Articles | Volume 9, issue 3
Earth Surf. Dynam., 9, 615–628, 2021
https://doi.org/10.5194/esurf-9-615-2021
Earth Surf. Dynam., 9, 615–628, 2021
https://doi.org/10.5194/esurf-9-615-2021

Research article 16 Jun 2021

Research article | 16 Jun 2021

Rarefied particle motions on hillslopes – Part 3: Entropy

David Jon Furbish et al.

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Particle energy partitioning and transverse diffusion during rarefied travel on an experimental hillslope
Sarah G. W. Williams and David J. Furbish
Earth Surf. Dynam., 9, 701–721, https://doi.org/10.5194/esurf-9-701-2021,https://doi.org/10.5194/esurf-9-701-2021, 2021
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Preprint withdrawn

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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, https://doi.org/10.1002/2016JF003970, 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, https://doi.org/10.1002/2015JF003552, 2015. 
Furbish, D. J. and Doane, T. H.: Rarefied particle motions on hillslopes – Part 4: Philosophy, Earth Surf. Dynam., 9, 629–664, https://doi.org/10.5194/esurf-9-629-2021, 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, https://doi.org/10.1002/wrcr.20074, 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.