  We study the out-of-equilibrium dynamics of $p$-wave superconducting quantum
wires with long-range interactions, when the chemical potential is linearly
ramped across the topological phase transition. We show that the heat produced
after the quench scales with the quench rate $\delta$ according to the scaling
law $\delta^\theta$, where the exponent $\theta$ depends on the power law
exponent of the long-range interactions. We identify the parameter regimes
where this scaling can be cast in terms of the universal equilibrium critical
exponents and can thus be understood within the Kibble-Zurek framework. When
the electron hopping decays more slowly in space than pairing, it dominates the
equilibrium scaling. Surprisingly, in this regime the dynamical critical
behaviour arises only from paring and, thus, exhibits anomalous dynamical
universality unrelated to equilibrium scaling. The discrepancy from the
expected Kibble-Zurek scenario can be traced back to the presence of multiple
universal terms in the equilibrium scaling functions of long-range interacting
systems close to a second order critical point.
