Context The second law of thermodynamics is fundamental in landscape ecology, and Shannon entropy has been employed as an important means of analyzing landscape patterns. However, the thermodynamic basis of Shannon entropy has been recently questioned because such entropy considers only probability and not configurational information. As a result, Boltzmann entropy (also called configurational entropy), which is the basic measure in thermodynamics, has been revisited, and some thoughts on its calculation have been put forward. Nevertheless, a comprehensive calculation method is still lacking.Objectives The objective of this study is to propose a feasible solution for the calculation of configurational entropy for landscape gradients. Methods To calculate the configurational entropy, the first step is to define a good macrostate and then to determine the number of microstates. The macrostate of a landscape gradient is defined as its abstract (i.e., upscaled) representation. The number of microstates is calculated by determining all the possible ways of downscaling from the macrostate to the original. Results Both simulated and real-life landscape patterns were used for experimental validation. The results show that the entropy calculated using the proposed method successfully captures the disorder of landscape gradients in terms of both composition and configuration. Conclusions Configurational entropy, calculated using the proposed method, can serve as a thermodynamics-based metric to describe gradient-based landscapes and their changes across space and through time. With this metric, it becomes possible to interpret landscape ecological processes based on thermodynamic insights.

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Entropy is a central concept in thermodynamics and plays a fundamental role in understanding nature. It is commonly computed using Shannon's equation, and has been widely used to characterize disorder and to bridge the gap between disorder and thermodynamic interpretations. However, the thermodynamic basis of Shannon entropy is questioned by researchers, and it is suggested to use Boltzmann entropy as an alternative. Very recently, the first and only computation method has been proposed for the Boltzmann entropy of a landscape gradient, but the method is not efficient as it involves a series of numerical processes, which are computation‐intensive and time‐consuming. To improve it, a novel method is proposed in this study by developing an analytical solution to the key mathematical problem of the original method and incorporating a parallelization strategy. Experimental results demonstrate that the proposed method is both effective and efficient. Developed based on the proposed method, a software tool (as well as its source code) is released for free use. The proposed method and the developed tool shall contribute to an easy computation of the Boltzmann entropies of not only landscape gradients, but also remote sensing images and other quantitative raster data.