  The spin-orbit coupling (SOC) in degenerate Fermi gases can fundamentally
change the fate of $s$-wave superfluids with strong Zeeman field and give rise
to topological superfluids and associated Majorana zero modes. It also
dramatically changes the thermodynamic properties of the superfluids. Here we
report the anomalous isothermal compressibility $\kappa_T$ in this superfluids
with both SOC and Zeeman field. We formulate this quantity from the Gibbs-Duhem
equation and show that the contribution of $\kappa_T$ comes from the explicit
contribution of chemical potential and implicit contribution of order
parameter. In the Bardeen-Cooper-Schrieffer (BCS) limit, this compressibility
is determined by the density of state near the Fermi surface; while in the Bose
Einstein condensate (BEC) regime it is determined by the scattering length.
Between these two limits, we find that the anomalous peaks can only be found in
the gapless Weyl phase regime. This anomalous behavior can be regarded as a
remanent effect of phase separation. The similar physics can also be found in
the lattice model away from half filling. These predictions can be measured
from the anomalous response of sound velocity and fluctuation of carrier
density.
