Articles | Volume 9, issue 3
Research article
16 Jun 2021
Research article |  | 16 Jun 2021

Rarefied particle motions on hillslopes – Part 3: Entropy

David Jon Furbish, Sarah G. W. Williams, and Tyler H. Doane

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Cited articles

Cover, T. M. and Thomas, J. A.: Elements of Information Theory, Wiley, New York, 1991. 
DiBiase, R. A., Lamb, M. P., Ganti, V., and Booth, A. M.: Slope, grain size, and roughness controls on dry sediment transport and storage on steep hillslopes, J. Geophys. Res.-Earth, 122, 941–960,, 2017. 
Fathel, S. L., Furbish, D. J., and Schmeeckle, M. W.: Experimental evidence of statstical ensemble behavior in bed load sediment transport, J. Geophys. Res.-Earth, 120, 2298–2317,, 2015. 
Furbish, D. J. and Doane, T. H.: Rarefied particle motions on hillslopes – Part 4: Philosophy, Earth Surf. Dynam., 9, 629–664,, 2021. 
Furbish, D. J. and Schmeeckle, M. W.: A probabilistic derivation of the exponential-like distribution of bed load particle velocities, Water Resour. Res., 49, 1–15,, 2013. 
Short summary
The generalized Pareto distribution of particle travel distances on steep hillslopes, as described in two companion papers (Furbish et al., 2021a, 2021b), is a maximum entropy distribution. This simply represents the most probable way that a great number of particles become distributed into distance states, subject to a fixed total energetic cost due to frictional effects of particle–surface collisions. The maximum entropy criterion is equivalent to a formal application of Occam's razor.