# I Is the second law of thermodynamics a law or a tautology?

1. Aug 28, 2016

### Monsterboy

2. Aug 28, 2016

### phinds

I don't have any deep understanding of the 2nd law BUT I notice that at the very start he sets up a straw-man and then knocks it down. That is trivially easy to do so OF COURSE he immediately concludes that the 2nd law is a tautology. He defines it as a tautology (or being equivalent to one) and then concludes that it is a tautology. I'm not impressed. Now, to be fair, I didn't read the whole article so perhaps he does more than I am aware of to tie his original tautology to the 2nd law.

3. Aug 30, 2016

### Staff: Mentor

I would agree that the 2nd law is a trivial statement, that systems evolve from a low probability state to a high probability state. But i don't see how this makes it a tautology. And I think that it is still very relevant to the question of the arrow of time, even if it may not be the only ingredient there.

What I don't like about the Muller's cosmological argument is that it doesn't explain the "local" arrow of time: systems that are incredibly small compared to any cosmological effect still exhibit an arrow of time.

I think it was Feynman who once said that the real mystery is why the universe started in such a low entropy state.

As an aside, Muller appears as a typical example of some "grand idea" physicists who promote their grand ideas by belittling previous ideas. Most often, it turns out that both the old and the new ideas have some merit.

4. Sep 2, 2016

### Monsterboy

I don't understand how the second law is defined in terms of probability , entropy of the universe continuously increases right ? Isn't that the point of the second law ? What is probability of entropy decreasing in the whole universe? Zero right ? So the increase in entropy is not "most probable" it is the only thing possible ?

5. Sep 3, 2016

### Staff: Mentor

The statement that the entropy is continually increasing is itself a probabilistic statement. Start with the definition (from statistical mechanics) of the entropy of a given state: it is the logarithm of the number of ways that the system can be in that state. Now consider fifty coins in a box: there is one way for them to be in the state "all fifty are heads-up", fifty ways for them to be in the state "49 heads and one tails", 1225 ways for them to be in the state "48 heads and 2 tails", and so forth, so those are states of ever-greater entropy. If I start with the box in the "49 heads and one tails" state, after I shake the box it is 1225 times more likely to end up in the higher-entropy "48 heads and two tails" state than in the lower-entropy "All fifty are heads-up" state. It's even more likely to end up in a state of even higher entropy; there are millions of ways to get a 25/25 split.

Thus, the probability that randomly shaking the box will do anything except increase its entropy is very low. If we were talking about the random motions of the $10^{25}$ air molecules in a typical room instead of fifty coins in a box, "very low" would become "utterly inconceivable" - and that's the second law.

6. Sep 4, 2016

### Monsterboy

Thanks Nugatory , what do you think about the relation between the arrow of time and the second law ?

7. Sep 5, 2016

### Pythagorean

I have a similar question, that may perhaps contribute to a more critical look at the thesis of this thread. Particularly, is the 2nd law generalizable to the whole universe? I have seen arguments from physicists both that it is and that it is not (most generally as part of the debate on the heat death of the universe). If you want a refresher on the arguments, see the 'criticism' section of the wiki on the heat death of the universe. It generally boils down to the "entropy of the universe" being undefinable.