# Entropy in a Black Hole: A Thermodynamic Paradox

• Bacat
In summary, thermodynamics states that the entropy of the universe will always increase, though this can temporarily decrease due to work processes. The entropy of a black hole is dependent on its event horizon, which suggests that minuscule particles with a large amount of information (Planck size nuggets) exist.
Bacat
In thermodynamics we have a law that says that the entropy of the universe must always increase, though the entropy of sub-system can temporarily decrease. This increase of entropy generally happens through work -> heat processes (ie friction). We also think of the diffusion of atoms in a disorganized way as an increase of entropy. So if I have 1 mole of gas in a box and I open the box, the gas expands freely and entropy is increased.

I was thinking about the theory of black holes the other day; the immense gravity of a black hole condenses matter so completely that light cannot escape. If this is the case, then it is reasonable to assume that matter with mass certainly cannot escape either, therefore heat cannot escape (which is transferred by the kinetic motion of matter). Therefore, a black hole condenses matter without heat loss. This seems to be a decrease in entropy (of the black hole system). But what about the surroundings?

Let a gas cloud collide with the black hole. Now the mole of gas which had expanded freely in a vacuum is condensed into a much smaller volume without heat loss. The pressure will increase so much that the gas will condense into a solid, thus we have lost 1 mole of gas. This implies a decrease in entropy in the surroundings.

$$\Delta S_{total} = \Delta S_{surr} + \Delta S_{sys}$$

So the total entropy of the universe has decreased due to the black hole, which seems to violate the second law of thermodynamics.

Can anyone shed light on this problem?

That's very interesting and I think offers a way out of the paradox. I appreciate the time you took to write all of that out and now to have linked to it. It looks as if Hawking Radiation manages to re-balance the entropy so that thermodynamics still hold.

Do you have information critical mass and the expansion of the universe also?

Cheers.

There are all sorts of interesting implications...black holes have maximal entropy (in a given region of space) while the other major singularity, the big bang, has low entropy. I just know there is something that hasn't been fully appreciated yet.

Further, since the entropy of a black hole is proportional to its event horizon (rather than its volume) that leads into the holographic principle as well as a minimal size to space...suggesting Planck size nuggets of one Planck unt area carry one unit of entropy (information).

## 1. What is entropy in the context of a black hole?

Entropy is a measure of the disorder or randomness in a system. In the context of a black hole, it refers to the number of possible microstates that can describe the black hole's internal structure.

## 2. How does entropy increase in a black hole?

In accordance with the second law of thermodynamics, entropy always increases in a closed system. As matter falls into a black hole, the black hole's mass and surface area increase, leading to an increase in entropy.

## 3. Why is there a thermodynamic paradox in black holes?

The thermodynamic paradox in black holes arises from the fact that their entropy (which should always increase) is actually proportional to their surface area, which remains constant. This seems to contradict the second law of thermodynamics.

## 4. What is the resolution to the black hole entropy paradox?

The resolution to the black hole entropy paradox comes from considering the quantum nature of black holes. In quantum theory, black holes are thought to have a finite temperature and emit radiation, known as Hawking radiation. This radiation carries away entropy, allowing the black hole's entropy to decrease over time and resolve the paradox.

## 5. How does the concept of Hawking radiation affect our understanding of black hole thermodynamics?

The concept of Hawking radiation has a significant impact on our understanding of black hole thermodynamics. It provides a mechanism for the decrease of black hole entropy, allowing it to be consistent with the second law of thermodynamics. It also connects black hole thermodynamics to quantum theory, which is essential for a complete understanding of these mysterious objects.

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