New metrics

[Mattehub]

Hi all, I am creating this issues about new metrics in order to list and discuss new information theoretic measures that might be included in the toolbox.

The metrics that we thought can be interesting to add are:

• The O-information gradient of order 2 and higher Tomas Scagliarini, 2023
• The PED Robin A. A. Ince, 2017 and Varley, 2023
• The Varadan's Synergy defined in Varadan, 2006. The name is the one the it is used in this review, Timme, 2014

[Mattehub]

For all these three metrics, the implementation is not very fast and could take some time. The gradient of order 2 and greater probably would be the fastest, I have already the code in Python without JAX, and I could translate it, by the beginning of next week. Something that would be fast adding to the toolbox is for instance the TDMI, information that a multiplet provides about its future.

[EtienneCmb]

Let's focus on the paper right now. We'll see after for the implementation of new metrics. The reason is that each time you add a metric, you need to add tests, examples, documention... BTW, don't forget the example showcasing phired/phisyn