What about the second law of thermodynamics?
First of all, the second law of thermodynamics says nothing about the possibility to live 1 billion years. Our huge Universe has enough amount of energy and negentropy to allow us live 1 billion years which is much better than just 100 years.
Moreove, our Universe isn't doomed to become unsuitable for life even after some huge number of years.
1) We don't really know much about our universe to speak confidently about it's fate. Attempts to invent the fate of the universe are like attempts by physicists of the past centuries to extrapolate Newtonian mechanics to all phenomena of nature without exception. It turned out that there are also wave functions and Schroedinger's equation, general relativity theory, the effects of which can not be ignored when we go drastically beyond the usual experiments available in the 16th century. Now physics is still extremely far from its full completion. Questions about the fate of the universe still radically go beyond the limits of experiments available by the beginning of the 21st century.
The current set of experimental observations is satisfied by an infinite number of different physical theories. All these theories give almost identical predictions when we put experiments that are not too different from those we put earlier, and therefore in such cases for convenience we can use the simplest theory from this infinite set of theories.
The question of the fate of the Universe sharply goes beyond the limits of any experiments we have conducted so far.
Different physical theories give very diverse answers to the question of the fate of the universe.
2) The very notion of "time" at the level of fundamental physics isn't intuitive and it doesn't even always has a clear physical meaning. Modern experimental observations do not contradict the possibility to turn off part of the universe from the general flow of time, or to create time machines.
3) The "second law of thermodynamics", which is inappropriately tied to cosmological models, is valid (hello, cap!) just for thermodynamics which doesn't include either gravity or quantum effects. Moreover, the second law of thermodynamics, like all thermodynamics, is applicable to systems in a state of (quasi) equilibrium, and the universe is not in this state, to put it mildly. Nonstationary systems are subject of study of physical kinetics. For example, cyclic non-stationary gravitating universe exists forever despite of second law of thermodynamics. Moreover, in order to prove the second law of thermodynamics, even for some complex systems of classical mechanics, one must prove its applicability specifically, proving in particular the ergodic hypothesis (which is hard to impossible to prove for any real processes). Also, the second law is applicable to isolated systems, and the isolation of the universe is in question, and certainly is not proven by anyone.
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The most that can now be said about the fate of the universe is:
May be, the universe is doomed to become uninhabitable. And maybe it's not doomed. There is no particularly serious evidence in favor of one of these options.