I’m aware that my assumptions are probably incorrect but I’ll state them as if they’re true.
If the universe is generally moving to its lowest energy state, and mass and energy are equivalent, then why wouldn’t the universe end up as all mass?
If the universe also moves towards higher entropy, and mass is lower entropy than energy, then how to reconcile question 1?
Oh wait, I’m thinking in terms of chemistry where matter moves towards its lowest energy state but it does so by releasing energy so I guess I can throw out point 1, which means I guess I can throw out this whole question. 
Entropy is related to the quality of energy i.e. it’s ability to do work.
Instinctively, you can think of it this way : Say you give the same energy to 1 gallon of water and 100 gallons of water. The 1 gallon water has a temperature rise of 100 F but the 100 gallon has a temperature rise of 1 F.
Although both the (1 gallon and 100 gallon) have received the same energy, the 100 gallon has more entropy I.e. the energy in the 100 gallon is more “degraded”
If you are familiar with the Carnot cycle, you can immediately see that higher the temperature of a source, higher will be the ability to do work.
I don’t think you can have mass instead of energy in science. They are equivalent. I mean once you have mass, you have energy. What are we talking about?
That’s just an approximation taught to Chemistry 101
In chemistry, species move such that the Gibbs free energy (related to entropy) is minimized.
We use the Gibbs free energy concept to estimate reaction products for which no equilibrium data is available.
Would you say a pound of U-235 and the result of a chain reaction fission of that pound are the same thing? They can be made equivalent mathematically by e=mc2 but they aren’t the same.
Then I guess it all depends on what the definition of “the same” is.
In the current context, I think what we are asking might be this: Suppose entropy has gotten almost all the way down to zero, and there’s no matter or energy at all remaining in the universe except for one piece of matter. Or if you prefer, some small amount of generic matter and some small amount of generic energy. What will happen to them? Let’s further suppose that there aren’t even any black holes left which would destroy the matter. What will happen? Is there some sort of natural process by which matter degrades into energy and then into nothing? Or might that piece of matter stay around forever?
(I presume that it is obvious how little I understand about entropy. I guess what I’m really asking is for a detailed description of what happened JUST BEFORE the end of “The Last Question”.
Entropy keeps increasing. It will not go down to zero but will tend to infinity.
Sunlight is a good example. If a certain amount of sunlight hits a solar panel, it can make you electrical energy that can do work (drive a fan for example). If the same amount of sunlight hits your shingles, it is converted to low level heat that doesn’t do much work.
Ultimately both the solar power and the shingles heat turn into low level energy (earth’s atmosphere heat). This is higher entropy (more disorder and less ability to do work) than the original sunlight.
This video from PBS Space Time is interesting: Reversing Entropy with Maxwell’s Demon
Thank you for the correction, am77494. I keep forgetting that entropy goes up, not down.
A lot of my confusion results from the terms used in discussions of entropy. I think I’m pretty clear on the idea that, over time, hot things and cold things will tend to average each other out, and high-density parts of the system will average out the low-density parts of the system, and the result is called equilibrium. The part I don’t get is why equilibrium is referred to as maximum disorder. To me, equliibrium is very orderly, and has a very low level of disorder, because it is the same everywhere. When you have different things all order the place moving in random way, to me that is very DISorderly.
I accept the fact that the scientists have adopted a convention to define entropy as they did. But it seems backward to me. Can someone explain it? Thanks in advance.
What would you consider to have more order, the sand on a beach or the same sand built up into sandcastle?
But everything moving all over the place in a random way is exactly what you get at equilibrium.
But “disorder” isn’t the best way to talk about entropy, anyway. More precisely, entropy is information. When I have an assembled jigsaw puzzle sitting on my table, it’s very easy to describe it completely: I need to tell you that it’s assembled, and then tell you two numbers to specify its position, and one to specify its orientation. Very little information, and hence, low entropy. On the other hand, when it’s taken apart and in its box, to completely describe its state, you’d need to specify the position and orientation of each of the thousand pieces.
Or consider moveable type. Suppose that Gutenberg has an assistant, who isn’t very bright, but Gutenberg has trained him to put the type away: All of the As in this little drawer, all of the Bs in this one, and so on, with all of the drawers in alphabetical order. When the type is all put away in that way, it’s very low entropy. But now suppose that Gutenberg has a bunch of pages all typeset: There’s a lot of information there. And his illiterate assistant comes in and sees that the letters are all jumbled up: This I is next to an n, instead of with all the other Is where it belongs, and then here’s an h in between a t and an e, and this next clump of letters at least has a couple of ns next to each other, as they should be, but there’s also a b, an e, a couple of gs and is (not next to each other), and another n. So the assistant does what he’s been trained to do, and reduces the entropy by putting the letters away… Thereby removing all of the information.
I posted a video from PBS Space Time just above your post. Prior to that video they published this video that I think (hope) might be helpful for you. These are not very long and made for the layman. I think it is an excellent series overall. Well worth a look.
Thank you all. Your descriptions are clear. I just need some time for it all to soak in.
The video I linked, while trying to be accessible, is a bit dense.
I think the Go board analogies are the best to get a feel for for it. I think the first video I linked above did a better job to explain it but both are worth watching.
YMMV
Thanks for the videos, Whack-a-Mole. I think I’m getting it.
My next question might be less scientific, and more historical. I understand that entropy is a measure of disorder, and entropy (of a given system) is always increasing, and equilibrium is the state of maximum entropy and maximum disorder.
But those same ideas could have been started in the reverse, if they had chosen to define entropy in terms of Order rather than DISorder, then my previous paragraph would have said that entropy is always DEcreasing, and equilibrium is the state of MINimum entropy and MINimum Order.
Same concepts and formulas, just in reverse. My phrasing is appealing to me for several reasons.
First, order is very useful, and there’s nothing one can do with a system which is in total disorder (unless an outside force enters), so TO ME it seems more reasonable to describe an equilibrium as have zero entropy than infinite energy.
Similarly, why describe something as increasing when it becomes LESS useful? I’m not coming up with good words to describe it, but this just smells like describing suction as a force. I’ve heard it said that there is no such thing as “suction”, and it should really be referred to as “negative pressure”. I recall that the characters in “The Last Question” often said that “the universe is running down”, and thus it seems more reasonable to me that we should say that entropy is always DEcreasing.
This, entropy is often described in terms of temperature, and temperature has a well-known concept of “absolute zero”. To me, it just sounds reasonable to link equilibrium and absolute zero with zero entropy as well.
Now, I totally concede that these things are arbitrary, and they could have gone either way, and the convention has agreed that “entropy is INcreasing.” My question is this totally historical: how did it end up that way?
The word entropy was put forth in 1865 by the German physicist Rudolf Clausius to denote what any type of energy turns into: a useless heat. He came up with this concept under the influence of the idea in the Second Law of Thermodynamics, which was probably a recent discovery. (Maxwell’s paradox led Rolf Landauer to find the heat equivalent of the erasure of one bit of information.)
They did and you are not the only one with the Minimization mindset 
The videos posted above are from the perspective of physics or information technology where those black round pieces (shown in the video) have no internal energy or can’t break apart or join up. In chemistry or chemical engineering, those dots have internal energy, break up or join up to form new compounds.
A more useful concept is that of Gibbs free energy (also called available energy) for chemical equilibrium . Gibbs free energy is minimized when a system goes to equilibrium.
For example for the reaction :
N2 + 3 H2 <—> 2 NH3
Given the pressure and temperature, you can find the equilibrium amounts (fractions) of each of the species by doing a Gibbs free energy minimization. (Aka the equilibrium constant)
Note that Gibbs free energy (and entropy) predicts what will happen at equilibrium, it doesn’t say how long it will take to get there.
Gibbs free energy tells us that at room temp/pressure, diamond will turn into graphite but it doesn’t tell you how many centuries it will take.