Abstract
Several methods have been recently proposed to calculate configurational entropy, based on Boltzmann entropy. Some of these methods appear to be fully thermodynamically consistent in their application to landscape patch mosaics, but none have been shown to be fully generalizable to all kinds of landscape patterns, such as point patterns, surfaces, and patch mosaics. The goal of this paper is to evaluate if the direct application of the Boltzmann relation is fully generalizable to surfaces, point patterns, and landscape mosaics. I simulated surfaces and point patterns with a fractal neutral model to control their degree of aggregation. I used spatial permutation analysis to produce distributions of microstates and fit functions to predict the distributions of microstates and the shape of the entropy function. The results confirmed that the direct application of the Boltzmann relation is generalizable across surfaces, point patterns, and landscape mosaics, providing a useful general approach to calculating landscape entropy.
Highlights
The calculation of configurational entropy of landscapes has emerged as a topic of considerable recent interest, as appreciation of the connections between thermodynamics and landscape processes becomes more apparent [1,2]
The goal of this paper is to show that the Cushman method is fully generalizable to surfaces, point patterns, and landscape mosaics
The goal of this paper is to show that the direct application of the Boltzmann relation for computing landscape entropy applies in the exact same way to measuring the entropy of point patterns and surfaces
Summary
The calculation of configurational entropy of landscapes has emerged as a topic of considerable recent interest, as appreciation of the connections between thermodynamics and landscape processes becomes more apparent [1,2]. Several recent methods have been proposed to calculate configurational entropy, based on Boltzmann entropy. The Cushman [3,4] method directly applies the classic and iconic Boltzmann relation (s = klogW) to spatial patterns. The Boltzmann relation states that the entropy of a system is proportional to the logarithm of the number of macrostate, or unique configurations, that produce the observed macrostate, or global system property. Other authors have proposed more complex solutions based on multiresolution analysis [5,6] and Wassenstein entropy [7,8].
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