Calculating the Wasserstein Metric-Based Boltzmann Entropy of a Landscape Mosaic

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Sustainable development appears to be the theme of our time. To assess the progress of sustainable development, a simple but comprehensive index is of great use. To this end, a multivariate index of sustainable development was developed in this study based on indicators of the United Nations Sustainable Development Goals (SDGs). To demonstrate the usability of this developed index, we applied it to Fujian Province, China. According to the China SDGs indicators and the Fujian situation, we divided the SDGs into three dimensions and selected indicators based on these dimensions. We calculated the weights and two indices with the entropy weight coefficient method based on collecting and processing of data from 2007 to 2017. We assessed and analyzed the sustainable development of Fujian with two indices and we drew three main conclusions. From 2007 to 2017, the development index of Fujian showed an increasing trend and the coordination index of Fujian showed a fluctuating trend. It is difficult to smoothly improve the coordination index of Fujian because the development speeds of Goal 3 (Good Health and Well-being) and Goal 16 (Peace, Justice, and Strong Institutions) were low. The coordination index of Fujian changed from strong coordination to medium coordination from 2011 to 2012 because the development speed of the environmental dimension suddenly improved. It changed from strong coordination to medium coordination from 2015 to 2016 because the values of the development index of the social dimension were decreasing. To the best of our knowledge, these are the first SDGs-based multivariate indices of sustainable development for a region of China. These indices are applicable to different regions.

Section: Discussionmentioning

confidence: 99%

Use of Entropy in Developing SDG-based Indices for Assessing Regional Sustainable Development: A Provincial Case Study of China

Wang

Gao

Song

et al. 2020

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“…The above limitations confirm that methods on how to derive Boltzmann entropy for spatial data are still an active area of research. Several concepts on how to compute the Boltzmann entropy on landscape patterns were proposed in recent years [ 28 , 29 , 30 , 31 , 32 , 33 ]. However, rarely the results of these methods were compiled and compared.…”

Section: Discussionmentioning

confidence: 99%

“…Fortunately, this step has been taken in recent years. Specifically, methods have been developed for computing the Boltzmann entropy of a landscape pattern represented either using a patch-mosaic model [ 28 , 29 , 30 , 31 ] or a gradient model [ 32 , 33 ], according to a recent review [ 34 ]. However, these methods are much more complicated than that of Shannon entropy in terms of the amount of computation, and they are challenging to implement in practice [ 35 ].…”

Section: Introductionmentioning

confidence: 99%

belg: A Tool for Calculating Boltzmann Entropy of Landscape Gradients

Nowosad

Gao

2020

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Entropy is a fundamental concept in thermodynamics that is important in many fields, including image processing, neurobiology, urban planning, and sustainability. As of recently, the application of Boltzmann entropy for landscape patterns was mostly limited to the conceptual discussion. However, in the last several years, a number of methods for calculating Boltzmann entropy for landscape mosaics and gradients were proposed. We developed an R package belg as an open source tool for calculating Boltzmann entropy of landscape gradients. The package contains functions to calculate relative and absolute Boltzmann entropy using the hierarchy-based and the aggregation-based methods. It also supports input raster with missing (NA) values, allowing for calculations on real data. In this study, we explain ideas behind implemented methods, describe the core functionality of the software, and present three examples of its use. The examples show the basic functions in this package, how to adjust Boltzmann entropy values for data with missing values, and how to use the belg package in larger workflows. We expect that the belg package will be a useful tool in the discussion of using entropy for a description of landscape patterns and facilitate a thermodynamic understanding of landscape dynamics.

“…By extending entropy-based biodiversity and complexity measures into spatially explicit landscapes, the field of landscape ecology has made particular use of entropy methods to describe spatial and topological patterning at different scales. Recent advances in the field have made use of more generalized statistical entropy formulations such as Renyi’s entropy [ 22 ] and generalized Boltzmann entropy for landscape mosaics and landscape gradients [ 23 , 24 ]. See Entropy Special Issue: Entropy in Landscape Ecology for other uses of entropy in this field [ 25 ].…”

Section: Uses Of Entropy In Biologymentioning

confidence: 99%

Use and Abuse of Entropy in Biology: A Case for Caliber

Roach

2020

Here, I discuss entropy and its use as a tool in fields of biology such as bioenergetics, ecology, and evolutionary biology. Statistical entropy concepts including Shannon’s diversity, configurational entropy, and informational entropy are discussed in connection to their use in describing the diversity, heterogeneity, and spatial patterning of biological systems. The use of entropy as a measure of biological complexity is also discussed, and I explore the extension of thermodynamic entropy principles to open, nonequilibrium systems operating in finite time. I conclude with suggestions for use of caliber, a metric similar to entropy but for time-dependent trajectories rather than static distributions, and propose the complementary notion of path information.