Weekly update (7/12/2026)

Workshop. This week we held a workshop on non-additive measure and generalized probabilities in physics. Additional information on our website and the recording are available on YouTube. The idea was to have few people so that we could have an in depth discussion about the subject, and it worked really well. Here a few highlights of the discussions from my perspective.

Imprecise probability. For agent information, I think the imprecise probability approach is really much better than Bayesianism, and it definitely marries a lot better with topological ideas, meaning that it can be adapted more easily to work in infinite dimensional cases. The idea is that you don’t model lack of information with a single probability distribution, but with a set of probability distributions. This gives you bounds on probability and expectation, so indeterminacy can be understood as the gap between your lower and upper bound. You can then tell apart when you are indifferent because you are not certain (i.e. you have no preference on any probability distributions) or because you believe the results are interchangeable (i.e. you decide that there is a uniform probability on the outcome). In our framework, we already saw that uncertainty on a parameter/measurement (e.g. the mass of electron) is represented by an open set… so this would simply be a set of probabilities.

Non-additive integral. We still do not know what type of non-additive integral we need to generalize expectation values to all ensemble spaces… but Zuzana Ontkovičová showed that we can characterize properties of the integral and see whether we can limit the scope. This may lead to new directions of attack.

Fraction and Renyi entropy. Alessio Benavoli was able to show that, at least for the classical simplex, there is a simple relationship between the fraction we defined in ensemble spaces and the Renyi entropy. If this relationship holds for the classical continuum and quantum mechanics, the fraction could be understood also as a generalization of the Renyi entropy to all ensemble spaces.

Lie algebras and ensemble spaces. Marcel Reginatto says that, in the context of Ensembles in configuration space, once you fix the type of observables/theory, you can recover the Poisson bracket and commutator from the same basic definition of Poisson structure. I’ll have to look into that more to understand what we can reuse. The main difference is that in their framework the ensembles are only in configuration space (i.e. position) while are ensembles are natively on both conjugate quantities.

And now I’ll have to catch up on all things I am behind… namely, I need to start writing a paper on the nature of quantum states that start stringing together all the preliminary result from Reverse Physics on quantum mechanics…