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Quasi-periodic oscillations (QPOs) have been widely observed in black holeX-ray binaries (BHBs), which often exhibit significant X-ray variations.Extensive research has explored the long-term evolution of the properties ofQPOs in BHBs. In contrast, such evolution in active galactic nuclei (AGNs) hasremained largely unexplored due to limited observational data. By using the 10new XMM-Newton observations for the narrow-line Seyfert 1 galaxy RE J1034+396from publicly available data, we analyze the characteristics of its X-ray QPOsand examine their long-term evolution. The hard-band (1--4 keV) QPOs are foundin all 10 observations and the frequency of these QPOs evolves ranging at$(2.47\text{--}2.83)\times10^{-4}\rm\ Hz$. Furthermore, QPO signals in the soft(0.3--1 keV) and hard bands exhibit strong coherence, although, at times, thevariations in the soft band lead those in the hard band (the hard-lag mode),while at other times, it is the reverse (the soft-lag mode). The observationspresented here serendipitously captured two ongoing lag reversals within abouttwo weeks, which are first seen in RE J1034+396 and also among all AGNs. Atransition in QPO frequency also takes place within a two-week timeframe, twoweeks prior to its corresponding lag reversal, indicating a possible coherencebetween the transitions of QPO frequency and lag mode with delay. The diagramof time lag versus QPO frequency clearly evidences this interconnectedevolution with hysteresis, which is, for the first time, observed among AGNs.

First Observational Evidence for an Interconnected Evolution between Time Lag and QPO Frequency among AGNs