Shannon entropy is a powerful concept. But what properties single out Shannon entropy as special? Instead of focusing on the entropy of a probability measure on a finite set, it can help to focus on the “information loss”, or change in entropy, associated with a measure-preserving function. Shannon entropy then gives the only concept of information loss that is functorial, convex-linear and continuous. This is joint work with Tom Leinster and Tobias Fritz.
You can see the slides now, here. I talk a bit about all these papers:
• John Baez, Tobias Fritz and Tom Leinster, A characterization of entropy in terms of information loss, 2011.
• Tom Leinster, An operadic introduction to entropy, 2011.
• John Baez and Tobias Fritz, A Bayesian characterization of relative entropy, 2014.
• Tom Leinster, A short characterization of relative entropy, 2017.
• Nicolas Gagné and Prakash Panangaden, A categorical characterization of relative entropy on standard Borel spaces, 2017.
• Tom Leinster, Entropy and Diversity: the Axiomatic Approach, 2020.
• Arthur Parzygnat, A functorial characterization of von Neumann entropy, 2020.
• Arthur Parzygnat, Towards a functorial description of quantum relative entropy, 2021.
• Tai-Danae Bradley, Entropy as a topological operad derivation, 2021.