On observability of Renyi's entropy

TL;DR

This paper demonstrates that Renyi's entropy is an observable quantity, addressing previous claims of instability by showing these issues are negligible or correctable, thus confirming its practical measurability.

Contribution

It refutes the belief that Renyi's entropy is unobservable by proving its stability and measurability in various systems, including fractals and continuous distributions.

Findings

The domain of instability has zero measure under Bhattacharyya measure.

Instabilities can be mitigated through coarse graining in measurements.

Renyi's entropy is observable in fractal and continuous systems.

Abstract

Despite recent claims we argue that Renyi's entropy is an observable quantity. It is shown that, contrary to popular belief, the reported domain of instability for Renyi entropies has zero measure (Bhattacharyya measure). In addition, we show the instabilities can be easily emended by introducing a coarse graining into an actual measurement. We also clear up doubts regarding the observability of Renyi's entropy in (multi--)fractal systems and in systems with absolutely continuous PDF's.