Rarefied particle motions on hillslopes – Part 3: Entropy

Abstract. Theoretical and experimental work (Furbish et al., 2021a, b) indicates that the travel distances of rarefied particle motions on rough hillslope surfaces are described by a generalized Pareto distribution. The form this distribution varies with balance between gravitational heating, due to conversion potential kinetic energy, frictional cooling, particle–surface collisions; it from bounded associated rapid thermal collapse an exponential representing isothermal conditions heavy-tailed net heating particles. in problem is maximum entropy constrained fixed energetic “cost” – total cumulative energy extracted collisional friction per unit available during motions. That is, among all possible accessible microstates many different ways arrange great number particles into distance states where each arrangement satisfies same cost represents most probable arrangement. Because idea applies equally provides unifying interpretation for these distinctive behaviors, including abrupt transition crossing conditions. analysis therefore novel generalization energy-based constraint using method infer non-exponential distributions Moreover, costs individual follow extreme-value cooling light-tailed heating. relative contribution reflected product effectively frequency–magnitude product.