  We present evidences for the connection between the potential of different
fields and complexity growth rates both in conformal and confining cases. By
studying different models, we also establish a strong connection between phase
transitions and the discontinuities in the complexity growth rates. In the
first example, for the dyonic black holes which are dual to van der Waals
fluids, we find a similar first order phase transition in the behavior of
complexity growth rate. We then compare the Schwinger effect and also the
behavior of complexity in the AdS and AdS soliton backgrounds and comment on
the connection between them. Finally, in a general Gubser model of QCD, we
present the connections between the potentials, entropies, speed of sounds and
complexity growth rates during crossover, first and second order phase
transitions and also the behavior of quasinormal modes.
