If this sounds complicated, it really isn't because these kind of concepts have been spoon fed to geeks since time memorial. If you're not a hardcore geek with a background in Star Trek or Doctor Who, this will probably confuse the hell out of you but then why are you reading indie fantasy/scifi to begin with?
On the City side of things, there is protagonist Theosophy who is one of the protectors of an academy-run dictatorship in a state of constant war as well as resource conservation. Theosophy is their best warrior but she's reckless and insubordinate (when are the best warriors not?). After trying to rescue one of the last remaining members of a blood (apparently incest is a problem here too), she ends up dumped in the village of Briony.
Briony is a woman who longs deeply for the opportunity to escape the dangerous village she lives in and seek refuge in the Academy (not the City but of a similar bent). To not put too fine a point on it but Briony is Belle from Disney Beauty and the Beast's pre-Beast. She's far too intelligent for her rural bumpkin associates and every reasonable suggestion she makes is shot down by her idiot companions.
A chance encounter in the woods convinces Briony that Theosophy is a spirit and inspires her the ambition that she can bring the "heroic" warriors of the City to her homeland to fight the monsters. Theosophy is interested in this idea, too, because the City is a urban hellscape that isn't really conducive to survival. Everything completely falls apart from this but the road to hell is paved in quantum physics.
I, more or less, enjoyed City of Hope and Ruin from start to finish. This is due to Briony and Theosophy's likable personalities that contrast well without making either woman weak. The setting idea and physics was enjoyable as is the action. I think the descriptions could have used a bit of work since I never got a feel for the city or farming communities beyond their basic generalities.
The contrast between the City and country's cultures are another element which makes it unique. The City's residents are hardened beyond belief and willing to do anything to survive but also highly educated. The country is superstitious and determined to stand their ground even if it means annihilation. In many ways, both women would be more at home in the other's world.
It should be noted Theosophy is a lesbian heroine and Briony is either bisexual or lesbian herself. This is something which should appeal to fans looking for better representation in media. The budding relationship between the two has a decent foundation but I didn't actually buy it at the end because it seemed to go from attraction to love a bit too quickly.
In conclusion, I recommend this book with the qualification it could have used a bit more background and description to establish things.