# Biophotons and Emergence of Quantum Coherence—A Diffusion Entropy Analysis

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## Abstract

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## 1. Introduction

#### 1.1. Introduction to Biophotons

^{2}surface of the living system. The spectral intensity seems to be quite flat for wavelengths ranging between 200 and 800 nm. After any type of stress (chemical agents, excitation by white or monochromatic light, temperature…) the emission increases of almost a factor ten and relaxes to the normal values quite slowly, following hyperbolic functions rather than an exponential law. Finally, the photocount statistics that account for the probability of having N photons within some time interval seems to follow a Poisson distribution. The biophoton emission is also very sensitive to the biological characteristics of the system under examination, and for this reason, this types of measures has been successfully applied to medical diagnostics, agriculture and ecology [7,8,9].

#### 1.2. Introduction to Complexity

## 2. Material and Methods

## 3. Theoretical Foundation

#### Definition of μ

## 4. Results

^{−4}for the whole set of data and are not reported in the table for clarity.

## 5. Discussion and Conclusions

#### 5.1. Results of This Paper

#### 5.2. Suggestions for Future Research Work

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Gurwitsch, A.G. Die Natur des spezifischen Erregers der Zellteilung. Arch. Entw. Mech. Org.
**1923**, 100, 11–40. [Google Scholar] [CrossRef] - Reiter, T.; Gabor, D. Ultraviolette Strahlung und Zellteilung. Wiss. Verffentlichungen Aus Dem Siemens-Konzern
**1928**, 4, 184. [Google Scholar] - Colli, L.; Facchini, U. Light Emission by Germinating Plants. Il Nuovo Cim.
**1954**, 12, 150–153. [Google Scholar] [CrossRef] - Colli, L.; Facchini, U.; Guidotti, G.; Dugnani Lonati, R.; Orsenigo, M.; Sommariva, O. Further Measurements on the Bioluminescence of the Seedlings. Experientia
**1955**, 11, 479–481. [Google Scholar] [CrossRef] - Popp, F.A.; Gu, Q.; Li, K.H. Biophoton Emission: Experimental Background and Theoretical Approaches. Mod. Phys. Lett. B
**1994**, 8, 1269–1296. [Google Scholar] [CrossRef] - Van Wijk, R. Light in Shaping Life: Biophotons in Biology and Medicine; Boekenservice: Almere, The Netherlands, 2014. [Google Scholar]
- Gallep, C.M.; Dos Santos, S.R. Photon-count during germination of wheat (Triticum aestivum) in waste water sediment solution correlated with seedling growth. Seed Sci. Technol.
**2007**, 35, 607–614. [Google Scholar] [CrossRef] - Musumeci, F.; Scordino, A.; Triglia, A.; Blandino, G.; Milazzo, I. Intercellular communication during yeast cell growth. Europhys. Lett.
**1999**, 47, 736. [Google Scholar] [CrossRef] - Grasso, F.; Grillo, C.; Musumeci, F.; Triglia, A.; Rodolico, G.; Cammisuli, F.; Rinzivillo, C.; Fragati, G.; Santuccio, A.; Rodolico, M. Photon emission from normal and tumor human tissue. Experientia
**1992**, 48, 10–13. [Google Scholar] [CrossRef] - Mauburov, S.N. Photonic Communications in Biological Systems. J. Samara State Tech. Univ. Ser. Phys. Math. Sci.
**2011**, 15, 260–265. [Google Scholar] - Kucera, O.; Cifra, M. Cell-to-cell signaling through light: Just a ghost of chance? Cell Comm. Signal.
**2013**, 11, 87. [Google Scholar] [CrossRef][Green Version] - Fels, D. Cellular Communication through light. PLoS ONE
**2009**, 4, e5086. [Google Scholar] [CrossRef] - Beloussov, L.V.; Burlakov, A.B.; Louchinskaia, N.N. Biophotonic Pattern of optical interaction between fish eggs and embryos. Indian J. Exp. Biol.
**2003**, 41, 424–430. [Google Scholar] - Tang, R.; Dai, J. Biophoton signal transmission and processing in the brain. J. Photochem. Photobiol. B Biol.
**2014**, 139, 71–75. [Google Scholar] [CrossRef] [PubMed] - Kumar, S.; Boone, K.; Tuszynski, J.; Barclay, P.; Simon, C. Possible existence of optical communication channels in the brain. Sci. Rep.
**2016**, 6, 36508. [Google Scholar] [CrossRef][Green Version] - Zangari, A.; Micheli, D.; Galeazzi, R.; Tozzi, A. Node of Ranvier as an Array of Bio-Nanoantennas for Infrared Communication in Nerve Tissue. Sci. Rep.
**2018**, 8, 539. [Google Scholar] [CrossRef][Green Version] - Cifra, M.; Brouder, C.; Nerudova, M.; Kucera, O. Biophotons, coherence and photocount statistics: A critical review. J. Lumin.
**2015**, 164, 38–51. [Google Scholar] [CrossRef][Green Version] - Duan, S.; Wang, F.; Zhang, Y. Research on the biophoton emission of wheat kernels based on permutation entropy. Opt. Int. J. Light Electron Opt.
**2019**, 178, 723–730. [Google Scholar] [CrossRef] - Bandt, C.; Pompe, B. Permutation Entropy: A Natural Complexity Measure for Time Series. Phys. Rev. Lett.
**2002**, 88, 174102. [Google Scholar] [CrossRef] [PubMed] - Falconi, M.; Loreto, V.; Vulpiani, A. Kolmogorov Legacy about Entropy, Chaos and Complexity; Springer: Berlin/Heidelberg, Germany, 2003; pp. 85–108. [Google Scholar]
- Latora, V.; Baranger, M. Kolomogorov-Sinai Entropy Rate versus Physical Entropy. Phys. Rev. Lett.
**1999**, 82, 520. [Google Scholar] [CrossRef][Green Version] - Allegrini, P.; Benci, V.; Grigolini, P.; Hamilton, P.; Ignaccolo, M.; Menconi, G.; Palatella, L.; Raffaelli, G.; Scafetta, N.; Virgilio, M.; et al. Compression and diffusion: A joint approach to detect complexity. Chaos Solitons Fractals
**2003**, 15, 517–535. [Google Scholar] [CrossRef][Green Version] - Scafetta, N.; Hamilton, P.; Grigolini, P. The thermodynamics of social processes: The teen birth phenomenon. Fractals
**2001**, 9, 193–208. [Google Scholar] [CrossRef][Green Version] - Scafetta, N.; Grigolini, P. Scaling detection in time series: Diffusion Entropy analysis. Phys. Rev. E
**2002**, 66, 036130. [Google Scholar] [CrossRef] [PubMed][Green Version] - Culbreth, G.; West, B.J.; Grigolini, P. Entropic Approach to the Detection of Crucial Events. Entropy
**2019**, 21, 178. [Google Scholar] [CrossRef][Green Version] - Grigolini, P. Emergence of biological complexity: Criticality, renewal and memory. Chaos Solitons Fractals
**2015**, 81, 575–588. [Google Scholar] [CrossRef] - Bohara, G.; West, B.J.; Grigolini, P. Bridging Waves and Crucial Events in the Dynamic of the Brain. Front. Physiol.
**2018**, 9, 1174. [Google Scholar] [CrossRef] - Attanasi, A.; Cavagna, A.; Del Castello, L.; Giardina, I.; Melillo, S.; Parisi, L.; Pohl, O.; Rossaro, B.; Shen, E.; Silvestri, E.; et al. Finite-Size Scaling as a Way to Probe Near-Criticality in Natural Swarms. Phys. Rev. Lett.
**2014**, 113, 238102. [Google Scholar] [CrossRef] - Vanni, F.; Luković, M.; Grigolini, P. Criticality and Transmission of Information in a Swarm of Cooperative Units. Phys. Rev. Lett.
**2011**, 107, 078103. [Google Scholar] [CrossRef] [PubMed][Green Version] - Contoyiannis, Y.F.; Diakonos, F.K.; Malakis, A. Intermittent Dynamics of Critical Fluctuations. Phys. Rev. Lett.
**2002**, 89, 035701. [Google Scholar] [CrossRef] [PubMed] - Schuster, H.G. Deterministic Chaos; VCH: New York, NY, USA, 1988. [Google Scholar]
- Bohara, G.; Lambert, D.; West, B.J.; Grigolini, P. Crucial events, randomness and multifractality in heartbeat. Phys. Rev. E
**2017**, 96, 062216. [Google Scholar] [CrossRef] [PubMed][Green Version] - Mahmoodi, K.; West, B.J.; Grigolini, P. Self-Organizing Complex Networks: Individual versus global rules. Front. Physiol.
**2017**, 8, 478. [Google Scholar] [CrossRef] [PubMed][Green Version] - Mahmoodi, K.; West, B.J.; Grigolini, P. Self-Organized Temporal Criticality: Bottom-up resilience versus top-down vulnerability. Complexity
**2018**, 2018, 8139058. [Google Scholar] [CrossRef][Green Version] - Mahmoodi, K.; Grigolini, P.; West, B.J. On social sensitivity to either zealot or independent minorities. Chaos Solitons Fractals
**2018**, 110, 185–190. [Google Scholar] [CrossRef] - Photon Counting Head H12386-210 Datasheet. Available online: https://www.hamamatsu.com/eu/en/product/type/H12386-210/index.html (accessed on 20 February 2021).
- Test Sheet Hamamatsu for the Phototube H12386-210, Serial Number 30050260. Available online: https://www.hamamatsu.com/resources/pdf/etd/H12386_TPMO1073E.pdf (accessed on 20 February 2021).
- Fox, M. Quantum Optics—An Introduction; OUP Oxford: Oxford, UK, 2006. [Google Scholar]
- Stanley, H.E.; Buldyrev, S.V.; Goldberger, A.L.; Goldberger, Z.D.; Havlin, S.; Mantegna, R.N.; Ossadnik, S.M.; Peng, C.K.; Simons, M. Statistical mechanics in biology: How ubiquitous are long-range correlations? Physica A
**1994**, 205, 214–253. [Google Scholar] [CrossRef] - Hurst, H.E. Long-term storage capacity of reservoirs. Trans. Am. Soc. Civ. Eng.
**1951**, 116, 770–799. [Google Scholar] [CrossRef] - Mandelbrot, B.B.; Walls, J.R. Noah, Joseph and operational hydrology. Water Resourc. Res.
**1968**, 4, 909. [Google Scholar] [CrossRef][Green Version] - Cakir, R.A.Ş.İ.T.; Grigolini, P.; Krokhin, A.A. Dynamical origin of memory and renewal. Phys. Rev. E
**2006**, 74, 021108. [Google Scholar] [CrossRef] [PubMed][Green Version] - Weiss, U. Quantum Dissipative Systems, 2nd ed.; World Scientific: Singapore, 1992. [Google Scholar]
- Grigolini, P.; Palatella, L.; Raffaelli, G. Anomalous Diffusion: An Efficient Way to Detect Memory in Time Series. Fractals
**2001**, 9, 439–449. [Google Scholar] [CrossRef] - Paradisi, P.; Allegrini, P.; Gemignani, A.; Laurino, M.; Menicucci, D.; Piarulli, A. Scaling and intermittency of brain events as a manifestation of consciousness. In AIP Conference Proceedings; American Institute of Physics: College Park, MD, USA, 2013; Volume 1510, p. 151. [Google Scholar] [CrossRef][Green Version]
- Allegrini, P.; Menicucci, D.; Bedini, R.; Fronzoni, L.; Gemignani, A.; Grigolini, P.; West, B.J.; Paradisi, P. Spontaneous brain activity as a source of ideal 1/f noise. Phys. Rev. E
**2009**, 80, 061914. [Google Scholar] [CrossRef] [PubMed][Green Version] - Barenblatt, G.I. Scaling, Self-Similarity and Intermediate Asymptotics; Cambridge Press: Cambridge, UK, 1996. [Google Scholar]
- Culbreth, G.; West, B.J.; Grigolini, P. Caputo Fractional Derivative versus Quantum Coherence. Entropy
**2021**, 23, 211. [Google Scholar] [CrossRef] - Mori, H. Transport, Collective Motion and Brownian Motion. Prog. Theor. Phyiscs
**1965**, 33, 423. [Google Scholar] [CrossRef][Green Version] - Scafetta, N.; Latora, V.; Grigolini, P. Levy scaling: The diffusion entropy analysis applied to DNA sequences. Phys. Rev. E
**2002**, 66, 031906. [Google Scholar] [CrossRef][Green Version] - Vanni, F.; Grigolini, P. Music as a mirror of mind. In Esthétique de la Complexité; Hermann: Paris, France, 2017. [Google Scholar]
- Pease, A.; Mahmoodi, K.; West, B.J. Complexity measures of music. Chaos Solitons Fractals
**2018**, 108, 82–86. [Google Scholar] [CrossRef] - Jelinek, H.F.; Tuladhar, R.; Culbreth, G.; Bohara, G.; Cornforth, D.; West, B.J.; Grigolini, P. Diffusion Entropy versus Multiscale and Renyi Entropy to detect progression of Autonomic Neuropathy. Front. Physiol.
**2020**, 11, 607324. [Google Scholar] [CrossRef] [PubMed] - Lukovic, M.; Grigolini, P. Power spectra for both interrupted and perennial aging process. J. Chem. Phys.
**2008**, 129, 184102. [Google Scholar] [CrossRef][Green Version] - Dlask, M.; Kukal, J.; Poplová, M.; Sovka, P.; Cifra, M. Short–time fractal analysis of biological autoluminescence. PLoS ONE
**2019**, 14, e0214427. [Google Scholar] [CrossRef][Green Version] - Miller, W.B., Jr. Biological information systems: Evolution as cognition-based information management. Prog. Biophys. Mol. Biol.
**2018**, 134, 1–26. [Google Scholar] [CrossRef] - Eigen, M. From Strange Simplicity to Complex Familiarity: A Treatise on Matter, Information, Life and Thought; OUP: Oxford, UK, 2013. [Google Scholar]
- Ford, B.J. On Intelligence in Cells: The Case for Whole Cell Biology. Interdiscip. Sci. Rev.
**2009**, 34, 350–365. [Google Scholar] [CrossRef][Green Version] - Dodig-Crnkovic, G. Modeling Life as Cognitive Info-Computation. In Language, Life, Limits; Beckmann, A., Csuhaj-Varj, E., Meer, K., Eds.; Springer: Cham, Switzerland, 2014; Volume 8493. [Google Scholar]
- Maturana, H.; Varela, F. Autopoiesis and Cognition: The Realization of the Living; D. Reidel Pub. Co.: Dordrecht, The Netherlands, 1980. [Google Scholar]
- Mahmoodi, K.; West, B.J.; Grigolini, P. Complexity Matching and Requisite Variety. arXiv
**2019**, arXiv:1806.08808. [Google Scholar] - Popp, F.A. Consciousness as Evolutionary Process Based on Coherent States. NeuroQuantology
**2008**, 6, 431. [Google Scholar] [CrossRef][Green Version] - Piao, D. On the stress-induced photon emission from organism: II, how will the stress-transfer kinetics affect the photo-genesis? SN Appl. Sci.
**2020**, 6, 1556. [Google Scholar] [CrossRef] - Piao, D. On the stress-induced photon emission from organism: I, will the scattering-limited delay affect the temporal course? SN Appl. Sci.
**2020**, 2, 1566. [Google Scholar] [CrossRef] - Mancuso, S. The Revolutionary Genius of Plants: A New Understanding of Plant Intelligence and Behaviour; Simon and Shuster: New York, NY, USA, 2018. [Google Scholar]
- Mancuso, S.; Viola, A. Brilliant Green: The Surprising History and Science of Plant Intelligence; Island Press: Washington, DC, USA, 2015. [Google Scholar]
- Van Wijk, R.; Van Wijk, E.; Pang, J.; Yang, M.; Yan, Y.; Han, J. Integrating Ultra-Weak Photon Emission Analysis in Mitochondrial Research. Front. Physiol.
**2020**, 11, 717. [Google Scholar] [CrossRef] [PubMed] - Prasad, A.; Gouripeddi, P.; Devireddy, H.R.N.; Ovsii, A.; Rachakonda, D.P.; Wijk, R.V.; Pospíšil, P. Spectral Distribution of Ultra-Weak Photon Emission as a Response to Wounding in Plants: An in Vivo Study. Biology
**2020**, 9, 139. [Google Scholar] [CrossRef] [PubMed] - Dal Lin, C.; Falanga, M.; De Lauro, E.; De Martino, S.; Vitiello, G. Biochemical and biophysical mechanisms underlying the heart and the brain dialog. Biophysics
**2020**, 8, 1–33. [Google Scholar] [CrossRef]

**Figure 1.**Technical design of the experimental setup used in our experiment. The photon-counting system consists of a Hamamatsu H12386-210 counting head. The germination chamber is built with black PVC to avoid any contamination of light from outside. At the top right a photo with the practical realization of our experimental set-up is shown.

**Figure 2.**Comparison between the signal generated by the germinating seeds and the signal in the dark condition. The raw data are the green (seeds) and red (dark count) points. The black and blue curves are the raw data (count/sec) averaged over one minute. In the inset the emission of seeds for a period of one hour has been reported in detail.

**Figure 3.**Comparison between the experimental counting distribution function (red squares) and the fit performed with a Poisson function (blue line).

**Figure 4.**Time evolution of the counting distribution function $p\left(n,\Delta t\right)$ (red dots) at different stage of the germinating process. Blue lines are fits done using Poisson functions.

**Figure 5.**Number of photons emitted during the germination of lentil seeds (green points). The red dashed lines represent the six different regions used for the DEA analysis.

**Figure 6.**Graphical representation of the Diffusion Entropy Analysis method (blue curve). The red dashed line is the fit of the intermediate region.

Exp. <n> | Exp. σ^{2} | Poisson <n> | |
---|---|---|---|

dark | 1.56 | 2.24 | 0.827 ± 0.03 |

1 | 14.40 | 14.60 | 14.51 ± 0.10 |

2 | 26.83 | 29.12 | 26.80 ± 0.21 |

3 | 22.21 | 24.84 | 21.90 ± 0.13 |

**Table 2.**The scaling factors obtained by DEA without and with stripes for the six different regions of the time series with seeds and for the whole region of the dark counts time series.

Without Stripes | With Stripes | |||
---|---|---|---|---|

$\mathit{\eta}$ | $\mathit{\mu}$ | $\mathit{\eta}$ | $\mathit{\mu}$ | |

dark counts | 0.575 | 2.739 | 0.508 | 2.968 |

region #1 | 0.773 | 2.293 | 0.596 | 2.677 |

region #2 | 0.796 | 2.254 | 0.558 | 2.792 |

region #3 | 0.736 | 2.358 | 0.526 | 2.901 |

region #4 | 0.737 | 2.355 | 0.496 | 3.016 |

region #5 | 0.694 | 2.440 | 0.509 | 2.964 |

region #6 | 0.725 | 2.377 | 0.504 | 2.984 |

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**MDPI and ACS Style**

Benfatto, M.; Pace, E.; Curceanu, C.; Scordo, A.; Clozza, A.; Davoli, I.; Lucci, M.; Francini, R.; De Matteis, F.; Grandi, M.; Tuladhar, R.; Grigolini, P. Biophotons and Emergence of Quantum Coherence—A Diffusion Entropy Analysis. *Entropy* **2021**, *23*, 554.
https://doi.org/10.3390/e23050554

**AMA Style**

Benfatto M, Pace E, Curceanu C, Scordo A, Clozza A, Davoli I, Lucci M, Francini R, De Matteis F, Grandi M, Tuladhar R, Grigolini P. Biophotons and Emergence of Quantum Coherence—A Diffusion Entropy Analysis. *Entropy*. 2021; 23(5):554.
https://doi.org/10.3390/e23050554

**Chicago/Turabian Style**

Benfatto, Maurizio, Elisabetta Pace, Catalina Curceanu, Alessandro Scordo, Alberto Clozza, Ivan Davoli, Massimiliano Lucci, Roberto Francini, Fabio De Matteis, Maurizio Grandi, Rohisha Tuladhar, and Paolo Grigolini. 2021. "Biophotons and Emergence of Quantum Coherence—A Diffusion Entropy Analysis" *Entropy* 23, no. 5: 554.
https://doi.org/10.3390/e23050554