If we don't assume any new physics and / or thermodynamics, then that constrains the discussion a lot. We have two basic ways of generating a lot of power, fission and fusion.
Fission uses fissile materials, which are relatively rare, not just on Earth, but in the Universe at large. There's plenty enough for us at our current energy generation needs, but not nearly enough for a galaxy spanning civilization. That leaves us with fusion.
Fusion reactors, as currently conceived use Helium-3 or something like that. There's enough of that around the solar system to power a civilization for a long time, even though the mass of oddball elements like Helium-3 make up a very tiny fraction of the total mass of the solar system (which is mostly the Sun with a smidgen of Jupiter).
Most of the solar system's mass is plain hydrogen: one proton and one electron.
Is it possible to fuse most / all of this mass in the solar system? Yes. We won't go into the details, but trying to fuse regular hydrogen (regular protons) together is highly impractical outside of the core of a star. Preferably a red dwarf type star which can more completely burn its fuel than our own Sun will, and live a lot longer to boot (a trillion years vs. ~10 billion for the Sun).
So now we're talking about some kind of solar collectors, and if you want to collect _all_ the energy from a star, you want a sphere of some sort. Or a swarm of objects in orbit achieving the same effect.
Hence Dyson sphere / swarm.