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. 2019 Apr 6;21(4):375. doi: 10.3390/e21040375

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© 2019 by the authors.

Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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Additivity under coarse-graining. If the cost for $Z = (X, Y)$ is the sum of the costs for X and the cost for Y given X, then the cost function is proportional to Shannon entropy.