Geometry of information: Classical and quantum aspects

In this article, we describe various aspects of categorification of the structures, appearing in information theory. These aspects include probabilistic models both of classical and quantum physics, emergence of F–manifolds, and motivic enrichments. ; © 2021 Published by Elsevier B.V. Received 27 April 2021, Revised 17 August 2021, Accepted 19 October 2021, Available online 27 October 2021. N. C. Combe acknowledges support from the Minerva Fast track grant from the Max Planck Institute for Mathematics in the Sciences, in Leipzig. M. Marcolli acknowledges support from NSF grants DMS-1707882 and DMS-2104330. The authors of this paper thank the reviewer for suggesting interesting questions related to this work. The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ; Submitted - 2107.08006.pdf