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Entropy 2016, 18(2), 46; doi:10.3390/e18020046

Relative Entropy in Biological Systems

1
Department of Mathematics, University of California, Riverside, CA 92521, USA
2
Centre for Quantum Technologies, National University of Singapore, Singapore 117543, Singapore
3
Department of Physics and Astronomy, University of California, Riverside, CA 92521, USA
*
Authors to whom correspondence should be addressed.
Academic Editor: Kevin H. Knuth
Received: 9 December 2015 / Revised: 18 January 2016 / Accepted: 21 January 2016 / Published: 2 February 2016
(This article belongs to the Special Issue Information and Entropy in Biological Systems)
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Abstract

In this paper we review various information-theoretic characterizations of the approach to equilibrium in biological systems. The replicator equation, evolutionary game theory, Markov processes and chemical reaction networks all describe the dynamics of a population or probability distribution. Under suitable assumptions, the distribution will approach an equilibrium with the passage of time. Relative entropy—that is, the Kullback–Leibler divergence, or various generalizations of this—provides a quantitative measure of how far from equilibrium the system is. We explain various theorems that give conditions under which relative entropy is nonincreasing. In biochemical applications these results can be seen as versions of the Second Law of Thermodynamics, stating that free energy can never increase with the passage of time. In ecological applications, they make precise the notion that a population gains information from its environment as it approaches equilibrium. View Full-Text
Keywords: Second Law; relative entropy; relative information; Kullback–Leibler divergence; free energy; Markov process; reaction network; game theory Second Law; relative entropy; relative information; Kullback–Leibler divergence; free energy; Markov process; reaction network; game theory
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Baez, J.C.; Pollard, B.S. Relative Entropy in Biological Systems. Entropy 2016, 18, 46.

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