Two Concepts of Holographic Complexity under Thermal and Electromagnetic Quenches

We study the evolution of holographic subregion complexity (HSC) in a thermally and magnetically quenched strongly coupled quantum field theory in 2+1 dimension. We illustrate two concepts of complexity in this theory, (1): how much information it takes to specify a state by studying the behavior of the final value of HSC in terms of the final temperature and magnetic field and (2): how long it takes to reach the state, by considering the time it takes for HSC to relax as a function of the final temperature and magnetic field. In the first concept, we observe that the effect of temperature and magnetic field on HSC is decreasing until the energy of the probe is comparable to the final temperature and magnetic field. We present an argue based on an ensemble of microstates corresponding to a given mixed macrostate. In the second concept, we show that the time of relaxation of HSC decreases with the increase of temperature and magnetic field for fixed value of the energy of the probe. We also compare the time evolution of HSC for two quenches, in the first concept. We observe that the absolute value of the ratio of the final value of HSC for two kinds of quenches depends on the energy of the probe.