21

**Physics, Astronomy & Cosmology / Re: How remiss is our attitude towards entropy?**

« **on:**08/01/2019 13:19:16 »

There’s another point from "Does time stand still in the quantum world? I think is worth a mention".Quote from: ChiralImagine four coins that can be either H or T. At regular intervals a coin is selected at random, and flipped such that it has a 50/50 chance of being H or T.

If the system starts out HHHH (the lowest possible entropy for the system), then after the first flip, entropy has a 50% chance of increasing and 50% chance of staying the same. Eventually the system will reach a state of maximal entropy, and can then only decrease or stay the same. Ultimately, as this game continues, the system will oscillate through all possible states with all levels of entropy (with each of the states essentially being favored by entropy).

This is great as an analogy, but like the frequently encountered deck of cards analogy, it can easily give a wrong impression.

Just changing the position or orientation of macroscopic objects from an arrangement that we define as orderly, to one that we define as disorderly doesn’t necessarily change its entropic state. Does turning a coin over alter the number of microstates accessible to its constituent particles?

Of course, the act of flipping the coin involves an increase in entropy, but this change is inherent in the "flipper", not in the coins as individual objects, or as a group.

Discounting the change in entropy of the universe caused by the action of flipping the coin, we can still determine the entropy of just the system defined by the coins.

There are 2

^{4}= 16 possible states

There is only way to have four heads: HHHH

and analogously only one way to have four tails TTTT

There are four ways to have three heads HHHT HHTH HTHH and THHH

and analogously four ways to have three tails TTTH TTHT THTT and HTTT

then the remaining six states have two of each

HHTT HTHT HTTH TTHH THTH and THHT

so, after 10000 flips, it is most likely that there are two of each, and only a 1/8 chance that they are all the same (1/16 HHHH + 1/16 TTTT)

This system is still small enough that there isn't a huge difference between the highest and lowest entropy states. But if we had 1200 coins, or as someone else pointed out in the other thread, 10

^{24}coins, then there is effectively zero chance that the coins would all have the same arrangement, once allowed to evolve from the lowest entropy state for a few turns.