# On the putative essential discreteness of q-generalized entropies

## TL;DR

This paper challenges previous claims that q-generalized entropies are incompatible with continuous Hamiltonian systems, demonstrating that mathematical nuances undermine those arguments and support their applicability.

## Contribution

It provides a critical analysis showing that earlier objections to q-generalized entropies in continuous systems are not conclusive due to overlooked mathematical subtleties.

## Key findings

- Previous arguments against q-entropies in continuous systems are unconvincing.
- Mathematical subtleties can reconcile q-generalized entropies with continuous Hamiltonian systems.
- The scope of non-extensive statistical mechanics remains broader than previously claimed.

## Abstract

It has been argued in [EPL {\bf 90} (2010) 50004], entitled {\it Essential discreteness in generalized thermostatistics with non-logarithmic entropy}, that "continuous Hamiltonian systems with long-range interactions and the so-called q-Gaussian momentum distributions are seen to be outside the scope of non-extensive statistical mechanics". The arguments are clever and appealing. We show here that, however, some mathematical subtleties render them unconvincing