The field of geography has three unique characteristics, namely, regionality, integration, and complexity. Among them, complexity has become increasingly crucial to geography in the current era. Entropy is a key concept and an indicator of the complexity of a system; thus, the research and application of entropy play a fundamental role in the development of geography. During recent years, Boltzmann entropy (i.e., thermodynamic entropy) has emerged as a research hotspot in the entropy for geography. Proposed as early as the year 1872, it is the core of the well-known Second Law of Thermodynamics. However, its application in geography had remained at a conceptual level for lack of computational methods with spatial data. Fortunately, much progress has been made globally towards computing and applying spatial Boltzmann entropy (i.e., the Boltzmann entropy of spatial data). This paper aims to perform a comprehensive review of such progress, in terms of the thermodynamic origination of Boltzmann entropy, the difficulties in applying it to geography, computational models and algorithms of spatial Boltzmann entropy, and all the applications up to now. Four major conclusions can be drawn as follows: (1) The current focus of research is placed on the Boltzmann entropy of spatial raster data. Models have been developed for computing Boltzmann entropy with both qualitative and quantitative raster data. (2) Many algorithms have been developed and can be classified into three categories, namely total edge-based, Wasserstein distance-based, and multiscale hierarchy-based. (3) It has witnessed two groups of applications of spatial Boltzmann entropy to geography, namely landscape ecology and remote sensing image processing. (4) Future research is recommended to develop algorithms for more types of spatial data, validating previous conclusions drawn using Shannon entropy, and extending the applications of spatial Boltzmann entropy.

The water-food-energy nexus (WFE) plays a key role in achieving sustainable development. In this study, we systematically analyzed the concept of the WFE nexus and review its recent progress. We found that the academic communities have not reached a unanimous understanding of the concept of the WFE nexus and research framework. The evaluation methodology of the WFE nexus presents a transition from the traditional sectoral research paradigm to the human-environment system paradigm that considers the intersection of natural science and social science. These methods can also be grouped into three categories: an evaluation based on a critical process, an evaluation based on the whole system, and a comprehensive evaluation that involves coupling the internal and external elements of the WFE nexus. A bibliometric analysis shows that the number of research papers concerning the WFE nexus increased exponentially during 2000 to 2019, and the increase was particularly significant after 2015. Environmental science, food science, and nutrition science are the three main disciplines in WFE nexus research. More important, we need to strengthen the application of geography thinking, that is, comprehensive and systematic thinking, to study the WFE nexus in the future. Based on the literature review, we found that existing research lacked a quantitative understanding of the mutual feedback among the WFE nexus and its evolution. Therefore, we suggest the following five priority areas for future research: establishing a multi-source database of the WFE nexus, revealing the mutual feedback mechanism of the WFE nexus, developing a coupling model of the WFE nexus, establishing a decision-making platform for the WFE nexus, and promoting the collaboration of multiple sectors related to the WFE nexus. This will help to achieve a synergetic sustainable development of the WFE nexus through system governance and scientific management.