# Does gravity tend to decrease the entropy?

• B
Gravity tends to make ordered structures of free particles. Does this mean that gravity is decreasing the entropy of these particles, or is there some compensating mechanisms in order to let the entropy increase (for example the emergence of gravity waves, though I doubt that's enough to compensate.

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Stephen Tashi
Gravity tends to make ordered structures of free particles. Does this mean that gravity is decreasing the entropy of these particles, or is there some compensating mechanisms in order to let the entropy increase (for example the emergence of gravity waves, though I doubt that's enough to compensate.
Shannon entropy is defined in scenarios that involve probability. Thermodynamic entropy is defined for gases in equilibrium conditions and this theory is developed using concepts of probability and statistics. If you are thinking of a set of particles that begin in particular positions and follow some deterministic law as gravity affects them , then you'll have to reveal what definition of entropy you have invented for such a set of particles before the question can be answered.

If you are thinking of the the particles in terms of a probabilistic model (e.g. a "gas" as a representation of many possible particular locations and velocities of the particles) then I think you should include a probabilistic representation of the earth to analyze the whole system. One possibility is that as you get less dispersion in the probability distribution for the particles, you get more dispersion in the probability distribution for the position and velocity of the earth. And to be democratic, you should consider the probability distribution for the position and velocity of each of the "particles" that compose the earth. I'm not making the bold assertion that I've actually made such a calculation and shown that entropy increases; I'm just suggesting that this type of analysis might show an entropy increase.

• Ilguercino
Khashishi
Penrose believes [based on what he has written in the road to reality] that gravitational entropy (on a cosmological scale) is highest when matter is in scattered clumps. When gravity pulls clumps of matter together, the gravitational entropy supposedly increases more than the entropy due to gas decreases. It is a hard problem, and I don't think there's a clear answer yet.

Khashishi
If you are talking about a small scale experiment, rather than the universe, then gravity is just a force like any other. You need to look at the total entropy change in an experiment, not just one part. You could make an analogy with the electromagnetic force, which is responsible for allowing chemicals to form, and for them to condense into solids and liquids. A solid is a lower entropy phase than a liquid. But when a liquid freezes into a solid, energy is released into the surroundings, increasing the entropy of the surroundings. The liquid will only freeze if the ambient temperature is below the freezing/melting point. If you look into the thermodynamic definition of temperature, this means that the liquid will only freeze if the energy released by the solidification will increase the entropy of the environment more than the decrease of entropy in the solidification.

Now, apply this same thought to gravity. Clumps form in a nebula and accrete into solar systems. But this must release energy, since the gravitational potential energy has decreased. The solar system is more ordered, but the energy increases the entropy elsewhere. It's only possible for these clumps to form if the temperature is low enough.

Consider the extreme: black holes. Black holes have an opposite temperature-energy relationship to most things. When you add energy to a black hole, the temperature goes down. Black holes of macroscopic size have very low temperatures. Temperature determines the direction which energy must flow to increase the entropy. Since the black hole is colder than the surroundings, total entropy increases as you feed matter into a black hole. (Energy flows spontaneously from hot to cold.) The surroundings get colder as it loses energy, but the black hole also gets colder as it gains energy, so the black hole will continue to eat up all the energy in the universe until there is very little energy left outside black holes. This is perhaps the state of maximum entropy. But who knows what dark energy does to the equation?

anorlunda
Staff Emeritus
A cloud can't collapse gravitationally unless it can radiate it's energy away. For example, a dark matter halo doesn't collapse to the galactic center precisely because it is dark.

So you must include the radiated energy as part of the system.

Stephen Tashi