The Second Law of Thermodynamics (2011)

Just like rolling 6 dice. We assume all configurations of the 6 dice have equal probability.

What's the probability of rolling exactly 1,1,2,6,3,5? It's the exact same probability as rolling 6,6,6,6,6,6. We instinctively assign these probabilities based of of assumption because we also assume each number has a 1/6 probability so rolling exactly a certain number for each roll yields (1/6)^6

It's the macrostates that are subjectively grouping these microstates in various ways. If I pick the macrostate where all dice are the same there's only 6 microstates for that. If I make up the macrostate for at least one dice is different that's every possible microstate except 6 microstates where they are all the same.

Delimited continuations are functions, and as such (in a world of algebraic types where we can take sums and products of types) exponentials of types, ran^dom.

[in particular, with the substitution of isomorphism for equality they follow the normal K-12 rules: C^(A+B) ~= C^A * C^B, etc.]

I'd just been glancing at https://en.wikipedia.org/wiki/Convex_conjugate#Examples and the pattern by which single-branched f(x) seems to often become a multibranch f(x) reminded me of how logic-reversing functions in general and logical implication in particular "adds branching": if we wish to establish x'y may be satisfied on one branch by not x but on the other requires y.

[and on the general topic: I like to think of temperature as tying together energy and entropy, where positive temperatures yield the familiar relationships but negative temperatures "unintuitive" ones]

how is it then, that things are becoming more spread out over time?

what is the property about the past, that it seems have a lot of uncommon states and not a lot of the common ones?

if common states are mathematically more likely to be common, why is it that the future has them and the past does not, in general?

like, why hasn't heat death happened? the probability thing seems to be almost proof-like, you cannot really argue against it. but clearly, the universe did, to a great degree, at some point in the past. why?

It's more likely for things to spread out then to concentrate in one corner when you randomly move all particles in a box. If all particles moved to one corner of a box you would assume there's an intelligence at work moving the particles because such movement is too low of a probability to happen without intelligent intervention.

>if common states are mathematically more likely to be common, why is it that the future has them and the past does not, in general?

Common states are called "common" because their are more of them in general. Think in terms of things with a few states like rolling dice. You have a machine that rolls rice continuously and checks the result. Use this as an analogy of particles of gas moving around in a box and then use that as an analogy of the universe.

Nobody knows why probability works this way. Probability is what differentiates the arrow of time.

>like, why hasn't heat death happened? the probability thing seems to be almost proof-like, you cannot really argue against it. but clearly, the universe did, to a great degree, at some point in the past. why?

Entropy is just a phenomenon of probability. Don't let the concept of entropy rule your brain and override what's going on. Heat death hasn't happened because entropy can be frozen. You freeze ice then the particles stop moving.

Additionally all of what I said above doesn't apply to things with gravity like black holes. With gravity things begin to automatically self organize into circular orbits or spherical planets. Why? It's because entropy isn't measuring disorder. That's a mistake. Entropy is just saying that systems drift towards high probability macrostates. In systems with gravity, spherical shapes and circular orbits ARE a higher probability macrostate then one where the particles disordered. In this system a higher entropic state is actually MORE ordered then a lower entropic macrostate.

I don't know if there's going to be a "heat" death, but for sure we are moving towards higher entropy as the law says. But this does not necessarily mean more disorder or things getting spread out.

That's it. I think the word entropy just confuses everyone. It's just someone observed these weird phenomenon with heat and called it entropy. Then we realized it's just a bunch of particles moving into high probability patterns.

Haven't you looked at the article I sent which says "quantum" in every other page. Haven't you heard of its author Roger Balian and his (two-volume) book From microphysics to macrophysics: methods and applications of statistical physics.

> Statistical mechanics is just a study of the application of probability to that macro phenomena. We still don't know why all of it works.

"We" may "know" different things - and have a different view on the relative importance of what is known and what it isn't.