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While the other answers are great and focus on tangible assets of the world, I'll try and find an answer that focuses instead on stylistic elements. I would say that a good way to get across apathy...
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Source: https://writers.stackexchange.com/a/45692 License name: CC BY-SA 3.0 License URL: https://creativecommons.org/licenses/by-sa/3.0/
#2: Initial revision
While the other answers are great and focus on tangible assets of the world, I'll try and find an answer that focuses instead on stylistic elements. I would say that a good way to get across apathy and an inorganic, unfeeling world would be to describe things in a cold, technical, repetitive and clinical manner. Eschew any flowery language when describing the architecture and surroundings, contrasting this with, say, how the narration describes their allies (if narration is associated with a character) or the heroes (if omniscient/detached). For example, imagine we have a dingy undercity that's topped with affluent skyscrapers, we could use the aforementioned clinical style to render something like this: _The cleaning droids never reached the bottom of JunCorptropolis. The upper levels teemed with hygenic towers and hygenic cyborgs, the trust fund babies of CEOs. The toxic waste and grime, like most things, flowed downwards. The upper city did not seem to care about the structural unsoundness of its foundations._ Contrast this with, say, a rebel cubby-hole filled with friends of the protag: _Waylan entered the hideout to find what remained of the Undercity Banditos. Each of them styled themselves as though they were a canvas; colourful hair and tattoos were the order of the day. Fixing his tie, Waylan felt a tad overdressed. He took a seat on the makeshift couch and slipped off his jacket, when a smooth-skinned, pierced young woman spoke._ _'So, how'd the undercover mission go?'_ This will give a clear divide between the organic, passionate cause of the people you want the reader to relate to, compared to the apathetic world that obviously needs to be changed.