We report on the second installment of an X-ray monitoring project of seven luminous radio-quiet quasars (RQQs). New {sl Chandra} observations of four of these, at $4.10leq zleq4.35$, yield a total of six X-ray epochs, per source, with temporal baselines of $sim850-1600$ days in the rest frame. These data provide the best X-ray light curves for RQQs at $z>4$, to date, enabling qualitative investigations of the X-ray variability behavior of such sources for the first time. On average, these sources follow the trend of decreasing variability amplitude with increasing luminosity, and there is no evidence for X-ray variability increasing toward higher redshifts, in contrast with earlier predictions of potential evolutionary scenarios. An ensemble variability structure function reveals that their variability level remains relatively flat across $approx20 - 1000$ days in the rest frame and it is generally lower than that of three similarly luminous RQQs at $1.33leq zleq 2.74$ over the same temporal range. We discuss possible explanations for the increased variability of the lower-redshift subsample and, in particular, whether higher accretion rates play a leading role. Near-simultaneous optical monitoring of the sources at $4.10leq zleq 4.35$ indicates that none is variable on $approx1$-day timescales, although flux variations of up to $sim25$% are observed on $approx100$-day timescales, typical of RQQs at similar redshifts. Significant optical-X-ray spectral slope variations observed in two of these sources are consistent with the levels observed in luminous RQQs and are dominated by X-ray variations.
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