  We consider a strongly coupled field theory with a critical point and nonzero
chemical potential at finite temperature, which is dual to an asymptotically
AdS charged black hole. We study the evolution of the rescaled holographic
subregion complexity near and far from the critical point. We explain two
distinct concepts of complexity in this theory and discuss that the state under
study is complex based on how much information is needed to specify the state
and is simple according to how many operations have to be done to reach the
state. It has been reported before that time evolution of holographic subregion
complexity contradicts the second law of complexity in these AdS-Vaidya-like
geometries, but we try to provide a compatible interpretation. We justify
decreasing of complexity using an increasing number of microstates of the mixed
state and speculate about the description of the relative complexity of the
initial state and the final state as a resource. We propose that in this
process complexity of the mixed state decreases and complexity of the
environment increases. We also observe that in this model, the rescaled
holographic subregion complexity is a good observable for probing the dynamical
critical exponent.
