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 Jūbei. 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 plans and 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.
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 Jūbei that Jin will become his greatest enemy. Jūbei 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 -No. 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.
Another example of the Power of Order, is Celica A. Mercury herself, as she was born for the sole purpose of resisting Seithr. The fact that no one else was born with this power after the Dark War, could imply that Seithr was incorporated into the Order, as both humans and the environment had adapted to it.
In BlazBlue: Centralfiction, Tsubaki and Makoto are shown to manifest it as well.