Information geometry of turbulent media

In the talk, we plan to discuss a method of geometrization of statistics on the example of random vectors and its application to turbulent media, by which we understand random vector fields on base manifolds.
We show that this approach gives rise to various geometric structures on the tangent as well as cotangent bundles.
Among these, the most important is the Mahalanobis metric on the tangent bundle, which allows us to obtain all the necessary ingredients for the description of flows in turbulent media.
As an illustration of the method, we consider its applications to flows of real gases based on Maxwell-Boltzmann-Gibbs statistics.