  In different many-body systems, the specific heat shows an anomalous
temperature dependence which signals the onset of phase transitions or
intrinsic features of the excitation spectrum. In a one-dimensional Bose gas,
we reveal an intriguing anomaly, although phase transitions cannot occur and
the microscopic complicated spectrum has not permitted so far a link with the
thermodynamics. We find that the anomaly temperature is ruled by the dark
soliton energy, corresponding to the maximum of the hole-excitation branch in
the spectrum. We rely on Bethe Ansatz to obtain the specific heat exactly and
provide interpretations of the analytically tractable limits. The dynamic
structure factor is computed with the Path Integral Monte Carlo method, gaining
insight into the pattern of the excitations. This allows us to formulate a
microscopic interpretation of the anomaly origin when the quantum and thermal
effects are comparable. We provide indications for future observations and how
the anomaly can be employed for in-situ thermometry and for identifying
different collisional regimes. The dark-soliton anomaly is a quantum simulator
of other anomalies in solid, electronic and spin chain systems.
