Context 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. The difficulty in practically applying this entropy lies in its computation with landscapes, and many solutions have attempted to address this. The latest solution for landscape mosaics is the Wasserstein metric-based method. Objectives The first objective is to provide a clarification of and a correction to the Wasserstein metric-based method. The second is to evaluate the method in terms of thermodynamic consistency using different implementations. Methods Two implementation methods, namely the von Neumann and the Moore neighborhood, were used, which led to two different Wasserstein metric-based entropies. Thermodynamic consistency, the fundamental property of entropy, was used as the evaluation principle. Three criteria (validity, reliability, and ability) were designed in terms of thermodynamic consistency, and corresponding indicators were proposed. Boltzmann entropies computed using all existing methods were used as benchmarks. Results 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. The reasons for both the good and poor performance of the Wasserstein metric-based entropies were identified. Conclusions The Wasserstein metric-based method can be safely used with the von Neumann neighborhood. Compared with the entropies produced by existing methods, the Wasserstein metric-based entropy has worse reliability but better ability (i.e., working range). The most reliable entropy was computed using the total edge-based method.

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基于 Wasserstein 度量的景观马赛克玻尔兹曼熵：对热力学一致性的澄清、校正和评估

上下文玻尔兹曼熵，也称为热力学熵，长期以来一直被提出并最近被重新强调为通过热力学见解深入了解景观动力学的基础。实际应用这种熵的困难在于它对景观的计算，许多解决方案都试图解决这个问题。景观马赛克的最新解决方案是基于 Wasserstein 度量的方法。目标 第一个目标是对基于 Wasserstein 度量的方法进行澄清和修正。第二个是使用不同的实现在热力学一致性方面评估该方法。方法 使用了两种实现方法，即冯诺依曼和摩尔邻域，这导致了两种不同的基于 Wasserstein 度量的熵。热力学一致性，熵的基本性质，被用作评估原则。从热力学一致性方面设计了效度、信度和能力三个标准，并提出了相应的指标。使用所有现有方法计算的玻尔兹曼熵用作基准。结果 计算和研究了针对 100,000 个景观的五个玻尔兹曼熵的三个指标（包括两个基于 Wasserstein 度量和三个使用现有方法）。确定了基于 Wasserstein 度量的熵性能好坏的原因。结论 Wasserstein 基于度量的方法可以安全地用于冯诺依曼邻域。与现有方法产生的熵相比，Wasserstein 基于度量的熵具有更差的可靠性但更好的能力（即 ， 工作范围）。使用基于总边缘的方法计算最可靠的熵。