Entropy and Black Holes: Understanding the Second Law of Thermodynamics

In summary, the conversation discusses the relationship between the entropy of a closed system and the presence of a black hole at its center. The second law of thermodynamics states that the final entropy (S2) must be greater than or equal to the initial entropy (S1). However, in the presence of gravity, a large number of particles uniformly distributed will have a lower entropy than when they are clumped together. This leads to the question of whether S1 < S2 or if the creation of new particles during radiation causes S2 to be greater than S1. It is determined that the end entropy is approximately 4/3 times the initial entropy, with the answer being discovered by W. H. Zurek in 1982
  • #1
jmcmahon
3
0
I am a little confused over something, so perhaps someone can tell me which one of the following statements is incorrect. (I don't know a lot about this, so forgive my ignorance).

Suppose that we have a closed system of some size, and we start in a state where we have a black hole at the center. So there is some entropy S1 at our initial condition. Now we let the system evolve and the black hole starts radiating and losing mass. At some point very far in the future the black hole radiates completely away and we are left with a lot of particles that are distributed (uniformly?) throughout our system. Our final condition here has some entropy S2. The second law of thermodynamics says that S2 >= S1. However, it was my understanding that in the presence of gravity a large number of particles uniformly distributed will have a lower entropy that when they are clumped together (like our original black hole). So it seems like S1 < S2. Or are so many particles created during the radiation that S2 > S1?
 
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  • #2
It looks like Zurek figured out the answer some time ago. The answer is that the end entropy is ~4/3 times the initial entropy.

For anyone else interested in this, see W. H. Zurek, Phys. Rev. Lett. 49 1683 (1982).
 

1. What is the Second Law of Thermodynamics?

The Second Law of Thermodynamics is a fundamental principle in physics that states that in any natural process, the total entropy of a closed system will always increase over time or remain constant. This law is important because it explains why certain phenomena, such as heat flow, occur in one direction and not the other.

2. How does entropy relate to the Second Law of Thermodynamics?

Entropy is a measure of the disorder or randomness in a system. The Second Law of Thermodynamics states that the total entropy of a closed system will either increase or remain constant. This means that in any natural process, the amount of disorder in a system will always increase or stay the same.

3. Why do black holes have such high entropy?

Black holes have a large amount of entropy because they have a very high gravitational pull that traps matter and energy inside their event horizon. This means that the particles inside a black hole are highly disordered and have no way of escaping, thus increasing the total entropy of the system.

4. How does the Second Law of Thermodynamics apply to black holes?

The Second Law of Thermodynamics applies to black holes in two ways. First, the formation of a black hole can be seen as an increase in entropy, as the matter and energy that make up the black hole become highly disordered. Second, the evaporation process of black holes, known as Hawking radiation, also follows the Second Law, as the entropy of the black hole decreases over time.

5. Can the Second Law of Thermodynamics be violated by black holes?

No, the Second Law of Thermodynamics is a fundamental law of the universe and cannot be violated. While it may seem that a black hole violates this law by decreasing its entropy through Hawking radiation, this process actually increases the entropy of the universe as a whole, thus following the Second Law.

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