Holographic complexity of local quench at finite temperature

This paper is devoted to the study of the evolution of holographic complexity after a local perturbation of the system at finite temperature. We calculate the complexity using both the complexity = action (CA) and the complexity = volume (CV) conjectures. The CV calculation is performed in the small backreaction approximation and the CA one in the probe particle approximation. We find that the CV complexity of the total state shows the unbounded late-time linear growth. The CA computation shows linear growth with fast saturation to a constant value. We estimate the CV and CA complexity linear growth coefficients and show that finite temperature leads to violation of the Lloyd’s bound for CA complexity. Also, it is shown that for the composite subsystem after the local quench, the state with minimal entanglement may correspond to the maximal complexity.