Acta Geographica Sinica ›› 2021, Vol. 76 ›› Issue (7): 1579-1590.doi: 10.11821/dlxb202107001

• Review Articles •     Next Articles

The review and applications of spatial Boltzmann entropy

GAO Peichao1,2,3(), CHENG Changxiu3,4(), YE Sijing3, SHEN Shi3, ZHANG Hong5,6   

  1. 1. State Key Laboratory of Earth Surface Processes and Resource Ecology, Beijing Normal University, Beijing 100875, China
    2. Department of Land Surveying and Geo-Informatics, The Hong Kong Polytechnic University, Hong Kong 999077, China
    3. Center for Geodata and Analysis, Faculty of Geographical Science, Beijing Normal University, Beijing 100875, China
    4. National Tibetan Plateau Data Center, Beijing 100101, China
    5. School of Urban & Regional Science, East China Normal University, Shanghai 210046, China
    6. Faculty of Geosciences & Environmental Engineering, Southwest Jiaotong University, Chengdu 611756, China
  • Received:2020-03-31 Revised:2021-03-25 Online:2021-07-25 Published:2021-09-25
  • Contact: CHENG Changxiu;
  • Supported by:
    Second Tibetan Plateau Scientific Expedition and Research Program(2019QZKK0608);Research Grants Council of Hong Kong(152219/18E);National Natural Science Foundation of China(41901316);Key Research and Development Program of Chengdu(2019-YF05-02119-SN);State Key Laboratory of Earth Surface Processes and Resource Ecology(2020-KF-03);Fundamental Research Funds for the Central Universities(2019NTST02)


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.

Key words: spatial data, Boltzmann entropy, Shannon entropy, spatial information theory, landscape ecology, reginal sustainability