No, it isn't. In the presence of gravity, a system of matter uniformly spread out with no variation in density has lower entropy than a system of matter clumped together into gravitationally bound objects. That is because the number of ways for the same amount of matter to be clumped together into gravitationally bound objects is much larger than the number of ways for that matter to be uniformly spread out with no variation in density.jeffinbath said:that is an example of a high entropy system becoming a low entropy system
Am I drastically oversimplifying by interpreting this thusly:Ken G said:Generally speaking, a good way to track entropy is to start with a situation where there is no change of entropy as a point of comparison. The situation where entropy does not change is any reversible change to a system that also has no net heat being exchanged with its environment. So that would be a gradual contraction in force balance with no heat being lost, which is something that basically does not happen (if it is in force balance, why would it contract unless there was heat being lost). So when you do see gravitational contraction, it is either happening out of force balance so is irreversible (and entropy increasing), or if it is in force balance (as with most astronomical objects), there is heat being lost to the environment (often in the form of thermal radiation emission). So when you see an object in force balance losing heat to its environment spontaneously, you pretty much know entropy is increasing there, by asking what it would need to look like for entropy to stay the same.
The system itself that is emitting heat would lose entropy because of the lost heat, but the heat wouldn't be lost if it wasn't going somewhere with even lower temperature, so the entropy rise elsewhere more than compensates for the loss to the system.DaveC426913 said:Am I drastically oversimplifying by interpreting this thusly:
- A system that is emitting heat is likely (must be?) increasing in entropy.
Yes, if it's only doing reversible things, which pretty much means is in force balance. Most astronomical systems are in a very good force balance, because free fall timescales are generally much faster than the system is really changing.DaveC426913 said:
- A system that is not emitting heat is likely (must be?) not be increasing in entropy.
Think the system and its environment. Entropy is rising if heat is being is being transferred from a higher to a lower temperature.DaveC426913 said:And the corollaries:
- A system that is increasing in entropy likely (must be?) emitting heat.
If you just look at the system, then to not change its entropy, you need it to be in force balance, and also not exchanging heat at all with its environment. But what matters is the entropy of the system and its environment. If the environment has the same temperature as the system, then heat exchange in either direction won't change the total energy. So for example in a Carnot cycle, you maintain force balance, and you make sure everything is reversible by making sure the system always exchanges heat with an environment that is at the same temperature as the system. But that requires careful engineering not present in astronomical systems, and in the latter there is usually either a pretty significant temperature difference (like the Sun and deep space), or a pretty significant departure from force balance (like a giant molecular cloud collapsing into forming stars). Those are the (total) entropy generating mechanisms that gravity creates, even though gravity is reducing the spatial volume that the system occupies.DaveC426913 said:
- A system that is not increasing in entropy likely (must be?) not emitting heat.
I must be, or you woulda said that.
It's the other way around, isn't it? The gain from momentum uncertainty is less than the loss from position uncertainty.Ken G said:particles move to higher momentum when they fall in towards each other, so gain in momentum space the states they lose in physical space. But in actual practice, the increase in the former exceeds the decrease in the latter
It's not so much an issue of the uncertainty principle, that's what sets the phase space volume of a single state, which is the reason the number of available states is proportional to the phase space volume. So whether the entropy rises or falls just depends on the phase space volume that each particle can access, and that depends on how the contraction occurs. If we want the system itself to not change entropy, we must make it reversible, so it has to stay in force balance, which means it will obey the virial theorem. Nonrelativistically, that means the internal kinetic energy will be half the (absolute value of) the potential energy. But if heat is not being lost (and no other changes are going on), the gained internal energy will equal all of the increase in (the absolute value of) the potential energy, not half of it. So requiring no heat exchange with the surroundings precludes the system from being in gravitational force balance.Bandersnatch said:It's the other way around, isn't it? The gain from momentum uncertainty is less than the loss from position uncertainty.
No. In the presence of gravity, "thermal equilibrium" in the sense of the matter or radiation being equally spread out everywhere at the same temperature is not high entropy. It's low entropy, because there's no gravitational clumping.timmdeeg said:the CMB represents a tiny patch of space which has been in thermal equilibrium before inflation and has been in a state of high entropy then
Ah I see, thanks for clarifying.PeterDonis said:No. In the presence of gravity, "thermal equilibrium" in the sense of the matter or radiation being equally spread out everywhere at the same temperature is not high entropy. It's low entropy, because there's no gravitational clumping.
Gravity does not directly defy the 2nd Law of Thermodynamics. Instead, it is a force that acts upon objects and can cause them to move in a way that appears to contradict the 2nd Law. However, when taking into account all the factors and energy exchanges involved, gravity obeys the 2nd Law.
An example of this is a ball rolling up a hill. According to the 2nd Law, energy should be lost in the form of heat as the ball moves up the hill. However, the force of gravity is able to overcome this loss of energy and pull the ball up the hill, seemingly defying the 2nd Law.
Entropy is a measure of the disorder or randomness in a system. The 2nd Law states that the total entropy of a closed system can never decrease. In the case of gravity, the force acts to decrease the entropy of the system by creating more order and structure. However, the overall entropy of the universe still increases, as the energy used by gravity is ultimately lost in the form of heat.
No, it is not possible for gravity to truly defy the 2nd Law. The 2nd Law is a fundamental law of physics that has been extensively tested and has never been found to be violated. Any apparent violations can be explained by taking into account all the factors and energy exchanges involved.
Energy conservation is a fundamental principle in physics that states that energy cannot be created or destroyed, only transformed from one form to another. In the case of gravity, energy is conserved as it is transferred from the potential energy of an object to its kinetic energy as it falls. This transfer of energy obeys the 2nd Law of Thermodynamics, as the total energy remains constant and entropy increases.