calculating absolute entropy using the boltzmann hypothesis

Simpson EH (1949) Measurement of diversity. Cartogr Int J Geogr Inf Geovisualization 31(1):26–34 Neumann J (1994) The topological information content of a map an attempt at a rehabilitation of information theory in cartography.

Li ZL, Huang PZ (2002) Quantitative measures for spatial information of maps. Acta Geod Et Cartogr Sinica 45(7):757–767 Li Z, Liu Q, Gao P (2016) Entropy-based cartographic communication models:evolution from special to general cartographic information theory. Li H, Reynolds JF (1993) A new contagion index to quantify spatial patterns of landscapes.

Leibovici DG, Claramunt C, Le Guyader D, Brosset D (2014) Local and global spatio-temporal entropy indices based on distance-ratios and co-occurrences distributions. Leibovici DG, Birkin MH (2015) On geocomputational determinants of entropic variations for urban dynamics studies. Leibovici DG (2009) Defining spatial entropy from multivariate distributions of co-occurrences. Foundations of geographic information science. Goodchild MF (2003) The nature and value of geographic information. Gatrell AC (1977) Complexity and redundancy in binary maps. Gao P, Zhang H, Li Z (2017) A hierarchy-based solution to calculate the configurational entropy of landscape gradients. ISPRS J Photogramm Remote Sens 50(5):2–12 Phys Rev E 67(5):051104įoody GM (1995) Cross-entropy for the evaluation of the accuracy of a fuzzy land cover classification with fuzzy ground data. Springer, New Yorkįeldman DP, Crutchfield JP (2003) Structural information in two-dimensional patterns: entropy convergence and excess entropy. Landscape Urban Plan 153:149–159ĭeza E, Deza MM (2016) Encyclopedia of distances. ĭíaz-Varela E, Roces-Díaz JV, Álvarez álvarez P (2016) Detection of landscape heterogeneity at multiple scales: use of the quadratic entropy index. Landscape Ecol 31(3):481–489Ĭushman SA (2018) Calculation of configurational entropy in complex landscapes. Landscape Ecol 30(1):7–10Ĭushman SA (2016) Calculating the configurational entropy of a landscape mosaic. Academic Press, New YorkĬushman SA (2015) Thermodynamics in landscape ecology: the importance of integrating measurement and modeling of landscape entropy. Am Cartogr 23(2):78–95īogaert J, Farina A, Ceulemans R (2005) Entropy increase of fragmented habitats: A sign of human impact? Ecol Indic 5(3):207–212īrillouin L (1956) Science and information theory. Geogr Anal 8(1):1–21ījoke JT (1996) Framework for entropy-based map evaluation. Our results show that the Wasserstein metric is suitable to capture the discrepancy using complex landscape mosaic data sets, which provides a numerically efficient approximation for the similarity in the histograms, reducing excessive expansion of the calculated result.īatty M (1976) Entropy in spatial aggregation. By calculating several spatial scale landscapes, we found that relative entropy can be a trade-off between the rationality of results and the cost of calculation. The calculation and simulation showed that the purposed metric captured disorder in the spatial landscape, and the result was consistent with the general configurational entropy.

We proposed a relative entropy using histograms to compare two ecosystems with the Wasserstein metric, and used six digital elevation models and five simulated data to calculate the entropy of the complex ecosystems. To calculate the spatial configurational entropy of a landscape mosaic based on a statistical metric. However, as the number of configuration combinations increases, configurational entropy becomes too complex to calculate, and its value is too large to be accurately represented in practical applications. Configurational entropy has received more attention because it better reflects the thermodynamic properties of physical and biological processes. Entropy is an important concept traditionally associated with thermodynamics and is widely used to describe the degree of disorder in a substance, system, or process.

Calculating absolute entropy using the boltzmann hypothesis