Entropy is not just about position, but about temperature as well. Objects with higher temperature have higher entropy since you have more options with how velocities are set, hence entropy increases as things gets pulled together by gravity and energy gets spread out among the particles, at least with a classical interpretation of gravity.
> Objects with higher temperature have higher entropy
That surely must be a bit too oversimplified, since that would imply that the beginning of the observable universe had more entropy than the current one (given that it was way hotter than the present)
We know that early universe was low entropy - that is the explanation for the 2nd law of thermodynamics. That is known as the past hypothesis. The laws of physics dictate that the most likely state to come from and go to, is higher entropy because there are vastly more high entropy states than low. That directly violates the 2nd law, but is not unreasonable. Imagine 2 boxes of gas with 10 gas molecules in side A and B. They are separated by a wall with a single small hole in it. Every now and then a gas molecule with go from one side to the other, A to B, without one going the other way. We just went from a high entropy state to a lower entropy state in a closed system.
But, coming from a high entropy state does not fit with the world we see, so we're pretty sure that the past hypothesis is true.
One of the leading theories about the early universe and how it lead to the world we know today, is inflation. In that theory "stuff" is basically created out of nothing, meaning that the early universe was small, hot, and with (relatively) few particles in a specific configuration. The inflation and reheating dramatically increased the entropy. In other words - there was much less stuff, and it needed to be in a particular configuration to expand into the universe as we know it. That is low entropy.
Note: I am not a theoretical physicist, so the above is my layman understanding of the topic.
So, I'm thinking about two asteroids in deep space. When they are drawn together in an orbit via gravity, this would seem to lower their entropy (a smaller number of possible microstates required to define their macrostate). So, gravity should produce some tidal forces that would heat them up to a greater extent than the entropy they lose for being brought closer together?
> When they are drawn together in an orbit via gravity, this would seem to lower their entropy (a smaller number of possible microstates required to define their macrostate).
What do you mean by macrostate? If the macrostate is related to the geometry of the asteroids considered as solid bodies (and the changes in their positions and orientations) I don't see why the entropy would be lower.
Isn't the relationship between macrostate and microstate the basis for entropy? Like, there can be more possible microstates (positions and momenta) for a given hot macrostate than a cool one.
In the case of the asteroids, I guess I'm thinking of number bits required to accurately model the system accurately. Is that an appropriate way to think about it?
I see it as lower because fewer cells in a matrix are needed to model the solid bodies...
In the typical example of statistical mechanics, the ideal gas, the macrostate is described with a few variables (say volume, pressure and temperature with PV proportional to T). The microstates correspond to the precise configuration of every gas atom. If we heat the gas at constant volume then the temperature, the pressure and the entropy will increase. You can also increase the entropy by expanding the volume at constant temperature.
But I fail to see the analogy with the asteroids. If the microstate is the atomic configuration it doesn’t seem to depend (at least significantly) on the macroscopic description of the position, momentum and angular momentum of the asteroids. The number of bits (?) is not a physical quantity (and why would you need less bits to describe the microstate?).
Ok, let me put it like this. Gravity seems to have a magic (I don't understand it) way to increase the pressure of stuff by decreasing the volume in which interactions are likely to occur. Fair? Increasing pressure decreases local entropy, since pressures tend to diffuse, not the other way around. To get pressures, we expect outside forces to create them. Pressures don't just statistically happen -- at least, not very strongly. So, gravity seems to create these pressures, and it isn't clear to me how this doesn't violate the second law.
I hope I'm not expressing myself too foolishly, but I really don't understand it. After much effort, I feel like I have a good understanding of entropy, though. Which is what makes gravity so weird to me.
I was trying to understand what kind of macrostates and microstates you were thinking of when you said entropy would decrease when the asteroids were closer. Maybe I should try to read one of those papers to see what they are about :-)
But you may not be looking at the whole picture. Just because a system occupies a smaller volume doesn’t mean the entropy is lower. In classical thermodynamics a gas can be compressed while keeping the entropy constant (at least in theory).
Edit: after a look at the first paper by Verlinde I still don’t know what are the microstates in this theory (they are related to string theory and intentionally left mostly undefined). But in any case your assumption that entropy decreases seems wrong by definition because an entropic force acts in the direction of increasing entropy.
