So no heat death, but every computation implies an energy loss, right ?
Even with the help of gravity, how do you prevent energy from escaping in EM form ? Even a black hole evaporate if I recall correctly.
So I can imagine we could live a loooong time, but indefinitely ? That sounds too good to be true to me, but I don't know much about the physic involved.
Unfortunately even if that is true, there is something called as entropy at play here.
Also I would advice you to read Isaac Asimov's "The last question" once. One thing discussed in that book is how quickly human kind or an intelligent being can grow in population and energy consumption.
So even before we reach the point of heat death, if we survive and move out to do the heavens. Then over time, we are likely to run out of resources and space eventually- may be even long before the heat death of the universe itself.