Q:

http://www.physlink.com/Education/AskExperts/ae213.cfm

These guys say that a closed system with significant gravity can lower its entropy, via "negative energy", violating the Second Law of Thermodynamics.

- Mike W

These guys say that a closed system with significant gravity can lower its entropy, via "negative energy", violating the Second Law of Thermodynamics.

- Mike W

A:

That's completely wrong. In the classical case, the potential energy lost as things clump gravitationally is converted largely to thermal energy, increasing entropy. That's just like any other energy conversion process. In more extreme General Relativistic cases, the clumping can produce a black hole. The black hole entropy is larger than that of whatever ingredients went into it, again obeying the Second Law. If the black hole then evaporates via Hawking radiation, the radiation has larger entropy than the black hole, again obeying the Second Law.

Perhaps the authors got confused by a peculiar property of gravitationally bound thermal systems- a negative heat capacity. That means that these systems are never realy in thermal equilibrium. But that's another discussion.

Mike W.

*(published on 10/18/2011)*

Q:

The entropy of a classical Black Hole (BH) is proportional to the area of its spherical horizon. If it is created by the combination of two BHs, it is evidence that the resulted BH will have less entropy than the sum of the entropies of the two smaller BHs it is created from. The radiation resulted from this combination is emitted from the space outside BHs' horizons and not by BHs themselves.

- Hadjidakis (age 67)

hellas

- Hadjidakis (age 67)

hellas

A:

The area of the black hole event horizons is proportional to the *square* of the mass. So a merger of two black holes increases the area and thus the entropy. The loss of energy due to gravitational waves is not enough to make the net area decrease. So even aside from the entropy of the waves, the BH entropy increases.

Mike W.

*(published on 02/17/2017)*