Thermodynamic Consistency of the Cushman Method of Computing the Configurational Entropy of a Landscape Lattice

There has been a recent surge of interest in theory and methods for calculating the entropy of landscape patterns, but relatively little is known about the thermodynamic consistency of these approaches. I posit that for any of these methods to be fully thermodynamically consistent, they must meet th...

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Autor principal:	Samuel A. Cushman
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	entropy Boltzmann configuration landscape Cushman method Science Q Astrophysics QB460-466 Physics QC1-999
Acceso en línea:	https://doaj.org/article/329e5019332c4d65839694aa3dd4e2fb
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spelling	oai:doaj.org-article:329e5019332c4d65839694aa3dd4e2fb2021-11-25T17:29:31ZThermodynamic Consistency of the Cushman Method of Computing the Configurational Entropy of a Landscape Lattice10.3390/e231114201099-4300https://doaj.org/article/329e5019332c4d65839694aa3dd4e2fb2021-10-01T00:00:00Zhttps://www.mdpi.com/1099-4300/23/11/1420https://doaj.org/toc/1099-4300There has been a recent surge of interest in theory and methods for calculating the entropy of landscape patterns, but relatively little is known about the thermodynamic consistency of these approaches. I posit that for any of these methods to be fully thermodynamically consistent, they must meet three conditions. First, the computed entropies must lie along the theoretical distribution of entropies as a function of total edge length, which Cushman showed was a parabolic function following from the fact that there is a normal distribution of permuted edge lengths, the entropy is the logarithm of the number of microstates in a macrostate, and the logarithm of a normal distribution is a parabolic function. Second, the entropy must increase over time through the period of the random mixing simulation, following the expectation that entropy increases in a closed system. Third, at full mixing, the entropy will fluctuate randomly around the maximum theoretical value, associated with a perfectly random arrangement of the lattice. I evaluated these criteria in a test condition involving a binary, two-class landscape using the Cushman method of directly applying the Boltzmann relation (s = klogW) to permuted landscape configurations and measuring the distribution of total edge length. The results show that the Cushman method directly applying the classical Boltzmann relation is fully consistent with these criteria and therefore fully thermodynamically consistent. I suggest that this method, which is a direct application of the classical and iconic formulation of Boltzmann, has advantages given its direct interpretability, theoretical elegance, and thermodynamic consistency.Samuel A. CushmanMDPI AGarticleentropyBoltzmannconfigurationlandscapeCushman methodScienceQAstrophysicsQB460-466PhysicsQC1-999ENEntropy, Vol 23, Iss 1420, p 1420 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	entropy Boltzmann configuration landscape Cushman method Science Q Astrophysics QB460-466 Physics QC1-999
spellingShingle	entropy Boltzmann configuration landscape Cushman method Science Q Astrophysics QB460-466 Physics QC1-999 Samuel A. Cushman Thermodynamic Consistency of the Cushman Method of Computing the Configurational Entropy of a Landscape Lattice
description	There has been a recent surge of interest in theory and methods for calculating the entropy of landscape patterns, but relatively little is known about the thermodynamic consistency of these approaches. I posit that for any of these methods to be fully thermodynamically consistent, they must meet three conditions. First, the computed entropies must lie along the theoretical distribution of entropies as a function of total edge length, which Cushman showed was a parabolic function following from the fact that there is a normal distribution of permuted edge lengths, the entropy is the logarithm of the number of microstates in a macrostate, and the logarithm of a normal distribution is a parabolic function. Second, the entropy must increase over time through the period of the random mixing simulation, following the expectation that entropy increases in a closed system. Third, at full mixing, the entropy will fluctuate randomly around the maximum theoretical value, associated with a perfectly random arrangement of the lattice. I evaluated these criteria in a test condition involving a binary, two-class landscape using the Cushman method of directly applying the Boltzmann relation (s = klogW) to permuted landscape configurations and measuring the distribution of total edge length. The results show that the Cushman method directly applying the classical Boltzmann relation is fully consistent with these criteria and therefore fully thermodynamically consistent. I suggest that this method, which is a direct application of the classical and iconic formulation of Boltzmann, has advantages given its direct interpretability, theoretical elegance, and thermodynamic consistency.
format	article
author	Samuel A. Cushman
author_facet	Samuel A. Cushman
author_sort	Samuel A. Cushman
title	Thermodynamic Consistency of the Cushman Method of Computing the Configurational Entropy of a Landscape Lattice
title_short	Thermodynamic Consistency of the Cushman Method of Computing the Configurational Entropy of a Landscape Lattice
title_full	Thermodynamic Consistency of the Cushman Method of Computing the Configurational Entropy of a Landscape Lattice
title_fullStr	Thermodynamic Consistency of the Cushman Method of Computing the Configurational Entropy of a Landscape Lattice
title_full_unstemmed	Thermodynamic Consistency of the Cushman Method of Computing the Configurational Entropy of a Landscape Lattice
title_sort	thermodynamic consistency of the cushman method of computing the configurational entropy of a landscape lattice
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/329e5019332c4d65839694aa3dd4e2fb
work_keys_str_mv	AT samuelacushman thermodynamicconsistencyofthecushmanmethodofcomputingtheconfigurationalentropyofalandscapelattice
_version_	1718412276655980544

Thermodynamic Consistency of the Cushman Method of Computing the Configurational Entropy of a Landscape Lattice

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