 122 (1945); Mandelstam L, Tamm I J. Phys. USSR 9 249 (1945)
  70. Sen D Curr. Sci. India 107 203 (2014)
  71. Landau L D, Lifshitz E M Kvantovaya Mekhanika. Nerelyativistskaya Teoriya 3rd ed., rev. and enlarged (Moscow: Nauka, 1974); Translated into English, Landau L D, Lifshitz E M Quantum Mechanics. Non-Relativistic Theory (Oxford: Pergamon Press, 1977)
  72. Binhi V N, Savin A V Phys. Usp. 46 259 (2003); Binhi V N, Savin A V Usp. Fiz. Nauk 173 265 (2003)
  73. Binhi V N Biofizika 70 390 (2025)
  74. Menskii M B Phys. Usp. 46 1163 (2003); Menskii M B Usp. Fiz. Nauk 173 1199 (2003)
  75. Louisell W H Quantum Statistical Properties Of Radiation (New York: Wiley, 1990)
  76. Blum K Teoriya Matritsy Plotnosti I Ee Prilozheniya (Moscow: Mir, 1983); Translated from English, Blum K Density Matrix Theory And Applications (New York: Plenum Press, 1981)
  77. Bertini I, Martini G, Luchinat C, in<?twb> Handbook Of Electron Spin Resonance. Data Sources, Computer Technology, Relaxation, And ENDOR (Eds C P Poole (Jr.), H A Farach) (New York: AIP Press, 1994), Ch. IV: Relaxation Data Tabulation
  78. Goldfarb D, Stoll S (Eds) EPR Spectroscopy : Fundamentals And Methods (Hoboken, NJ: John Wiley and Sons, 2018)
  79. Liedvogel M et al PLoS ONE 2 (10) e1106 (10)
  80. Valiev K A, Kokin A A Kvantovye Komp’yutery. Nadezhdy I Real’nost’ (Quantum Computers: Hopes And Reality) (Izhevsk: Regulyarnaya i Khaoticheskaya Dinamika, 2001)
  81. Canfield J M, Belford R L, Debrunner P G Mol. Phys. 89 889 (1996)
  82. Brocklehurst B, McLauchlan K A Int. J. Rad. Biol. 69 (1) 3 (1996)
  83. Buchachenko A L, Berdinsky V L, Kuznetsov D A Biophysics 51 (3) 489 (2006); Buchachenko A L, Berdinsky V L, Kuznetsov D A Biophysics 51 (3) 489 (2006)
  84. Hore P J Proc. Natl. Acad. Sci. USA 109 1357 (2012)
  85. Thoradit T et al Front. Plant Sci. 14 1266357 (2023)
  86. Salikhov K M Chem. Phys. 82 (1-2) 145 (1983)
  87. Ivanov K L et al Mol. Phys. 100 1197 (2002)
  88. Cintolesi F et al Chem. Phys. 294 385 (2003)
  89. Efimova O, Hore P J Biophys. J. 94 1565 (2008)
  90. Solov’yov I A, Chandler D E, Schulten K Biophys. J. 92 2711 (2007)
  91. Solov’yov I A, Schulten K Biophys. J. 96 4804 (2009)
  92. Ritz T Procedia Chem. 3 (1) 262 (2011)
  93. Cai J Phys. Rev. Lett. 106 100501 (2011)
  94. Jones J A, Hore P J Chem. Phys. Lett. 488 (1-3) 90 (2010)
  95. Bandyopadhyay J N, Paterek T, Kaszlikowski D Phys. Rev. Lett. 109 110502 (2012)
  96. Lee A A et al J. R. Soc. Interface 11 20131063 (2014)
  97. Zhang Y, Berman G P, Kais S Phys. Rev. E 90 042707 (2014)
  98. Jain R et al Proc. R. Soc. London A 477 20200778 (2021)
  99. Wong S Y, Benjamin P, Hore P J Phys. Chem. Chem. Phys. 25 975 (2023)
  100. Kominis I K Phys. Rev. E 80 056115 (2009)
  101. Gauger E M et al Phys. Rev. Lett. 106 040503 (2011)
  102. Lambert N et al New J. Phys. 15 083024 (2013)
  103. Abragam A Yadernyi Magnetizm (Moscow: IL, 1963); Translated from English, Abragam A The Principles Of Nuclear Magnetism (Oxford: Clarendon Press, 1961)
  104. Standley K J, Vaughan R A Electron Spin Relaxation Phenomena In Solids (New York: Plenum Press, 1969)
  105. Lebedev Ya S, Muromtsev V I EPR I Relaksatsiya Stabilizirovannykh Radikalov (EPR And Relaxation Of Stabilized Radicals) (Moscow: Khimiya, 1972)
  106. Weil J A, Bolton J R Electron Paramagnetic Resonance : Elementary Theory And Practical Applications (Hoboken, NJ: Wiley, 2007)
  107. Kowalewski J, Mäler L Nuclear Spin Relaxation In Liquids: Theory, Experiments, And Applications (New York: Taylor and Francis, 2006)
  108. Petasis D T EPR Spectroscopy (Berlin: de Gruyter, 2022)
  109. Hemminga M A, Berliner L J ESR Spectroscopy In Membrane Biophysics (Biological Magnetic Resonance, Vol. 27) (New York: Springer, 2007)
  110. Möbius K, Savitsky A Appl. Magn. Reson. 54 207 (2023)
  111. Bazhin N M, Salikhov K M EPR. Relaksatsiya Svobodnykh Radikalov V Zhidkostyakh (EPR. Relaxation Of Free Radicals In Liquids ) (Novosibirsk: NGU, 1973)
  112. Sato H et al Mol. Phys. 105 2137 (2007)
  113. Klug C S, Feix J B Biomedical EPR Pt. B Methodology, Instrumentation, And Dynamics (Biological Magnetic Resonance, Vol. 24, Eds S R Eaton, G R Eaton, L J Berliner) (New York: Kluwer Acad., Plenum Publ., 2005) p. 269
  114. Biller J R et al J. Magn. Reson. 236 47 (2013)
  115. Brustolon M, Segre U Appl. Magn. Reson. 7 405 (1994)
  116. Mailer C et al J. Magn. Reson. 91 475 (1991)
  117. Borovkov V I, Molin Yu N Dokl. Phys. Chem. 396 (4-6) 123 (2004); Borovkov V I, Molin Yu N Dokl. Ross. Akad. Nauk 396 633 (2004)
  118. Kubarev S I, Pshenichnov E A, Shustov A S Theor. Exp. Chem. 15 (1) 10 (1979)
  119. Brocklehurst B Chem. Soc. Rev. 31 301 (2002)
  120. Hedin E M K et al J. Biochem. Biophys. Methods 60 117 (2004)
  121. Commoner B, Heise J J, Townsend J Proc. Natl. Acad. Sci. USA 42 710 (1956)
  122. Ivancich A et al J. Am. Chem. Soc. 123 5050 (2001)
  123. Trubitsin B V, Tikhonov A N J. Magn. Reson. 163 257 (2003)
  124. Jeschke G Biochim. Biophys. Acta BBA Bioenergetics 1707 (1) 91 (2005)
  125. Antholine W E Biomedical EPR Pt. A Free Radicals, Metals, Medicine And Physiology (Biological Magnetic Resonance, Vol. 23, Eds S R Eaton, G R Eaton, L J Berliner) (New York: Kluwer Acad., Plenum Publ., 2005) p. 417
  126. Tikhonov A N et al Biochim. Biophys. Acta BBA Bioenergetics 1777 285 (2008)
  127. Connor H D et al J. Am. Chem. Soc. 130 6381 (2008)
  128. Liu A "Electron paramagnetic resonance (EPR) in<?twb> enzymology" Wiley Encyclopedia Of Chemical Biology (Ed. T P Begley) (New York: John Wiley and Sons, 2008)
  129. Biskup T et al Angew. Chem. Int. Edit. 48 404 (2009)
  130. Schleicher E, Weber S EPR Spectroscopy. Applications In Chemistry And Biology (Topics In Current Chemistry, Vol. 321, Eds M Drescher, G Jeschke) (Berlin: Springer, 2012) p. 41
  131. Schnegg A et al J. Phys. Chem. B 106 9454 (2002)
  132. Stoner J W et al J. Magn. Reson. 170 (1) 127 (2004)
  133. Laguta O et al Appl. Phys. Lett. 120 120502 (2022)
  134. Shushin A I Chem. Phys. Lett. 181 (2-3) 274 (1991)
  135. Afanasyeva M S et al Russ. Chem. Rev. 76 599 (2007); Afanasyeva M S et al Usp. Khim. 76 651 (2007)
  136. Hiscock H G et al Proc. Natl. Acad. Sci. USA 113 4634 (2016)
  137. Zadeh-Haghighi H, Rishabh R, Simon C Front. Phys. 11 1026460 (2023)
  138. Steiner U E, Wu J Q Chem. Phys. 162 (1) 53 (1992)
  139. Kattnig D R, Solov’yov I A, Hore P J Phys. Chem. Chem. Phys. 18 12443 (2016)
  140. Worster S, Kattnig D R, Hore P J J. Chem. Phys. 145 035104 (2016)
  141. Fedin M V et al Russ. Chem. Bull. 55 1703 (2006); Fedin M V et al Izv. Ross. Akad. Nauk Ser. Khim. (10) 1642 (2006)
  142. Breuer H-P, Petruccione F Teoriya Otkrytykh Kvantovykh Sistem (Moscow-Izhevsk: RKhD, Inst. Komp’yut. Issled., 2010); Translated from English, Breuer H-P, Petruccione F The Theory Of Open Quantum Systems (Oxford: Oxford Univ. Press, 2002)
  143. Duglav A V Spin-reshetochnaya Relaksatsiya Elektronov I Yader V Dielektricheskikh Kristallakh S Paramagnitnymi Primesyami (Spin-lattice Relaxation Of Electrons And Nuclei In Dielectric Crystals With Paramagnetic Impurities) (Kazan: Kazan. Univ., 2018)
  144. Aminov L K, Malkin B Z Dinamika I Kinetika Elektronnykh I Spinovykh Vozbuzhdenii V Paramagnitnykh Kristallakh (Dynamics And Kinetics Of Electron And Spin Excitations In Paramagnetic Crystals) (Kazan: Kazan. Univ., 2008)
  145. Redfield A G IBM J. Res. Dev. 1 (1) 19 (1957)
  146. Brocklehurst B J. Chem. Soc. Faraday Trans. 2 72 1869 (1976)
  147. Fedin M V, Purtov P A, Bagryanskaya E G J. Chem. Phys. 118 192 (2003)
  148. Walters Z B Phys. Rev. E 90 042710 (2014)
  149. Kattnig D R et al New J. Phys. 18 063007 (2016)
  150. Haberkorn R Mol. Phys. 32 1491 (1976)
  151. Ivanov K L et al J. Phys. Chem. A 114 9447 (2010)
  152. Buchachenko A L, Vasserman A M Stabil’nye Radikaly (Stable Radicals) (Moscow: Khimiya, 1973)
  153. Timmel C R et al Mol. Phys. 95 (1) 71 (1998)
  154. Cai J, Plenio M B Phys. Rev. Lett. 111 230503 (2013)
  155. Xiao D-W et al Phys. Rev. Lett. 124 128101 (2020)
  156. Van Kampen N G Stochastic Processes In Physics And Chemistry 3rd ed. (Amsterdam: Elsevier, 2007)
  157. Binhi V Phys. Rev. E 112 014409 (2025)
  158. Torrey H C Phys. Rev. 76 1059 (1949)
  159. Hore P J, Mouritsen H Annu. Rev. Biophys. 45 (1) 299 (2016)
  160. Bagryansky V A, Borovkov V I, Molin Yu N Dokl. Phys. Chem. 382 (4-6) 62 (2002); Bagryansky V A, Borovkov V I, Molin Yu N Dokl. Ross. Akad. Nauk 382 794 (2002)
  161. Bianco G, Ilieva M,Åkesson S Biol. Lett. 15 20180918 (2019)
  162. Feintuch A, Vega S EPR Spectroscopy: Fundamentals And Methods (Eds D Goldfarb, S Stoll) (Chichester: John Wiley and Sons, 2018) p. 143
  163. Isserlis L Biometrica 12 (1-2) 134 (1918)
  164. Wang M C, Uhlenbeck G E Rev. Mod. Phys. 17 323 (1945)
  165. Uhlenbeck G E, Ornstein L S Phys. Rev. 36 823 (1930)
  166. Coffey W T, Kalmykov Yu P, Waldron J T The Langevin: With Applications To Stochastic Problems In Physics, Chemistry And Electrical Engineering (World Scientific Series In Contemporary Chemical Physics, Vol. 14) 2nd ed. (Singapore: World Scientific, 2004)
  167. Akhmanov S A, D’yakov Yu E, Chirkin A S Statisticheskaya Radiofizika I Optika. Sluchainye Kolebaniya I Volny V Lineinykh Sistemakh (Statistical Radiophysics And Optics. Random Oscillations And Waves In Linear Systems) (Moscow: Fizmatlit, 2010)
  168. Orlando T, Kuprov I, Hiller M J. Magn. Reson. Open 10-11 100040 (2022)
  169. Binhi V N Biophysics 40 671 (1995); Binhi V N Biofizika 40 677 (1995)
  170. Binhi V N J. Chem. Phys. 151 204101 (2019)
  171. Berestetskii V B, Lifshitz E M, Pitaevskii L P Quantum Electrodynamics (Oxford: Pergamon Press, 1982); Translated from Russian, Berestetskii V B, Lifshitz E M, Pitaevskii L P Kvantovaya Elektrodinamika (Moscow: Nauka, 1974)
  172. Brocklehurst B J. Chem. Soc. Faraday Trans. 2 75 123 (1979)
  173. Scaramozzino D et al Int. J. Mol. Sci. 22 10501 (2021)
  174. Leenders R et al Eur. J. Biochem. 211 (1-2) 37 (1993)
  175. Lau J C S et al J. R. Soc. Interface 7 (Suppl. 2) S257 (2010)
  176. Palekar D, Shiue M, Lien E J Pharm. Res. 13 1191 (1996)
  177. Haynes W M(Ed.-in-Chief), Lide D R, Bruno T J (Associate Eds) CRC Handbook Of Chemistry And Physics 97th ed. (Boca Raton, FL: CRC Press, 2017)
  178. Atherton N M Principles Of Electron Spin Resonance (Chichester: Ellis Horwood, 1993)
  179. Fournel A et al J. Chem. Phys. 109 10905 (1998)
  180. Moser C C et al Nature 355 796 (1992)
  181. Harkins T T, Grissom C B Science 263 958 (1994)
  182. Kadomtsev B B, Kadomtsev M B Phys. Usp. 40 609 (1996); Kadomtsev B B, Kadomtsev M B Usp. Fiz. Nauk 166 651 (1996)
  183. Kadomtsev B B Dinamika I Informatsiya (Moscow: Redaktsiya Zhurnala "Uspekhi Fizicheskikh Nauk", 1997)
  184. Fischer H Chem. Phys. Lett. 100 255 (1983)
  185. Hamilton C A et al Mol. Phys. 65 423 (1988)
  186. Saik V O, Ostafin A E, Lipsky S J. Chem. Phys. 103 7347 (1995)
  187. Sacher M, Grampp G Berichte Bunsengesell. Phys. Chemie 101 971 (1997)
  188. Paul S et al Sci. Rep. 7 11892 (2017)
  189. Schulten Z, Schulten K J. Chem. Phys. 66 4616 (1977)
  190. Stass D V, Tadjikov B M, Molin Yu N Chem. Phys. Lett. 235 (5-6) 511 (1995)
  191. Letuta U G et al Bioelectromagnetics 38 511 (2017)
  192. Krylov V et al Front. Physiol. 13 1040083 (2022)
  193. Sinčák M, Sedlakova-Kadukova J Processes 11 282 (2023)
  194. Kaspranskii R R, Binhi V N, Koshel’ I V Fiz. Biol. Med. (1) 77 (2024)
  195. Ritz T et al Nature 429 177 (2004)
  196. Engels S et al Nature 509 353 (2014)
  197. Bojarinova J et al Sci. Rep. 10 3473 (2020)
  198. Leberecht B et al J. Comp. Physiol. A 208 97 (2022)
  199. Phillips J, Painter M Lynx Nová Série 53 (1) 219 (2022)
  200. Kobylkov D et al J. R. Soc. Interface 16 20190716 (2019)
  201. Frankevich E L, Pristupa A I, Lesin V I Chem. Phys. Lett. 54 (1) 99 (1978)
  202. Lesin V I et al Phys. Status Solidi B 84 513 (1977)
  203. Slichter C P Principles Of Magnetic Resonance 3rd ed. (Heidelberg: Springer-Verlag, 1996)
  204. Kavokin K V Bioelectromagnetics 30 402 (2009)
  205. Bargatin I V, Grishanin B A, Zadkov V N Phys. Usp. 44 597 (2001); Bargatin I V, Grishanin B A, Zadkov V N Usp. Fiz. Nauk 171 625 (2001)
  206. Fok V A et al Usp. Fiz. Nauk 16 436 (1936)
  207. Kilin S Ya Phys. Usp. 42 435 (1999); Kilin S Ya Usp. Fiz. Nauk 169 507 (1999)
  208. Kholevo A S Vvedenie V Kvantovuyu Teoriyu Informatsii (Introduction To Quantum Information Theory) (Moscow: MTsNMO, 2002)
  209. Valiev K A Phys. Usp. 48 1 (2005); Valiev K A Usp. Fiz. Nauk 175 3 (2005)
  210. Nielsen M A, Chuang I L Kvantovye Vychisleniya I Kvantovaya Informatsiya (Moscow: Mir, 2006); Translated from English, Nielsen M A, Chuang I L Quantum Computation And Quantum Information (Cambridge: Cambridge Univ. Press, 2000)
  211. Zheltikov A M, Scully M O Phys. Usp. 63 698 (2020); Zheltikov A M, Scully M O Usp. Fiz. Nauk 190 749 (2020)
  212. Hogben H J, Biskup T, Hore P J Phys. Rev. Lett. 109 220501 (2012)
  213. Vesperini A, Bel-Hadj-Aissa G, Franzosi R Sci. Rep. 13 2852 (2023)
  214. Horodecki R et al Rev. Mod. Phys. 81 865 (2009)
  215. Eltschka C, Siewert J J. Phys. A 47 424005 (2014)
  216. Werner R F Phys. Rev. A 40 4277 (1989)
  217. Vedral V et al Phys. Rev. Lett. 78 2275 (1997)
  218. Audretsch J Entangled Systems. New Directions In Quantum Physics (Weinheim: Wiley-VCH, 2007)
  219. Breus T K, Binhi V N, Petrukovich A A Phys. Usp. 59 502 (2016); Breus T K, Binhi V N, Petrukovich A A Usp. Fiz. Nauk 186 568 (2016)
  220. Krylov V V et al Int. J. Biometeorol. 63 241 (2019)
  221. Pishchalnikov R Y et al Biomed. Signal Proces. Control 51 401 (2019)
  222. Dorokhov V B et al Geofiz. Protsessy Biosfera 20 (3) 76 (2021)
  223. Binhi V N Cells 12 724 (2023)
  224. Binhi V N, Rubin A B Fiz. Biol. Med. (1) 44 (2023)
  225. Binhi V N, Prato F S Bioelectromagnetics 38 (1) 41 (2017)
  226. Binhi V N, Savin A V Phys. Rev. E 65 051912 (2002)
  227. Bajtoš M et al Front. Public Health 13 1535155 (2025)
  228. Binhi V N, Rubin A B Electromagn. Biol. Med. 26 (1) 45 (2007)
  229. Dhiman S K, Wu F, Galland P Protoplasma 260 767 (2023)
  230. Binhi V N, Prato F S Sci. Rep. 8 13495 (2018)
  231. Orgel L E Proc. Natl. Acad. Sci. USA 67 1476 (1970)

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