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### Mathematical proof of the Second Law of Thermodynamics [duplicate]

Can you formalize statistical mechanics, like some people have done with relativity, and prove the second law of thermodynamics from more foundational axioms?
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### Explanation of why doesn't heat flow spontaneously from a colder to a hotter body [duplicate]

The second law of thermodynamics says that heat cannot spontaneously flow from a colder to a hotter reservoir but only with the expenditure of mechanical energy. This is taken as a postulate or law in ...
279 views

### Can statistical mechanics explain the second law completely? [duplicate]

Statistical mechanics is restricted to the postulate of the equal a priori probability, but this postulate does not need to be considered for thermodynamics, so the valid ranges of statistical ...
7k views

### Why are the laws of thermodynamics “supreme among the laws of Nature”?

Eddington wrote The law that entropy always increases holds, I think, the supreme position among the laws of Nature. If someone points out to you that your pet theory of the universe is in ...
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### Is there any proof for the 2nd law of thermodynamics?

Are there any analytical proofs for the 2nd law of thermodynamics? Or is it based entirely on empirical evidence?
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### Is a world with constant/decreasing entropy theoretically impossible?

We can imagine many changes to the laws of physics - you could scrap all of electromagnetism, gravity could be an inverse cubed law, even the first law of thermodynamics could hypothetically be broken ...
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### Why does the nature always prefer low energy and maximum entropy?

Why does the nature always prefer low energy and maximum entropy? I've just learned electrostatics and I still have no idea why like charges repel each other. http://in.answers.yahoo.com/question/...
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### Entropy as an arrow of time

From what I understand, entropy is a concept defined by the experimentalist due to his ignorance of the exact microstate of a system. To say the number of accessible microstates $W$ of the universe is ...
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### Mathematical proof of non-negative change of entropy $\Delta S\geq0$

I understand that we can prove that for any process that occurs in an isolated and closed system it must hold that $$\Delta S\geq0$$ via Clausius' theorem. My question is, how can I prove this in a ...
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### Why can't the entropy of an isolated system decrease? [duplicate]

I read that heat cannot flow from cooler body to hotter because for that entropy of the system becomes negative. Why is that so? Why we cannot have negative entropy?
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### How does the second law of thermodynamics follow from low entropy of early universe?

One of the explanations of the second law of thermodynamics is that it goes back to the low entropy in the early universe (How do you prove the second law of thermodynamics from statistical mechanics?)...
In classical thermodynamics, entropy is postulated to exist and be a monotone, convex, extensive state function $S(E,V,N)$. In statistical mechanics, the picture becomes blurrier. Let's restrict our ...