An efficient analytical method for computing the Boltzmann entropy of a landscape gradient

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.