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Open AccessReview

Relative Entropy in Biological Systems

by John C. Baez 1,2,* and Blake S. Pollard 3,*
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
Entropy 2016, 18(2), 46; https://doi.org/10.3390/e18020046
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)
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
MDPI and ACS Style

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

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