You are given insulated cylinder with a barrier in the middle. Left side of the cylinder filled with ideal gas A, and the right side filled with gas B. If given a particle one can distinguish A from B. The pressure and temperature on both sides are the same. Then you remove the barrier and gases mix. Question: how much work you need to do to revert the system into the original state? Hint: the work is equal to entropy difference between two states.

More generally, if you have proper insulated system and leave it be for a while. All of sudden you will have to do some work to come back to the original state despite energy conservation law holds.

Note that you're describing equilibrium as a unique situation where the number of possible states is at a maximum. Now how can a situation be unique if it has the maximum number of possible states? Clearly the situation is as far from unique as it can be.

To resolve the contradiction requires distinguishing between features of the probability distribution and features of a random sample (i.e. a possible state) and also needs an explanation how it even makes sense to view a deterministic physical system (leave quantum mechanics for now) as a random variable.

The theory that links everything together is ergodic theory, which has a couple of handy theorems. One is that for a certain kind of dynamical system the average over time and the average over the 'possible states' agree. Such a system can also be assigned an entropy. It even suggests that generally a system will be found around states with a probability close to 2^-entropy (this is not absolutely always true ..but close enough for physicists)

Now what does such a system look like? Well we need a state space (easy) and a measure on it which is constant as the system evolves (i.e. we can pick a region in the state space, evolve it and its volume will stay constant). The last part is tricky, but as it turns out classical mechanics gives us the phase space and the canonical volume on it (basically the standard notion of volume) which fit the bill. This gives a probability distribution on the state space and an entropy equal to log(volume in phase space), which matches the definitions in statistical physics but also gives a solid foundation for some of the seemingly arbitrary choices.

So there you have it, that's why a system can have a probability distribution attached to it, despite being deterministic, why 'high entropy states' are common, and why physical systems have a uniform distribution (and therefore an entropy which is the log of the number of states).

This also explains physicists got away with using a uniform distribution without worrying about which variables they used. By pure 'coincidence' the standard choice of variables that physicists use have this incredibly nice property that makes everything work out. I'm not sure if this is too well known so it might be worth abusing this to 'prove' a perpetuum mobile is possible to stop people using uniform distributions without due deliberation.

Right? I think this could be a really interesting basis for a sci-fi novel - the first space-faring civilization in the entire universe trying to force every form of life to keep "entropy usage" to a minimum, so they can prolong their own life span.

And a space full of children is exponentially faster at increasing entropy.

Laymen to the extreme but, didn't it? The thing about the low entropy of the universe near the big bang, gravity naturally bringing things together, and such?

to my best understanding, to go from high entropy state to low entropy state you need work to do. The sun is a source of energy to do the work

I've always referred to the inverse as "information" or "order".

If entropy is the distribution of potential over negative potential, emergence is that where an outcome creates potential (of some discrete domain).

The mystifying relationship with thermodynamic entropy is that through accelerating entropy in other domains (burning), the entropy in the primary domain (eternal drag) is supplanted by the potentials provided by the external domain.

Entropy and energy are orthogonal anyway. You can understand entropy without the need to even use the word "energy."

Entropy is an aspect of probability, it is in fact a numerical phenomenon.

But even this is not the full story, because I can take a mass-spring network, and no matter how I choose to coarse-grain it, I will not see the entropy corresponding to that coarse-graining increase, because the trajectory of a mass-spring system is periodic. Entropy increase requires that the system is ergodic with respect to the chosen coarse-graining operation, i.e. that over long times the trajectory visits the coarse-grained states in a "random" and uniform way. It's not at all obvious to me why the dynamics of particles bouncing around in a box have this property, and particles attached in a mass-spring network do not; and neither the Sabine nor the Veritaserum videos address this or why we should expect all practical real-world physical systems to be ergotic with respect to practical coarse-graining mechanisms.

I posted it without realizing somebody else had already posted it.

Gotta love Prof. Hossenfelder.

To be clear, he does have a PhD but it is in physics education research, not physics.

Why do you think so? (Most to me seem reasonable but one on speed of electricity stands out as badly done (he redid the video but it too could have been better).)

This sounds quite bitter, as does griping about him mentioning his PhD.

His videos have excellent production quality, and do a great job of communicating advanced STEM concepts to laypeople in an entertaining way.

Maybe you don't like them, but that doesn't mean they are bad. Given their popularity, it would seem they are anything but.

What makes it weird is that black holes must necessarily* have the maximum amount of entropy for a specific volume. So not only the entropy of a black hole is proportional to its surface area, but the entropy of some volume of space can not grow beyond that. In particular entropy cannot be proportional to volume without limit, the density must be 0 on average for a big enough region.

*: According to some people anyway.

> Suppose I show you a snapshot of a random universe, would you be able to tell if the entropy of the universe is going to increase or decrease as the time progresses?

Yes, if it has low entropy then entropy will probably increase; if it has high entropy then the entropy will probably fluctuate up and down statistically.

> Let's assume that universe's entropy would increase. Consider another universe exactly the same as current universe, but all the particles' velocities reversed. Then this universe's entropy would decrease.

The key is that you're exponentially unlikely to find yourself in a universe where all the particles' velocities are reversed. See this: https://en.wikipedia.org/wiki/Fluctuation_theorem

The probability that a system randomly evolves in a way that reduces entropy is very very small.

Something similar could perhaps be said for the video’s approach; “what do we get from the sun?” is an ambiguous question, not necessarily a fair setup to ask a lay person when you have entropy in mind as the answer. We do get energy from the sun, that is a correct answer, and we use some of it before it goes away. But, there is the nice a-ha that all the energy from the sun eventually leaves the earth, right?

[1] “An energy crisis or energy shortage is any significant bottleneck in the supply of energy resources to an economy.“ https://en.wikipedia.org/wiki/Energy_crisis

I think it's not so much a shortage of energy, but that there thermodynamic equilibrium and thus no available energy to do anything.

I don't think this will ever happen tho, it's pretty clear to me that making energy more dense is a universal process.

Useful work, aka information, is work that can be employed in dynamics vis a vis processing. Useless work, aka heat, is the devil's share of the energy expenditure which is lost as entropy when undergoing a process.

If it only existed in our minds and not in physical reality that would mean it would be possible to construct a device that decreases global entropy on average.

Global warming occurs because the previous equilibrium between incoming and outgoing energy has been broken by changes in the composition of the atmosphere.

So until we reach a new equilibrium long after the atmosphere composition ceases to change, the outgoing energy will be less than the incoming energy.

The Earth is taking on energy every day from the sun. If we didn’t release it all back, the earth would be warming much much faster. It only remains relatively cool because it releases almost as much as it receives.

Another important note is that long term energy is not only stored as heat on earth. It’s stored as potential energy in the atoms of cells in plants and animals. Think of how cold a gallon of gasoline is, yet how much energy it stores.

For an example think of hot asphalt from a summer day. It gets real hot all day and slowly cools down at night. Sometimes it can be pretty warm to stand on the road even if it’s a cool night.

Within the human timescale, the Earth is retaining some (tiny fraction) of heat. That tiny fraction of heat is a very small window of heat that life can tolerate. It’s not too much and not too little. If the earth were to retain just a tiny bit more, suddenly life can’t tolerate it. On the scale of the universe, the difference between those realities is minuscule, even though it’s enormous to us.

https://en.m.wikipedia.org/wiki/Albedo