[nihakue]

I'm not in any way qualified to have a take here, but I have one anyway:

My understanding is that entropy is a way of quantifying how many different ways a thing could 'actually be' and yet still 'appear to be' how it is. So it is largely a result of an observer's limited ability to perceive / interrogate the 'true' nature of the system in question.

So for example you could observe that a single coin flip is heads, and entropy will help you quantify how many different ways that could have come to pass. e.g. is it a fair coin, a weighted coin, a coin with two head faces, etc. All these possibilities increase the entropy of the system. An arrangement _not_ counted towards the system's entropy is the arrangement where the coin has no heads face, only ever comes up tails, etc.

Related, my intuition about the observation that entropy tends to increase is that it's purely a result of more likely things happening more often on average.

Would be delighted if anyone wanted to correct either of these intuitions.

[fsckboy]

>purely a result of more likely things happening more often on average

according to your wording, no. if you have a perfect six sided die (or perfect two sided coin), none/neither of the outcomes are more likely at any point in time... yet something approximating entropy occurs after many repeated trials. what's expected to happen is the average thing even though it's never the most likely thing to happen.

you want to look at how repeated re-convolution of a function with itself always converges on the same gaussian function, no matter the shape of the starting function is (as long as it's not some pathological case, such as an impulse function... but even then, consider the convolution of the impulse function with the gaussian)

[tshaddox]

> My understanding is that entropy is a way of quantifying how many different ways a thing could 'actually be' and yet still 'appear to be' how it is. So it is largely a result of an observer's limited ability to perceive / interrogate the 'true' nature of the system in question.

When ice cubes in a glass of water slowly melt, and the temperature of the liquid water decreases, where does the limited ability of an observer come into play?

It seems to me that two things in this scenario are true:

1) The fundamental physical interactions (i.e. particle collisions) are all time-reversible, and no observer of any one such interaction would be able to tell which directly time is flowing.

2) The states of the overall system are not time-reversible.

[CaptainNegative]

The temperature of an object is a macroscopic property basically depending on the kinetic energy of the matter within it, which in a typical cup of water varies substantially from one molecule to the next. If before you could guess a little bit about the kinetic energy of a given water molecule based on whether it is part of the ice or not, after melting and sufficient time to equilibrate the location of a particular molecule gives you no additional information for estimating its velocity.

[dynm]

It's tricky when you think of a continuous system because the "differential entropy" is different (and more subtle) than the "entropy". Even if a system is time-reversible, the "measure" of a set of states can change.

For example: Say I'm at some distance from you, between 0 and 1 km (all equiprobable). Now I switch to being 10x as far away. This is time-reversible, but because the volume of the set of states changed, the differential entropy changes. This is the kind of thing that happens in time-reversible continuous systems that can't happen in time-reversible discrete systems.

[russdill]

This is based on entropy being closely tied to your knowledge of the system. It's one of many useful definitions of entropy.

[867-5309]

> 'actually be' and yet still 'appear to be'

esse quam videri