# Entropy increase and information loss in Markov models of evolution

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## Abstract

Markov models of evolution describe changes in the probability distribution of the trait values a population might exhibit. In consequence, they also describe how entropy and conditional entropy values evolve, and how the mutual information that characterizes the relation between an earlier and a later moment in a lineage’s history depends on how much time separates them. These models therefore provide an interesting perspective on questions that usually are considered in the foundations of physics—when and why does entropy increase and at what rates do changes in entropy take place? They also throw light on an important epistemological question: are there limits on what your observations of the present can tell you about the evolutionary past?

### Keywords

Entropy Evolution Markov model Mutual information## Notes

### Acknowledgments

We thank the editor and referee for useful suggestions. ES thanks the William F. Vilas Trust of the University of Wisconsin-Madison for financial support and MS thanks the Royal Society of New Zealand for funding under its James Cook Fellowship scheme.

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