The Power of Order (秩序の力, Chitsujo no Chikara) is a somewhat unclear ability. It is mentioned several times in the series. According to Kokonoe, it comes from the ability to hold true to one's convictions no matter what. Ones with the power of order can also sense phenomenon intervention. According to Rachel Alucard, Noel Vermillion is but one of the few people that can nullify the power of order. As of now, it is known to give the bearer the ability to destroy phenomena and resist phenomena intervention, very powerful as it allowed Jin Kisaragi to overcome Yukianesa's influence and increased his power enough to force Hazama to retreat from their battle. In Hakumen's case, it allowed him to survive within the Boundary for 100 years, while the experience heavily damaged Hakumen's memories and existence, also cutting his power to 20%, he managed to remain as a person in during all that time in the same place that turned Arakune into his current form when he just came in contact with it. It also may be the reason why its bearers have animosity towards sources of phenomena intervention such as the Black Beast and the Murakumo Units (and by extension: Ragna and Noel respectively), making Hakumen and Jin hostile towards them.
Jin, however, remains unaware of this power until Ragna tells him what he knows about it from a previous conversation with Jubei. It is stated that this power remains dormant in him, it is possible that Yukianesa acts like a seal or limiter on Jin's Power of Order as shown of how stronger he became when he could control the sword or that the weapon itself is needed to for some reason to fully access the Power, justifying Jin's fixation to keep using Yukianesa as his weapon of choice despite knowing the blade is influencing him and having some sort of conflict with it and taking in count it was a gift from Saya, Jin's sister whom he despises, making it even stranger that Jin decides to keep using it as his main weapon, a gift that not only puts a heavy emotional strain on him but is also something given to him by a person he hates.
Hazama is shown to have known about this power for quite some time. But his second encounter with Jin further implies that Jin's power of order is unique in a sense: by that point he already knew about the power, as he already had said several times Jin was useful because his power of order was convenient for a while, had faced Hakumen and won and had also seen every possibility in the world, despite all that he is caught off by surprise in his second fight with Jin in Continuum Shift, being badly defeated before he decides to flee, impressed and amused of how strong the Power of Order can be, all this while declaring that he would have lost the fight had it gone on and with Kokonoe (who ordered Tager to stop Jin, giving Hazama his chance to escape) saying that Hazama had just realized the full potential of the power of order and just now could develop some kind of counter measure. Given Hazama's cunning plans and genius strategies it was extremely unlikely for him to be caught off guard like this, furthering the idea that Jin's power is unique or potentially stronger than Hakumen's, something never seen before, unique to the Jin Kisaragi of the current timeline.
Another possible proof of it is that Hakumen, while still was Jin Kisaragi, was considerably weaker than Ragna, while the present timeline Jin, while still weaker than his brother, is capable of holding a fight,hurting him and even tiring him out before being defeated. The other hint given for this idea of Jin having a different power is that Hakumen's relationship with Saya in his childhood was good, the brothers loved each other, while Jin hated his own sister for some reason or at least started to at some point.
The Power of Order may also be linked to Jin's emotional state or even his sanity, as seen during the events of Calamity Trigger and Continuum Shift; during the Ikaruga War the NOL itself faced some troubles with the war, yet Jin was strong enough to subdue the nation in two days by himself, but after that and his personality change his power seems to have gotten weaker as he was being easily defeated by Noel in Calamity Trigger before he went to face Ragna and how even Tsubaki herself was shocked to find out she had actually defeated Jin in a fight during her story mode in Continuum Shift. However when Jin finally got grip of his senses and could overcome his obsessions he became strong enough to defeat Tsubaki, dispel Phantom's field and then track down Hazama and get the upper hand. After this during his fight with Mu-12 he was classified in the same threat rank as Hakumen (SS) who a while before had easily defeated Jin as well, hinting that the episode with Tsubaki that made him get his objectives clear indeed made him stronger just by harmonizing his emotions.
Jin has been referred to as the world's "antibody" that will cure the "darkness" that Ragna is; from this statement it can be presumed that the Power of Order is an opposite element to the destructive nature of the Black Beast's darkness or Ragna's power to change the world. This is the reason why Ragna is told by Jubei that Jin will become his greatest enemy. Jubei also said that the Power of Order is neither good or bad, only a force that will oppose Ragna's already great power in order to maintain balance in the world. Rachel also states that this power seeks to keep the world stable but in a way that seems negative, while Mu-12 refers to Jin as the "Endbringer", what makes even more unlikely that the Power of Order is good in nature and is rather just a tool to be used by Jin as how he sees fit, even Ragna points out that they should not act by their given roles but as who they wish to be and the way they want to.