2013/06/18 by Laurent Nottale, Nottale, Laurent
Biochemistry, Genetics and Molecular Biology · Medicine · Physics and Astronomy · #Advanced Mathematical Theories and Applications #Biofield Effects and Biophysics #FOS: Physical sciences #Fractal and DNA sequence analysis #General Physics (physics.gen-ph)
paper · pdf · doi:10.48550/arxiv.1306.4311
openalex publication_date 2013/06/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We review in this paper the use of the theory of scale relativity and fractal space-time as a tool particularly well adapted to the possible development of a future genuine theoretical systems biology. We emphasize in particular the concept of quantum-type potentials, since in many situations the effect of the fractality of space -- or of the underlying medium -- amounts to the addition of such a potential energy to the classical equations of motion. Various equivalent representations -- geodesic, quantum, fluid mechanical, stochastic -- of these equations are given, as well as several forms of generalized quantum potentials. Examples of their possible intervention in high critical temperature superconductivity and in turbulence are also described, since some biological processes may be analog in some aspects to these physical phenomena. These potential energy extra contributions could have emerged in biology from the very fractal nature of the medium, or from an evolutive advantage, since they involve spontaneous properties of self-organization, morphogenesis structuration and multi-scale integration.