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Article

Statistical Physics of Fissure Swarms and Dike Swarms

by
Agust Gudmundsson
Department of Earth Sciences, Royal Holloway University of London, Queen’s Building, Egham TW20 0EX, UK
Geosciences 2025, 15(8), 301; https://doi.org/10.3390/geosciences15080301
Submission received: 7 May 2025 / Revised: 22 July 2025 / Accepted: 23 July 2025 / Published: 4 August 2025

Abstract

Fissure swarms and dike swarms in Iceland constitute the main parts of volcanic systems that are 40–150 km long, 5–20 km wide, extend to depths of 10–20 km, and contain 2 × 1014 outcrop-scale (≥0.1 m) and 1022–23 down to grain-scale (≥1 mm) fractures, suggesting that statistical physics is an appropriate method of analysis. Length-size distributions of 565 outcrop-scale Holocene fissures (tension fractures and normal faults) and 1041 Neogene dikes show good to excellent fits with negative power laws and exponential laws. Here, the Helmholtz free energy is used to represent the energy supplied to the swarms and to derive the Gibbs–Shannon entropy formula. The calculated entropies of 12 sets and subsets of fissures and 3 sets and subsets of dikes all show strong positive correlations with sets/subsets length ranges and scaling exponents. Statistical physics considerations suggest that, at a given time, the probability of the overall state of stress in a crustal segment being heterogeneous is much greater than the state of stress being homogeneous and favourable to the propagation of a fissure or a dike. In a heterogeneous stress field, most fissures/dikes become arrested after a short propagation—which is a formal explanation of the observed statistical size-length distributions. As the size of the stress-homogenised rock volume increases larger fissures/dikes can form, increasing the length range of the distribution (and its entropy) which may, potentially, transform from an exponential distribution into a power-law distribution.
Keywords: tension fractures; normal faults; dikes; exponential laws; power laws; entropy; stress-homogenisation tension fractures; normal faults; dikes; exponential laws; power laws; entropy; stress-homogenisation

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MDPI and ACS Style

Gudmundsson, A. Statistical Physics of Fissure Swarms and Dike Swarms. Geosciences 2025, 15, 301. https://doi.org/10.3390/geosciences15080301

AMA Style

Gudmundsson A. Statistical Physics of Fissure Swarms and Dike Swarms. Geosciences. 2025; 15(8):301. https://doi.org/10.3390/geosciences15080301

Chicago/Turabian Style

Gudmundsson, Agust. 2025. "Statistical Physics of Fissure Swarms and Dike Swarms" Geosciences 15, no. 8: 301. https://doi.org/10.3390/geosciences15080301

APA Style

Gudmundsson, A. (2025). Statistical Physics of Fissure Swarms and Dike Swarms. Geosciences, 15(8), 301. https://doi.org/10.3390/geosciences15080301

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