Assuming that heat death or Big Freeze would be the final outcome for the universe, what would happen with energy? According to Big Freeze, the universe will expand forever and it will reach a state of thermodynamical equilibrium. It is said that the temperature of the universe will reach an asymptotically absolute zero value (or alternatively a very close value to zero).
But, as I understand, to reach absolute zero K, one must perform an infinite amount of work. And also, since quantum system have a minimum ground state of energy, how could vacuum go "below" that minimum level and reach absolute zero K? Wouldn't the temperature (and therefore energy density) of the vacuum be constant (reaching the value of the ground state)?
 A: Energy is conserved in a closed system. Expanding universe is not a closed system.
Work is required to pump the heat against the gradient, from a hot to cold object. Thst is not the case with the cooling universe.
Zero temperature would require infinitely expanded universe, which is so large that particles cant interact. Then it will be meaningless to measure temperature.
If a chunk of matter would exist in such a universe, and it will be bound to itself stronger than universe can pull it apart with expansion, then this chunk will over a very long time emit all of its energy as photons. Then particles of this chunk will lower their energy to the same state, and this chunk will behave almost like a single particle.
A: As the universe expands, the energy it contains becomes progressively more dilute, and the differences in temperature between different parts of it (which are required for useful work to be extracted between hotter and colder regions) will become progressively smaller. In this scenario, it is not required for the overall temperature of the universe to hit zero in order for it to become impossible to extract from it the energy required to sustain life.
