Thermodynamic Consideration on Volcanic Landforms

  • Naoto Kaneko
  • Hiroyuki NagahamaEmail author
Conference paper
Part of the Advances in Science, Technology & Innovation book series (ASTI)


Based on the first law of thermodynamics in the view point of non-equilibrium thermodynamics, the concept of entropy is expressed in terms of the probability of various states and treatments of the distribution of energy. From the general hypothesis of forming volcanoes by physical constraints, typical shape for the longitudinal profiles of volcanoes is determined which enables us to observe in the field or map. Weathering and erosion are insufficient to determine the shape, height, and geometries of volcanoes. However, solutions become possible by introducing the concept that the distribution of energy tends toward the most probable. This solution leads to a theoretical definition of the thermodynamics and geometry of volcanic landforms that agrees closely with field observations. The most probable state for certain physical systems can also be illustrated by Lorentz plot. The average longitudinal profiles and angle of repose were so derived. They have the properties implied by the theory. The regularity derived from the average longitudinal profiles has some of the principal properties demonstrated by the concept of entropy. Specifically, the height of volcano and distance from its summit are exponentially inversely-proportional.


Entropy Volcanic landform Non-equilibrium thermodynamic Digital elevation model (DEM) Angle of repose 


  1. 1.
    Kaneko, N., Muto, J., Nagahama, H.: Plasticity index effects on mechanical bifurcation: soils and soft-sediment deformation. GEOMATE 13(36), 19–25 (2017)CrossRefGoogle Scholar
  2. 2.
    Niiseki, S., Satake, M.: Derivation and discussion on Rowe’s principle of energy ratio minimum. In: Proceedings of the Annual Conference JMCE, 3rd edn., vol. 36, pp. 5–6 (1981, in Japanese)Google Scholar
  3. 3.
    Rowe, P.W.: The stress-dilatancy relation for static equilibrium of an assembly of particles in contact. Proc. R. Soc. A. 269(1339), 500–527 (1962)CrossRefGoogle Scholar
  4. 4.
    Terada, T.: On the form of volcanoes. Bull. Eqk. Res. Inst., Univ. Tokyo. 7(2), 207–221 (1929)Google Scholar
  5. 5.
    Reissner, H.: Zum Erddruckproblem. In: Proceedings of the 1st International Congress Applied Mechanics, Delft, pp. 295–311 (1924)Google Scholar
  6. 6.
    Leopold, L.B., Walter, B.L.: The concept of entropy in landscape evolution. In: Geological Survey Professional Paper, pp. A1–20 (1962)Google Scholar

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Authors and Affiliations

  1. 1.Department of Earth ScienceTohoku UniversitySendaiJapan

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