Gao PC, Li ZL (2019b) Computation of the Boltzmann entropy of a landscape: a review and a generalization. Gao PC, Li ZL (2019a) Aggregation-based method for computing absolute Boltzmann entropy of landscape gradient with full thermodynamic consistency. Wiley, New Yorkįrazier AE (2019) Emerging trajectories for spatial pattern analysis in landscape ecology. Cambridge University Press, Cambridgeįorman RTT, Godron M (1986) Landscape ecology. Proc R Soc Lond 113(765):621–641įorman RTT (1995) Land mosaics: the ecology of landscapes and regions. Springer, Tokyo, Japanĭenbigh K (1981) How subjective is entropy? Chem Br 17:168–185ĭirac PAM (1927) The physical interpretation of the quantum dynamics. In: Cushman SA and Huettmann F (eds) Spatial complexity, informatics, and wildlife conservation. Entropy 20(4):298Ĭushman SA, Evans JS, McGarigal K (2010) Landscape ecology: past, present, and future. Landsc Ecol 31(3):481–489Ĭushman SA (2018) Calculation of configurational entropy in complex landscapes. Landsc Ecol 30(1):7–10Ĭushman SA (2016) Calculating the configurational entropy of a landscape mosaic. Ann Phys 79(4):368–397Ĭostanza JK, Riitters K, Vogt P, Wickham J (2019) Describing and analyzing landscape patterns: where are we now, and where are we going? Landsc Ecol 34(9):2049–2055Ĭushman SA (2015) Thermodynamics in landscape ecology: the importance of integrating measurement and modeling of landscape entropy. Landsc Ecol 11(5):257–266Ĭlausius R (1850) Über die bewegende Kraft der Wärme und die Gesetze, welche sich daraus für die Wärmelehre selbst ableiten lassen. Discret Dyn Nat Soc 2016:4863907Ĭhildress WM, Rykiel EJ, Forsythe W, Li BL, Wu H-i (1996) Transition rule complexity in grid-based automata models. Phys A 391(3):767–778Ĭhen YG, Wang JJ (2016) Describing urban evolution with the fractal parameters based on area-perimeter allometry. Sitzungsberichte Akademie der Wissenschaften 66:275–370Ĭhen YG (2012) The rank-size scaling law and entropy-maximizing principle. Geogr Anal 42(4):395–421īoltzmann L (1872) Weitere Studien über das Wärmegleichgewicht unter Gasmolekülen. The most reliable entropy was computed using the total edge-based method.īatty M (2010) Space, scale, and scaling in entropy maximizing. Compared with the entropies produced by existing methods, the Wasserstein metric-based entropy has worse reliability but better ability (i.e., working range). The Wasserstein metric-based method can be safely used with the von Neumann neighborhood. The reasons for both the good and poor performance of the Wasserstein metric-based entropies were identified. The three indicators of the five Boltzmann entropies (including two based on the Wasserstein metric and three using existing methods) against 100,000 landscapes were computed and investigated. Boltzmann entropies computed using all existing methods were used as benchmarks. Three criteria (validity, reliability, and ability) were designed in terms of thermodynamic consistency, and corresponding indicators were proposed. Thermodynamic consistency, the fundamental property of entropy, was used as the evaluation principle. Two implementation methods, namely the von Neumann and the Moore neighborhood, were used, which led to two different Wasserstein metric-based entropies. The second is to evaluate the method in terms of thermodynamic consistency using different implementations. The first objective is to provide a clarification of and a correction to the Wasserstein metric-based method. The latest solution for landscape mosaics is the Wasserstein metric-based method. The difficulty in practically applying this entropy lies in its computation with landscapes, and many solutions have attempted to address this. Boltzmann entropy, also called thermodynamic entropy, has long been suggested and recently reemphasized as a basis for achieving a profound understanding of landscape dynamics with thermodynamic insights.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |