Legendre transformation and information geometry for the maximum entropy theory of ecology

Pedro Pessoa

doi:10.3390/psf2021003001

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arXiv · 2103.11230

Legendre transformation and information geometry for the maximum entropy theory of ecology

Pedro Pessoa

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Abstract

Here I investigate some mathematical aspects of the maximum entropy theory of ecology (METE). In particular I address the geometrical structure of METE endowed by information geometry. As novel results, the macrostate entropy is calculated analytically by the Legendre transformation of the log-normalizer in METE. This result allows for the calculation of the metric terms in the information geometry arising from METE and, by consequence, the covariance matrix between METE variables.

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Pedro Pessoa. 2021-03-20. Legendre transformation and information geometry for the maximum entropy theory of ecology. https://doi.org/10.3390/psf2021003001

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