From the perspective of landscape, it is important to evaluate the landscape sustainability of ecologically fragile areas and explore temporal and spatial evolution laws to promote their sustainable development. Presently, most studies on the analysis of landscape Boltzmann entropy (also called configurational entropy) are based on a single landscape, and most of these studies are theoretical discussions. However, there are few case studies on landscape ecology. The main objectives of this paper are to explore a quantitative relationship between Boltzmann entropy and landscape sustainability, to propose a method for evaluating landscape sustainability based on Boltzmann entropy, and to evaluate the sustainability of diverse landscapes in Mizhi County, Shaanxi Province, China. This article uses digital elevation model (DEM) data with a spatial resolution of 30 m in Mizhi County. The remote sensing data on Mizhi County from 2000 were obtained by the Landsat Enhanced Thematic Mapper (ETM) + sensor, and the high-resolution image of Mizhi County from 2015 was obtained by the Gaofen-1 satellite. In this article, the subbasins are taken as the evaluation unit, and the Boltzmann entropy of Mizhi County is calculated based on the experts’ scoring of landscape sustainability in the study area. Through the analysis of landscape sustainability results from 216 subbasins in Mizhi County in 2000 and 2015, the following conclusions are drawn: (1) the evaluation matrix proposed in this paper is effective, and the Boltzmann entropy obtained by this method can directly reflect the level of landscape sustainability; (2) during the research period, the landscape sustainability of Mizhi County showed a good trend overall, especially the three townships of Taozhen, Shadian, and Shigou, which were significantly improved, and these findings were consistent with the field investigation; (3) on the spatial level, the landscape sustainability of mid-eastern Mizhi County is relatively poor compared to that in other regions, but the sustainability is also slowly increasing.
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