In this physics thought experiment, a Boltzmann brain is a fully formed brain, complete with memories of a full human life in our universe, that arises due to extremely rare random fluctuations out of a state of thermodynamic equilibrium. Theoretically, over an extremely large but not infinite amount of time, by sheer chance, atoms in a void could spontaneously come together in such a way as to assemble a functioning human brain. Like any brain in such circumstances (the hostile vacuum of space with no blood supply or body), it would almost immediately stop functioning and begin to deteriorate.
By one calculation, a Boltzmann brain would appear as a quantum fluctuation in the vacuum after a time interval of 10^10^50 years. This fluctuation can occur even in a true Minkowski vacuum (a flat spacetime vacuum lacking vacuum energy). Quantum mechanics heavily favors smaller fluctuations that "borrow" the least amount of energy from the vacuum. Typically, a quantum Boltzmann brain would suddenly appear from the vacuum (alongside an equivalent amount of virtual antimatter), remain only long enough to have a single coherent thought or observation, and then disappear into the vacuum as suddenly as it appeared. Such a brain is completely self-contained, and can never radiate energy out to infinity.
Sources:
https://en.wikipedia.org/wiki/Timeline_of_the_far_future https://en.wikipedia.org/wiki/Boltzmann_brain