Maximum Entropy: Black Hole

In summary, The conversation discusses the relationship between black holes and entropy, specifically in regards to Hawking Radiation. The question is raised about how Hawking Radiation occurs from a thermodynamic standpoint, given that a black hole contains the maximum amount of entropy. It is suggested that this may be due to the entropy bound of a black hole only applying to a bounded region of space, while Hawking Radiation occurs at infinity.
  • #1
TriTertButoxy
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I originally posted this question in the subsection "Beyond the Standard Model." Unfortunately, nobody replied. Hopefully, someone here might be more insightful.

I read somewhere that a system consisting of a single black hole contains the maximum possible amount of entropy represented by the mass of the black hole. The third law of thermodynamics says that entropy must increase, in general, for all processes.

So, suppose I consider the Hawking Radiation -- the process by which Black Holes evaporate. If the black hole contains the maximal amount of entropy, how does Hawking Radiation occur from a thermodynamic standpoint?
 
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  • #2
I guess that the point is that the entropy bound given by the entropy of a black hole (the Bekenstein bound) refers to a bounded region of space. The detection of Hawking radiation, on the contrary, occurs "at infinity".
 
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  • #3


First of all, it's important to note that the maximum entropy of a black hole is not a constant value, but rather depends on the mass and other properties of the black hole. This maximum entropy is known as the Bekenstein-Hawking entropy and is given by the formula S = kA/4, where k is the Boltzmann constant and A is the surface area of the black hole.

Now, the third law of thermodynamics states that entropy must increase or remain constant in all processes, but it does not specify the rate at which it must increase. In the case of a black hole, the entropy increases due to the absorption of matter and energy, but it also decreases through the process of Hawking radiation.

Hawking radiation occurs when pairs of particles are created near the event horizon of a black hole, with one particle falling into the black hole and the other escaping as radiation. This process decreases the mass and therefore the entropy of the black hole.

So, from a thermodynamic standpoint, the total entropy of the system (black hole + surrounding environment) is still increasing, even though the entropy of the black hole itself may decrease. This is because the escaping radiation carries away information about the black hole, thus increasing the total entropy of the system.

In summary, the maximum entropy of a black hole does not prevent Hawking radiation from occurring. The third law of thermodynamics is still satisfied, as the total entropy of the system continues to increase.
 

1. What is maximum entropy in relation to black holes?

Maximum entropy is a concept in thermodynamics that relates to the amount of disorder or randomness in a system. In the context of black holes, it refers to the maximum amount of entropy that can be contained within the event horizon, which is the point of no return for matter and energy falling into the black hole.

2. How does maximum entropy relate to the information paradox of black holes?

The information paradox of black holes refers to the conflict between the laws of thermodynamics and quantum mechanics in regards to what happens to information (or entropy) when it falls into a black hole. Maximum entropy plays a role in this paradox because it suggests that all information that enters a black hole is lost, as the maximum amount of entropy within the black hole cannot be exceeded.

3. Can maximum entropy be used to calculate the size of a black hole?

Yes, maximum entropy can be used to calculate the size of a black hole. This calculation is based on the assumption that the maximum amount of entropy within a black hole is proportional to its surface area, rather than its volume. This relationship is known as the Bekenstein-Hawking formula.

4. How does the concept of maximum entropy apply to the Hawking radiation of black holes?

Hawking radiation is the process by which black holes emit radiation due to quantum effects near the event horizon. Maximum entropy plays a role in this process because it suggests that the radiation emitted by a black hole contains all the information that has fallen into it, and thus decreases the entropy of the black hole.

5. Is there a maximum limit to the entropy that can be contained within a black hole?

The concept of maximum entropy suggests that there is a limit to the entropy that can be contained within a black hole, which is proportional to its surface area. However, this limit is theoretical and has not been definitively proven. Some theories, such as the holographic principle, propose that the maximum entropy of a black hole may be related to the amount of information encoded on its event horizon.

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