Entropy theory for group actions has been extended beyond the case of amenable groups, with key insights and results initiated by Lewis Bowen and Brandon Seward. We will briefly discuss and put in context some of their definitions, and then proceed to consider negatively curved groups. We will explain a Shannon-Macmillan-Breiman theorem for pointwise convergence of information functions along (almost all almost-) geodesics in the group. We will then define “orbital entropy” using the limits in the SMB theorem, and using an important inequality due to Seward, show that it coincides with Rokhlin entropy.

Based on joint work with F. Pogorzelski (Leipzig University).