The issue of entropy gets raised from time to time in connection with bounce cosmologies. People who think of entropy as an ABSOLUTE physical quantitity, rather than an observer-dependent one, occasionally ask how it apparently got to be so low at the start of expansion (if the start was a rebound from prior contracting phase.) I responded in the context of separate discussion so, for convenience, I'll save the reply here where I can refer to it easily.
If you look at how entropy is
defined you see it is
observer-dependent because it depends on the observer's coarse-graining---the macrovariable versus microvariable distinction. Entropy is the logarithm of the number of microstates (based on degrees of freedom irrelevant to the observer) comprising one grand macrostate (based on d.o.f that he actually interacts with and which affect him).
Any observer has a coarse-graining map corresponding to the lumping together of microstates into macrostates (consolidating all those which don't make any difference to the observer). Entropy measures the "size" in the particular macrostate we're in. The amount of information in it, that we ignore.
There's a group of people who think of entropy as absolute, who don't think that when you talk about it you have to specify a coarse-graining map. It is difficult for them to accept bounce cosmology because it looks to them as if "the entropy" (an absolute quantity) was reset to zero at the bounce. And there are other people who don't have that problem.
If you think of entropy as defined for a particular coarse-graining, then you don't encounter that mental obstacle. There is a pre-bounce guy and according to his coarsegraining the entropy increases astronomically as you go into the bounce, and it never thereafter declines! Because everything post-bounce is irrelevant to him, like it was inside the horizon of a black hole, the whole universe.
The post-bounce guy has a DIFFERENT coarsegraining and he sees the entropy initially low, everything about the bounce matters to him, is of vital importance, affects him thru variables he interacts with. Then as the U expands and diversifies regions of phase space become indifferent and irrelevant to him and entropy (for the post-bounce guy) increases.
The second law holds for any particular guy's entropy---defined based on his coarse-graining of the world.
This has been pointed out by various people. I think probably it would have come up in your Abhay&Ivan interview documentary video. As I recall Thanu Padmanabhan stated it clearly. Entropy is observer-dependent, or words to that effect. I've lost track of all the people who have made that point. Recently it came up here:
http://arxiv.org/abs/1407.3384
Why do we remember the past and not the future? The 'time oriented coarse graining' hypothesis
Carlo Rovelli
(Submitted on 12 Jul 2014)
Phenomenological arrows of time can be traced to a past low-entropy state. Does this imply the universe was in an improbable state in the past? I suggest a different possibility:
past low-entropy depends on the coarse-graining implicit in our definition of entropy. This, in turn depends on our physical coupling to the rest of the world. …
Some more reading, if curious:
http://arxiv.org/abs/gr-qc/9901033
http://arxiv.org/abs/hep-th/0310022
http://arxiv.org/abs/hep-th/0410168
To give a bit of the flavor I'll quote a passage from Don Marolf's 2004 paper
==quote
http://arxiv.org/abs/hep-th/0410168 from conclusions==
the realization that observers remaining outside a black hole associate a different (and, at least in interesting cases, smaller) flux of entropy across the horizon with a given physical process than do observers who themselves cross the horizon during the process. In particular, this second mechanism was explored using both analytic and numerical techniques in a simple toy model. We note that similar effects have been reported
35 for calculations involving quantum teleportation experiments in non-inertial frames. Our observations are also in accord with general remarks
36,37 that, in analogy with energy,
entropy should be a subtle concept in General Relativity.
We have concentrated here on this new observer-dependence in the concept of entropy. It is tempting to speculate that this observation will have further interesting implications for the thermodynamics of black holes. For example, the point here that the two classes of observers assign different values to the entropy flux across the horizon seems to be in tune with the point of view (see, e.g., Refs. 38,39,40,41,42) that the Bekenstein-Hawking entropy of a black hole does not count the number of black hole microstates, but rather refers to some property of these states relative to observers who…
==endquote==
For context see:
https://www.physicsforums.com/showthread.php?p=4810929#post4810929