# How does the universe so conspire that entropy increase?

1. Aug 5, 2015

### stedwards

How does the universe so conspire such that ΔS≥0, entropy increases?

2. Aug 6, 2015

### Staff: Mentor

Schroeder's textbook "An Introduction to Thermal Physics" takes a whole chapter to explain this in detail mathematically. But the basic idea can be stated in a few sentences from the beginning of that chapter:

(that is, processes for which ΔS > 0)
Suppose we have one mole (6.02 x 1023 molecules) of an ideal gas in a box. If all the gas molecules were to spontaneously migrate to the left half of the box, that would represent a decrease in entropy. However, this is highly unlikely. If the probability that any single molecule is in the left half of the box is 0.5, then the probability that all of them (one mole of them) are in the left half, and a perfect vacuum in the other half, is $0.5^{6.02 \times 10^{23}}$, which is a fantastically tiny number. Even if there were only 100 molecules in the box, the probability

However, if there are two molecules in the box, the probability is 0.25 that both of them are in the left half; if there are three, the probability is 0.125; etc. With a small number of molecules, it is rather common for entropy to decrease; with a large number (or even a fairly modest number), it is so rare that we might as well say "never" for all practical purposes.

Going further, if we start with all the molecules in the left side of the box, it is generally overwhelmingly probable that they will "spread out" to fill the entire box more or less uniformly within a very short period of time, increasing the entropy of the system in the process.

Last edited: Aug 6, 2015
3. Aug 7, 2015

### Philip Wood

Perhaps the question to ask is why it had/has as little entropy then/now as it did/does...

4. Aug 7, 2015

Staff Emeritus
Why not let the OP tell us what he means instead of guessing?

5. Aug 7, 2015

### Philip Wood

Don't know whether this is directed at post 3. Here I was suggesting that another viewpoint might give insight. There was no attempt to guess anything.

6. Aug 7, 2015

### DrDu

The second law of thermodynamics says that the entropy of an adiabatically isolated system (much smaller than the universe) can only increase. It makes no statement about the entropy of the universe. So no conspiracy there.

7. Aug 7, 2015

### stedwards

With the laws of physics apparently symmetric in time (more correctly, CPT), why should entropy increase have a preferred temporal direction?