Shannon entropy is a measure of disorder. It is a function of a probability distribution without having any physical meaning by itself. And yet, it can give insight into physical processes, in particular when a system is undergoing change. The process of self-organisation is ubiquitous in complex systems. I will give two examples of natural systems which undergo self-organisation: a glass forming material and a differentiating stem cell. The point of transition in each case is detected with tools from information theory.

I will begin with highlighting the importance of disorder and order in the natural dynamics of complex systems and give the basics of information theory needed to follow this talk. I will then explain briefly the experimental set-up for each system before discussing the information theoretic analysis of the data and role of information in the transition from disorder to order.  

The talk is based on the following papers:
1. Ladyman, J., Lambert, J. & Wiesner, K. What is a complex system? European Journal for Philosophy of Science 3, 33–67 (2013), also available at http://philsci-archive.pitt.edu/8496/
2. Dunleavy, A. J., Wiesner, K., Yamamoto, R. & Royall, C. P. Mutual information reveals multiple structural relaxation mechanisms in a model glass former. Nat Commun 6, (2015).
3. Wiesner, K., Teles, J. Hartnor, M., Petersen, C. Hematopoietic stem cells -- Entropic landscape oF differentiation. arXiv:q-bio (November 2017).