  Bipartite fluctuations can provide interesting information about entanglement
properties and correlations in many-body quantum systems. We address such
fluctuations in relation with the topology of Dirac and Weyl quantum systems,
in situations where the relevant particle number is not conserved, leading to
additional volume laws scaling with the Quantum Fisher information. Through the
example of the $p+ip$ superconductor, we build a relation between charge
fluctuations and the associated winding numbers of Dirac cones in the
low-energy sector. Topological aspects of the Hamiltonian in the vicinity of
these points induce long-range entanglement in real space. We provide a
detailed analysis of such fluctuation properties, including the role of gap
anisotropy, and discuss higher-dimensional Weyl analogues.
