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Any black body in space radiates and ends up very cold, might even crystallize. The law of increasing entropy holds for closed systems, in this case the whole system: "all the radiation that left the black body + the black body itself" microstates. In the sense that a black hole behaves as a black body the same holds true, it cannot be considered a ...

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Then the number of microstates corresponding to this macrostate should be 1 (since all the particles are identical). The particles may be identical (have the same intrinsic physical properties), but that does not in any way mean that they are not distinct. It is most natural to assume the particles are distinct (they can be placed to different places, ...

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No, black holes do not violate the 2nd Law of Thermodynamics. Imagine that we want to violate the 2nd Law of Thermodynamics by throwing some volume of ideal gas into a black hole. This would seem to violate the 2nd law because when it is outside the black hole the ideal gas contributes some calculable amount of entropy to the total entropy of the universe. ...

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Entropy is not a force, no. It is a "chaos factor", if you will. The more entropy, the less structured a system is. A system will always move towards the state that is most probable. The most probable state (macro-state) will be the state with most micro-state configurations. Consider as an example four coins of heads H and tails T. Flip them and you can ...

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Edit: Looks like Steeven beat me to it with a similar explanation, but I'll leave mine here for posterity. Entropy is just a property of a system (in a given state), in other words a state function. I hope that by elaborating on the statistical interpretation of entropy you will gain some intuitive notion of the meaning of entropy. Consider the following ...

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It's a simple permutation problem. Suppose there are $N$ distinguishable particles. Let $n_L$ be the number of particles distributed in the left & $n_R$ distributed at the right compartment. First of all, you are to select a particle for the first place of $N$ places. How many ways can it be done? It can be done in $N$ ways; now the second place can ...

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