标度相对论中的宏观量子型势
Macroscopic quantum-type potentials in scale relativity
摘要：
在本文中，我们回顾了使用的尺度相对论和分形时空作为一种工具，特别适合于未来真正的理论系统生物学的可能发展。我们特别强调量子型势的概念，因为在许多情况下，空间或底层介质的分形效应相当于在经典运动方程中增加了这样的势能。给出了这些方程的各种等价表示--测地线、量子、流体力学、随机--以及几种形式的广义量子势。它们可能干预高临界温度超导性和湍流的例子也被描述，因为一些生物过程可能在某些方面类似于这些物理现象。这些潜在的能量额外的贡献可能已经出现在生物学中从非常分形性质的介质，或从进化的优势，因为它们涉及自发性质的自组织，形态发生结构化和多尺度集成。
英文摘要：
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.
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