In physics, students are often confused about entropy, and I think that's partially because they try to think of it as being a property of the system. But a property of logarithms says log ( A B ) = log A + log B, so you can find your total entropy by finding your entropy for each individual system and adding. If your first system has A microstates and your second has B microstates, then there are A B possibilities for the combined microstate of both them together (like we saw with the partial sums and dice). That works with the formula, because it says S = log 1 = 0.īoltzmann’s formula also tells us about what happens where there are two independent systems. If there's only 1 microstate, we know everything there is no information missing, and the entropy is zero. The entropy is denoted by Sand the number of microstates by Ω, so: The number of digits is given the mathematical name “logarithm”. We've been measuring entropy in how many digits the number of microstates has. This is just about one digit less entropy than when I simply told you the sum, so by telling you the partial sums, I gave you a little bit less than one digit of information. There are 420 microstates for the first five dice and 780 for the second five, making 420*780 = 327,600 microstates in all. If I tell you that the first five dice add to 13 and the second five add to 17, you know that the sum is 30, like before, but you have extra information this time, since you know the intermediate sums as well. Different macrostates have different entropy. What if I said the sum of the ten dice was 59? There are only 10 microstates for that, so now you only have one digit of entropy. It turns out there are 2,930,455 microstates that go with the macrostate of having a sum of 30, so you have about 6.5 digits of entropy regarding the numbers on the dice. Those exact numbers on the dice are called a microstate. You can't tell from that what the exact numbers on each die are, so you have entropy-you're missing information. Īs another toy example, suppose I roll ten dice and tell you that the sum is 30.
Your entropy regarding where I live has gone down by about 5 digits.
#ENTROPY EXPLAINED CODE#
A zip code is a 5-digit number, so I've given you 5 digits of information.
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