### Functional Equations IX: Entropy on a Metric Space

#### Posted by Tom Leinster

Yesterday’s functional equations class can be described in two ways:

From a mathematical point of view, I gave a definition of the entropy of a probability distribution on a metric space. The high point was a newish maximum entropy theorem (joint work with Mark Meckes).

From a biological point of view, it was all about measuring the diversity of a community in a way that factors in the varying similarity between species. This approach is well-adapted to situations where there’s no clear division into “species” — for instance, communities of microbes. It also addresses a point made yesterday on this blog. All this is based on joint work with Christina Cobbold.

You can read the notes from yesterday’s class on pages 35–38 here.

Posted at April 5, 2017 12:38 PM UTC