Was it established what power source the mine field used in order to be infinitely self-replicating? Could it be something to do with the gravity well of the wormhole?
Each mine contained a replicator unit, so some sort of matter-energy converter tech. Memory Alpha has a lot of info: https://memory-alpha.fandom.com/wiki/Self-replicating_mine
Supposedly, the only time these mines would need a lot of energy would be when they had to replicate - other than that they just needed a little for being in standby mode. When was that the case? When another mine in their proximity had detonated So perhaps they had a mechanism in place that partially harvested the power of the nearby explosion. (Of course for this to be 100% efficient all power would have to be captured, meaning there would be no power "left" to damage the intruder so this system cannot have been 100% efficient by definition, but it might have been possible to reclaim some energy that way). Else than that, yeah, the power of plot/imagination/whatever . Perhaps the blessing of the Emissary helped, too. Or the " Orb of Mines" (an as of yet unknown orb). You name it.
According to the DS9 Technical Manual, the replicator systems of the mines were designed to extract particles from the zero-point vacuum domain to replenish raw material used to make more mines. It doesn't say if the same function was used to charge power cells too, but it wouldn't be far fetched since it was already there.
I gather the replicator, which is good at dereplicating stuff, too, would also be reclaiming materials from whatever it destroyed. Perhaps relatively little energy would be involved in replication that utilized preexisting materials, as opposed to whole-cloth synthesis out of essentially nothing? And perhaps matter typically found in ex-starship debris would be energetic on its own right, allowing for replenishment of not just the mine bodies but their explosive contents as well? Or then replicating energetic materials is no costlier than replicating inert ones, due to the replication principle somehow. This need not be "energy out of nowhere" if it works from the "replicating inert stuff is already energetically expensive" end of things, but it makes things more difficult for our heroes... What is relevant plotwise is that our heroes never worry about this little detail; it's not brought up in the discussion at all! IMHO that rules out exceptional sources of power, or a requirement for those - and/or establishes the replicators as already trivially capable of self-sustaining acts. After all, the use of replicators is the one and only novel thing the heroes ever discuss, and solves all their problems at one stroke. The system would probably have to be a lot more than 100% efficient in order to work in its intended application. The Dominion would inevitably attempt to use "Sperrbrechers", sacrificial bodies that blow holes in the minefield, and could keep on sending thousands if not millions of those into the minefield if need be (sail the whole station into the field, or equip endless cheap rocks with beacons that make them look like targets to the mines and then shove those in). The field would have to remain effective at least for several weeks (Sisko's projected timetable of recapture) and in fact remained so for months (the true outcome). Timo Saloniemi
Solar power, magic mushroom gas, the great space unicorn farting, the great space unicorn farting on the magic mushrooms that are absorbed by the mines in a symbiotic relationship... A replicator generating enough power, requiring nearby material (hydrogen?) is interesting but just how much hydrogen and other particles are available in such a confined space to make it viable. In other words: Solar power, magic mushroom gas, the great space unicorn farting, the great space unicorn farting on the magic mushrooms that are absorbed by the mines in a symbiotic relationship...
Bingo! "By Inferno's Light" it was unheard of for a starship can warp towards a sun but it did??? ENT "Regeneration" there's an alien doctor who figured out a way not to become a Borg something the best scientist still can't figure out close to 300 years in the future??? "JJTrek ST & ID" Scotty can transport Kirk and himself to a starship during warp travel, and Khan energizes a solar system away after an assault on the Starfleet brass??? PIC "The Impossible Box" Picard in the Beta Quadrant was able to transport Soji & himself to Nepenthe as the writers neglect the fact that the universe is expanding??? It's bullshit writing like these I can't take the work or the dilemma seriously because the magic moments are so contrived.