3 ms·

I like the first part, entropy is essentially a measure of degeneracy for a state (the elementary definition is the log of the number of states multiplied by a

I like the first part, entropy is essentially a measure of degeneracy for a state (the elementary definition is the log of the number of states multiplied by a unitful constant). Technically, if you're a supposed super-intelligence, that is good at remembering detail, every state of a system can be distinguishable and thus have small entropy. For example, consider a finite number of legos in a room. A computer could potentially remember where every lego is placed, while person can't do as well but could distinguish between a state where the legos are strewn about or built into a castle. So, the person would lump all the disordered states into just one state (the "mess" state) and give it a high entropy compared to the number of organized states (castles or ships made out of the legos). I guess I always knew this, and this is sort of what we mean when we say "high entropy" but it's kind of fun to say it out explicitly like this. Most of the others seem like conflating the strict applicability of a theory vs. it's practical limits, like that QM doesn't really mean "small" or (equivalently) high energy, it just means when you're near the Heisenberg uncertainty limit for the observations you're making, which in most cases means small. Allow me to add another one: "Special Relativity means when you go faster, time slows down for you!" And another (controversial may be): "In Schrodinger's cat, the cat is both dead and alive at the same time!"

Xcelerate 8y ago
> every state of a system can be distinguishable and thus have small entropy Which corresponds quite well to the fact that the entropy of a pure state is zero (since S=−tr[ρlnρ]). Entropy is better described as a property that arises between systems.
kgwgk 8y ago
One way to look at it is that the entropy is not a property of the system but a property of the knowledge an observer has about the system. A macroscopic state is not a physical object. The same microscopic state may correspond to different macroscopic states for different observers.
PopePompus 8y ago
> For example, consider a finite number of legos in a room. This works with legos, but not subatomic particles. No matter how smart you are, you can't distinguish between two states which differ only by having two electrons swapped.
- noobermin 8y ago
  Fair. This is mainly for macroscopic systems, not fundamental particles or other species that cannot be distinguished at all, then all you can do is lump the states together and give it a degeneracy.

Xcelerate 8y ago

> every state of a system can be distinguishable and thus have small entropy Which corresponds quite well to the fact that the entropy of a pure state is zero (since S=−tr[ρlnρ]). Entropy is better described as a property that arises between systems.

kgwgk 8y ago

One way to look at it is that the entropy is not a property of the system but a property of the knowledge an observer has about the system. A macroscopic state is not a physical object. The same microscopic state may correspond to different macroscopic states for different observers.

PopePompus 8y ago

> For example, consider a finite number of legos in a room. This works with legos, but not subatomic particles. No matter how smart you are, you can't distinguish between two states which differ only by having two electrons swapped.

noobermin 8y ago
Fair. This is mainly for macroscopic systems, not fundamental particles or other species that cannot be distinguished at all, then all you can do is lump the states together and give it a degeneracy.