Although it is now generally accepted by physicists working on quantum information theory and quantum thermodynamics that the entropy of the universe is conserved, mainstream science still promotes an image of the universe where entropy is increasing. I am collecting examples of claims that the entropy of the universe is conserved.
Here is one such example:
What is crucial now is that a theorem of quantum mechanics tells us that if we consider a sufficiently larger system, the whole entropy of this larger system is conserved and therefore the process is fully reversible (Fredkin and Toffoli 1982; Auletta and Wang 2014, Sec. 9.7). In other words, we have a local growth of entropy embedded in a larger system in which the entropy is conserved. This fact is also the scientific basis of quantum computation — the attempt at understanding and building reversible quantum computers (Nielsen and Chuang 2000). In other words, as far as quantum computers make no information selection, they are reversible devices (Bennett 1973). Now, this has some important implications:
* It is likely that the entropy of the whole universe is conserved if it obeys the laws of quantum mechanics. Now, since a quantum system that does not interact with other systems is assumed to have zero entropy (representing the maximal order possible in nature), it is also likely that the whole universe has zero entropy. Note that in order to conserve entropy one needs to conserve energy, which is, however, a weaker requirement since we can have different forms of energy according to whether the entropy is higher or lower.
* We can only have local shifts in order and disorder but the whole always preserves the same amount of order (which does not imply that the consequences of these shifts are illusionary, they are just locally contextual). Somebody could consider this to be in contradiction with the second law. However, the latter only tells us that the entropy of an isolated system cannot decrease, which implies that it can either increase or be conserved.
* The latter point implies that quantum correlations (e.g. entanglement) cannot be destroyed, since they are the basis of the quantum order. In fact, we know that we would need an infinite amount of time to fully destroy them (see Paz et al. 1993). What can be done at this level is either strengthening or weakening certain correlations: in fact, the ‘intensity’ of the correlation can be measured and the best measure is an informational one, based on the notion of the mutual information among subsystems or components of the quantum system (Barnett and Phoenix 1989; Oliver and Zurek 2001; Auletta and Wang 2014, Sec. 11.7).
Emergence: selection, allowed operations, and conserved quantities
