自然界的多尺度原理(Principium luxuriæ):将多尺度热力学与生物和非生物复杂系统联系起来

IF 3.6 2区 数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Fractal and Fractional Pub Date : 2024-01-04 DOI:10.3390/fractalfract8010035
P. Venegas-Aravena, E. Cordaro
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引用次数: 0

摘要

为什么分形出现在如此多的科学领域?产生它们的物理原理是什么?虽然分形确实自然地出现在许多物理系统中,但迄今为止还无法从第一物理原理中推导出分形。不过,一种拟议的解释可以揭示分形产生背后的内在原理。这就是多尺度热力学观点,它指出外部能量的增加可以启动能量传输机制,促进多余能量在不同尺度上的耗散或释放。在这一框架内,幂律模式(其次是分形)可以作为一种几何表现形式出现,以消散能量来响应外力。在这种情况下,这些幂律模式的指数(热力学分形维度 D)可作为小尺度和大尺度熵产生平衡的指标。因此,当一个系统在微观(宏观)层面释放多余能量的效率更高时,D 会趋于增大(减小)。这一原理被称为 "奢侈原理"(Principium luxuriæ),听起来很有希望用于描述多尺度和复杂系统,但其真正的适用性仍存在不确定性。因此,这项研究探索了不同的物理、天体物理、社会学和生物系统,试图通过 "复杂性原理"(Principium luxuriæ)的视角来描述和解释这些系统。所分析的物理系统与突发行为、混沌理论和湍流相对应。其次是宇宙演化和地貌学。此外,还分析了人体器官几何、衰老、人脑发育和认知、道德进化、自然选择和生物死亡等生物系统。研究发现,这些系统可以通过热力学分形维度来重新解释和描述。因此,有人提出分形产生背后的物理原理是 "奢侈原理"(Principium luxuriæ),可定义为 "相互影响的系统可在多个尺度上引发反应,以此消散相互作用产生的多余能量"。这就是为什么这个框架有可能在各个领域发现新的发现。例如,有人认为,宇宙中 D 的减少可能会在许多领域产生突现行为和复杂性的扩散,或重新解释自然选择。
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The Multiscale Principle in Nature (Principium luxuriæ): Linking Multiscale Thermodynamics to Living and Non-Living Complex Systems
Why do fractals appear in so many domains of science? What is the physical principle that generates them? While it is true that fractals naturally appear in many physical systems, it has so far been impossible to derive them from first physical principles. However, a proposed interpretation could shed light on the inherent principle behind the creation of fractals. This is the multiscale thermodynamic perspective, which states that an increase in external energy could initiate energy transport mechanisms that facilitate the dissipation or release of excess energy at different scales. Within this framework, it is revealed that power law patterns, and to a lesser extent, fractals, can emerge as a geometric manifestation to dissipate energy in response to external forces. In this context, the exponent of these power law patterns (thermodynamic fractal dimension D) serves as an indicator of the balance between entropy production at small and large scales. Thus, when a system is more efficient at releasing excess energy at the microscopic (macroscopic) level, D tends to increase (decrease). While this principle, known as Principium luxuriæ, may sound promising for describing both multiscale and complex systems, there is still uncertainty about its true applicability. Thus, this work explores different physical, astrophysical, sociological, and biological systems to attempt to describe and interpret them through the lens of the Principium luxuriæ. The analyzed physical systems correspond to emergent behaviors, chaos theory, and turbulence. To a lesser extent, the cosmic evolution of the universe and geomorphology are examined. Biological systems such as the geometry of human organs, aging, human brain development and cognition, moral evolution, Natural Selection, and biological death are also analyzed. It is found that these systems can be reinterpreted and described through the thermodynamic fractal dimension. Therefore, it is proposed that the physical principle that could be behind the creation of fractals is the Principium luxuriæ, which can be defined as “Systems that interact with each other can trigger responses at multiple scales as a manner to dissipate the excess energy that comes from this interaction”. That is why this framework has the potential to uncover new discoveries in various fields. For example, it is suggested that the reduction in D in the universe could generate emergent behavior and the proliferation of complexity in numerous fields or the reinterpretation of Natural Selection.
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来源期刊
Fractal and Fractional
Fractal and Fractional MATHEMATICS, INTERDISCIPLINARY APPLICATIONS-
CiteScore
4.60
自引率
18.50%
发文量
632
审稿时长
11 weeks
期刊介绍: Fractal and Fractional is an international, scientific, peer-reviewed, open access journal that focuses on the study of fractals and fractional calculus, as well as their applications across various fields of science and engineering. It is published monthly online by MDPI and offers a cutting-edge platform for research papers, reviews, and short notes in this specialized area. The journal, identified by ISSN 2504-3110, encourages scientists to submit their experimental and theoretical findings in great detail, with no limits on the length of manuscripts to ensure reproducibility. A key objective is to facilitate the publication of detailed research, including experimental procedures and calculations. "Fractal and Fractional" also stands out for its unique offerings: it warmly welcomes manuscripts related to research proposals and innovative ideas, and allows for the deposition of electronic files containing detailed calculations and experimental protocols as supplementary material.
期刊最新文献
On the Impacts of the Global Sea Level Dynamics Research on Application of Fractional Calculus Operator in Image Underlying Processing The Multiscale Principle in Nature (Principium luxuriæ): Linking Multiscale Thermodynamics to Living and Non-Living Complex Systems A Numerical Scheme and Application to the Fractional Integro-Differential Equation Using Fixed-Point Techniques Correction: Panchal et al. 3D FEM Simulation and Analysis of Fractal Electrode-Based FBAR Resonator for Tetrachloroethene (PCE) Gas Detection. Fractal Fract. 2022, 6, 491
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