Maximum Entropy Distributions of Scale-Invariant Processes

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Maximum Entropy Distributions of Scale-Invariant Processes

Veronica Nieves, Jingfeng Wang, Rafael L. Bras, and Elizabeth Wood

Phys. Rev. Lett. 105, 118701 – Published 9 September 2010

Abstract

Organizations of many variables in nature such as soil moisture and topography exhibit patterns with no dominant scales. The maximum entropy (ME) principle is proposed to show how these variables can be statistically described using their scale-invariant properties and geometric mean. The ME principle predicts with great simplicity the probability distribution of a scale-invariant process in terms of macroscopic observables. The ME principle offers a universal and unified framework for characterizing such multiscaling processes.

Received 15 July 2010

DOI:https://doi.org/10.1103/PhysRevLett.105.118701

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