Isolated brains could randomly fluctuate into existence: Imagine you're an isolated brain floating lonely through the vast expanse of the Universe with all your thoughts and perceptions just figments of your imagination. There'd even be a name for you: you'd be a Boltzmann brain. Boltzmann brains are of interest to physicists, in particular to cosmologists. The idea is that, according to quantum mechanics, there is energy in empty space which can fluctuate, producing particles as it does so.
Physicists have dreamed up some bizarre ideas over the years, but a decade or so ago they outdid themselves with the concept of Boltzmann brains – fully formed, conscious entities that form spontaneously in outer space.