Natural Fractals as Irreversible Disorder: Entropy Approach from Cracks in the Semi Brittle-Ductile Lithosphere and Generalization
Abstract
:1. Introduction
- Earthquakes spatial distributions [24],
- Earthquake slip patterns [25],
- Structural geology [27],
- Galaxies clustering [28],
- Self-organized criticality (SOC) systems [29],
- High energy collisions data [32],
- Fractal electrodynamics [33],
- Fractal structures of spacetime and mass [34],
- Snowflakes dendrites distribution [35],
- Neuropsychiatric disorders [38],
- Ecology [39],
- Economics [40],
- Urbanism [41],
- Laws [42],
2. Results and Discussion
2.1. Entropy of Fractals Cracks Distribution
Entropy Change in Terms of Spatial Parameters
2.2. Entropy Change in Terms of External Stress Change
Seismic Moment and Entropy
2.3. Entropy and Fractal Geometry Generalization for Linear Nonequilibrium Thermodynamics
Multifractal Entropy for Linear Nonequilibrium Thermodynamics
2.4. Discussion
3. Conclusions
- As Equation (8) is always positive, it is implied that the generation of cracks are the manifestation of irreversible process.
- The pre-failure and failure process can be linked by means of the entropy changes.
- The seismic moment and magnitude exist if external stress, that increases of the entropy of the lithosphere, and increases in the number of cracks and electromagnetic signals also exist.
- It is possible to estimate an expected seismic magnitude in terms of the entropy change/stress change.
- Entropy rapidly increases before earthquakes.
- No entropy increase, no earthquake.
- The seismo-electromagnetic theory explains the non-seismic pre-earthquakes signals and gives physical foundations to the generation of earthquakes.
- The tendency in which nature creates fractals corresponds to a geometrical manifestation of that tendency in which the universe increases the entropy.
- Fractals rising in several fields and topics reveals the increase of ‘disorder’ of those systems.
- The phenomenological coefficients can describe geometrical properties of forces and fluxes.
- The Constructal law is one geometrical application of Onsager’s relations.
- The entropy density is defined as , which represents the quadratic time derivative of those forces () that generate the fractal geometry . No changing force implies no fractality.
- More work must be done in order to link metric tensor, fractal entropy and multiscale thermodynamics.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Venegas-Aravena, P.; Cordaro, E.G.; Laroze, D. Natural Fractals as Irreversible Disorder: Entropy Approach from Cracks in the Semi Brittle-Ductile Lithosphere and Generalization. Entropy 2022, 24, 1337. https://doi.org/10.3390/e24101337
Venegas-Aravena P, Cordaro EG, Laroze D. Natural Fractals as Irreversible Disorder: Entropy Approach from Cracks in the Semi Brittle-Ductile Lithosphere and Generalization. Entropy. 2022; 24(10):1337. https://doi.org/10.3390/e24101337
Chicago/Turabian StyleVenegas-Aravena, Patricio, Enrique G. Cordaro, and David Laroze. 2022. "Natural Fractals as Irreversible Disorder: Entropy Approach from Cracks in the Semi Brittle-Ductile Lithosphere and Generalization" Entropy 24, no. 10: 1337. https://doi.org/10.3390/e24101337