Is it possible to demolish the wall of the living room to have a double volume ceiling? thanks. Image as shown

Do you mean hack and demolish the ceiling slab in order to obtain a double volume ceiling? It's potentially doable but subject to where the beams and walls of the floor above. Most likely you can do so but it'll mess up your first floor and won't be able to completely obtain a full double volume ceiling over the living room, just a partial one.

Won't be able to tell unless a layout is shared.

normally a proper double volume need to be pre-designed. i.e. the beams would have to be around the double volume area instead of crossing in the middle.

need to open the ceiling and see where are the beams first then only can be sure.