Is increase in entropy synonymous with the flow of time?

Causation can flow in either direction. ONLY the second law requires an arrow of time. Causality only goes in one directly, and that direction is determined by one and only one thing – entropy.

this is clearly contradictory, and suggests causation is a consequence of entropy.

And no causality clearly is directional. Sometimes, you gotta remember that calculation is merely a tool. You need to use your mind too. And think hey, cause precedes effect...always.

With all due respect and in honesty, there is a "flow" to causation, consider that as the "direction of time".

Entropy has no direct connection to spacetime.

Khashishi
There's a difference between talking about the "arrow of time" and time itself. Time is just a dimension with similarities and differences to a direction in space. The arrow of time is our conscious perception of time flowing in one direction. Entropy is invoked as an explanation for the arrow of time but not of time itself.

Ok, now suppose entropy did increase faster (with respect to atomic clocks based on some frequency of oscillation of some crystal). Entropy isn't some single value which you can just adjust for the whole universe. Every system and subsystem has its own value of entropy, and entropy itself is a subjective value, so it's not really possible to answer the question.

Would Earth spin faster? Well, the Earth's angular momentum came from the angular momentum in some vortex of swirling dust as the Earth formed. I guess the initial state of the solar system had some various patches of dust moving in random directions. If you increase the entropy, I suppose you might have more swirls or faster swirls. You might get more planets with smaller mass and smaller rotation or higher rotation. Who knows? It's too undefined.

This is an interesting question. How much entropy is there in the universe? Lets call it S. Now we must have some value dS/dt = X. You're asking for what happens if dS/dt = 2X.

Now keep this in mind: normal matter has little entropy compared to event horizons. These event horizons could be black hole event horizons but any event horizon would do. There is an event horizon in the universe that is called the cosmological event horizon, which exists because somethings are so far away that light emitted today from their current position cannot reach us at t = ∞ due to the expansion of space.

The entropy of the observable universe is almost entirely contained in the blackbody radiation in the CMB and the cosmological event horizon and dS/dt is caused almost entirely by the expansion of the cosmological event horizon's surface area. Regular matter contributes almost nothing to the entropy. so I think dS/dt = 2X would not affect us at all.

Is increase in entropy synonymous with the flow of time?
Yes. There are two separate concepts here, the dimension of time which the laws of physics are with respect to. And the direction of time which the laws of physics don't define since they are time symmetric.

Which leaves two questions:
1. why is there a difference between the two directions along the time dimension?
Because we are 'on a hill' where entropy is increasing, so things don't act the same in the two time directions.

2. why does time appear to flow forwards?
<opinion>
Because any reasonably constructed creature is able to store information about the environment in the low entropy direction because it is massively less information than the present, i.e. memories. And such a creature would use rules to approximate the environment in the high entropy direction (which is too much information to store), i.e. predictions of the future. i.e. time flow is a sensation of living creatures (phenomenological), rather than a rule of physics.

Recently NASA has scientists that are talking about warp speed - something a few years ago was only science fiction in Star Trek. Energy is required and thus there would seemingly be a tremendous increase in entropy. Let me quote from GCN: "According to NASA scientists, it might be possible to break the laws of special relativity with a ship shaped like a sphere that could be placed between two regions of space-time, with one expanding and one contracting. This requires matter with special properties and could break Einstein's law because the ship isn't actually moving faster than light; space itself is being moved, and the ship is simply falling through the hole — called a wormhole — it created.
That much had been worked out as early as 1994 by physicist Miguel Alcubierre. However, in addition to the special matter, his plan also required energy equivalent to the mass-energy of the planet Jupiter."
In this case, if it can be done, it would seem that there would be very little flow; thus, the answer would be that they could not reasonably be synonymous. It was entropic spiral and the degradation of the earth thread that originally brought me to this website, since I had just re-read the new book Entropic Spiral is Evolution's Flush. I will not go into the details of the book since it appears it may be against one of the rules and I would like to continue writing here. You can find the book using a search engine and the book, not extremely technical, references several well-documented books which can help with this subject.
Using the input from NASA it appears that using the wormhole theory much energy could be expended with the possibility of little entropy resulting. This does not appear to contradict what I have been reading; however, the entropy "flow" does appear to be increasing in certain areas - especially genetic entropy.

I like thinking about time with an entropy perspective. In some ways its more intuitive than the usual relativistic way of looking at it. Clocks are devices which increase in entropy in a 'regular' fashion, with regular being defined as having constant ratios with other 'clocks'. The beginning of the universe has the lowest entropy possible, and thus was the earliest time possible. The macrostate of the small early universe has very, very few microstates associated with it. The end game of a heat death is a macrostate with the most possible microstates associated with it, this would be the end of time. If the universe is a closed system then both the early universe and late universe are accessible microstates and the entropy is constant, but any sub-system considered would not necessarily be like that.

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Hypothetically speaking....if doubling the "rate" of entropy caused time to speed up, then as we measure rates with respect to time, there would be no change would there?

I am not sure I can back this statement up with sound arguments, but I think time is a quantity/entity that does not require entropy for rate or direction. Rather the opposite. Entropy cannot increase (or decrease) without the time dimension to exist within.