Landscape Ecology

, Volume 34, Issue 8, pp 1837–1847 | Cite as

Aggregation-based method for computing absolute Boltzmann entropy of landscape gradient with full thermodynamic consistency

  • Peichao Gao
  • Zhilin LiEmail author
Short Communication



The second law of thermodynamics is a central organizing principle of nature, whose core concept, Boltzmann entropy, is fundamentally important in landscape ecology research. However, the use of this entropy has remained at a conceptual level in landscape ecology for one and a half centuries. It was not until very recently that methods were developed for computing the Boltzmann entropy of landscape gradients and mosaics.


The aim of this study was to examine the computational method (i.e., resampling-based method) for landscape gradients. The first objective was to validate whether the Boltzmann entropy computed using this method was thermodynamically consistent (i.e., consistent with statistical thermodynamics). The second objective was to propose a different method for computing thermodynamically consistent entropy.


A kinetic-theory-based approach was proposed for testing the thermodynamic consistency of entropy. This approach was applied to both relative and absolute Boltzmann entropies by the resampling-based method, revealing that the absolute Boltzmann entropy is only partly consistent. Hypothesis-driven experiments were designed to determine the cause.


The cause was demonstrated to be the generalization technique for generating the macrostate of a landscape gradient, which is called resampling. A different computational method was developed on the basis of an alternative technique (i.e., aggregation).


Validation of its thermodynamic consistency is necessary even if a “thermodynamic” entropy is computed strictly according to the formula. The entropy computed using the aggregation-based method passed the validation and is recommended to be used in linking landscape ecological processes with statistical thermodynamics.


Landscape gradient Landscape entropy Boltzmann entropy Configurational entropy Thermodynamic consistency 



This research was supported by the Research Grants Council of Hong Kong (No. PolyU 152219/18E). The first author is also supported in part by National Natural Science Foundation of China (No. 41771537), National Key Research and Development Plan of China (No. 2017YFB0504102), and the high-performance computing service from the Center for Geodata and Analysis, Faculty of Geographical Science, Beijing Normal University.

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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of Land Surveying and Geo-InformaticsThe Hong Kong Polytechnic UniversityKowloonHong Kong
  2. 2.Faculty of Geographical ScienceBeijing Normal UniversityBeijingChina

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