Entropy measures the agregate behaviour of many iid copies of a random variable or, more generally, agregate behaviour of trajectories of a stochastic process, which may arise, for example, as a coarse-graining of a deterministic dynamical system.

For a single variable the entropy is the only possible measurement. However, for more complicated configurations of random variables there are other quantities, that depend only on long term behaviour of the variables.

To investigate these other measuremnts we define so called tropical limit of random variables, that consists of many copies of the variables considered on a large scale.

We also hope that understanding tropical limits would allow us to address some classical questions, for example the question about the shape of the entropic cone, information decomposition question, etc.