What is “move together” besides a force? And forces cause accelerations.
The usual analogy here is that of a rubber band, which owes its elasticity to an entropic force. Over long distances (so slackness doesn’t come into play) and low speeds (so the speed of sound isn’t an issue), rubber bands clearly apply a constant force that can cause acceleration.
The reversibility of the emergent force follows directly from the reversibility of the microscopic dynamics, because if you reverse that, you reverse the whole system.
That’s not a very satisfying answer. If I start with a room with hot air on the left side and cold air on the right side, after a time, the room will come to equilibrium at some middle temperature. In theory I could “reverse the whole system”, and get back to the hot and cold room. But that never happens.
On the other hand, if I have a mass at the outer point of an elliptical orbit, it naturally comes back to where it started in a way that a room’s temperature distribution never will.
But the orbit has nothing to do with the reversibility of the force—the system just happens to revisit a state it occupied previously. It’s just a periodic motion. Roughly, reversibility concerns the question of whether you can play the movie backwards as well as forwards, and have, in both directions, a physically valid process. So, reversibility of gravity means e.g. that if you have an orbit, and reverse the motion, you again will get an orbit. And this is exactly what you get out of reversing the microdynamics underlying the emergent force. Whether or not this occurs is a red herring.
Something which has absolutely nothing whatsoever to do with a force.
That has the same ring as “centrifugal force isn’t real.” If it looks like a force, and acts like a force, then we may as well call it a force.
Some entropic systems, like mixing gases, only accelerate for a short period of time. We can probably explain that by adding a friction term of some kind. Other entropic systems, like rubber bands, actually do behave like other forces (they behave very similarly to springs). And entropic explanation of gravity likewise doesn’t prohibit constant acceleration over a wide range of parameters.
And if it doesn’t look like a force nor act like a force, then we may as well not call it one. Two cars in opposite lanes of a highway may approach each other, but there’s no force, nor anything that resembles one, between them.
Sure there is: each car is exerting a force to counteract air and road friction. If you eliminated friction, the cars would accelerate toward each other and the force would be more obvious.
Again, rubber bands demonstrate the principle nicely. Stretch a rubber band, attach a weight, and it will accelerate that weight by applying a force. The force comes from entropy.
Or maybe you’re not familiar with the principles of rubber elasticity? To be clear–quoting from Wikipedia:
Maybe I’m misreading you, but it sounds as though you think entropic systems must all behave like two gases slowly drifting into each other. Not true, as rubber demonstrates.
Without friction, how exactly are the cars accelerating?
ETA: I guess you mean gravity here? But they’re approaching because they’re already approaching, not because of their miniscule gravitational attraction.
I don’t think the car analogy is really a productive one. My point was just that forces may be involved even if there’s no acceleration.
Let’s go back to the original statement under dispute:
The error Chronos made (as I see it) is the assumption that entropic systems cannot behave time-symmetrically, and therefore can’t really model gravity. I cite an idealized rubber band as a counterexample: it is an entropic system, but just like an idealized spring it can oscillate forever. Instead of swishing between potential and kinetic energy, it swishes between low-entropy/low-velocity and high-entropy/high-velocity. This operation is lossless in principle and can act time-symmetrically.
Since a rubber band can emulate a spring, and no one disputes that springs exert forces, I claim that entropic force is a real concept.
What do you mean, a rubber band doesn’t store potential energy? Of course it does.
Ok, I worded that badly. There is of course potential energy, but it is not the electromagnetic potential of the atomic bonds, the way it is with a normal steel spring. The potential is from the configuration space of the polymers–that is to say, entropy. When you stretch a rubber band, the atoms are more linearly arranged instead of jumbled. Just as a chain has only one way of being stretched to the maximum length, but many different ways if the ends are closer together (and the closer they are, the more configurations there are).
This entropic potential, if you will, is the source of the force in a rubber band. It manifests itself almost indistinguishably to forces like electromagnetism, and not at all like diffusing gases. I see no reason why an entropic model of gravity can’t have the same behavior.
But you’re not digging deep enough. Ultimately, the force exerted by a rubber band is electromagnetic. The “entropic potential” you speak of is simply an emergent phenomenon which can be used to explain why the complicated configuration of electromagnetic forces result in a bulk tension force, and it wouldn’t exist without electromagnetism. Similarly, any gravitational force “resulting from entropy” must, ultimately, be the result of the action of one or more of the fundamental forces, and thus cannot serve as the explanation for those forces.
FWIW, in my view both of these approaches to the semantics reduce things too far, given that the discussion is about what is “fundamental”.
For the first, entropy doesn’t increase on its own. A system will evolve to a higher entropy state only if there are some underlying dynamics to cause the microstate to change. Since you can usefully discuss the second law without reference to any particular underlying dynamics, it is tempting to think that you can skirt them entirely. However, even when working with the macroscopic concept of entropy you must still deal with temperature and thermal equilibrium, and the latter concept requires the presence of microscopic dynamics.
For the second, it is true that thermalization here proceeds by collisions that are mediated by a particular force, but saying that the resulting entropic force is one-and-the-same with that collision-mediating force misses the essence of the entropic force. Of note, the force is not due to a change in electromagnetic potential energy. It’s due to a change in temperature, or equivalently kinetic energy.
Are you saying that a rubber band that’s under greater tension is always at a higher temperature? Stretching or relaxing a rubber band will of course change its temperature, but if I stretch a rubber band, and then wait a long time for it to come back to the same temperature as its environment, I’ll still be able to get work out of letting it contract.
Of course not.
And it will cool as you do it, as that useful work is being sourced from the kinetic energy in the band and not from, say, electromagnetic potential energy.
Wait, I think I understand: It’s similar to a compressed gas piston, no (except with much more complicated microphysics)? Which I suppose technically means that the energy isn’t actually being stored in the rubber band itself, but rather in the environment around the rubber band.
That’s right, although just like with the PV work of the piston, an ideal rubber band doesn’t need input from the environment. It can operate adiabatically.
That’s a fair point. There has to be some kind of underlying microdynamics. They don’t necessarily need to have any similarity to the macrodynamics, though.
You could model the rubber band as a set of point masses linked by massless, arbitrarily stiff rods. Give it a bit of initial energy (i.e., heat it up), and it will want to contract. The rods are way stiffer than the system as a whole–they could even have a totally different force law (exponential, say) but it wouldn’t change much.
Likewise, the rules of the Mikado toy model don’t specify anything about attraction, but nevertheless the result is something that resembles gravity.
Like Pasta said, it doesn’t need heat from the environment, though it needs to be some finite temperature to start with. And also like the piston, it cools off as it does work, and if the temperature falls below ambient you can get a bit more work out of it if there’s heat exchange.
I considered bringing up the gas piston in the first place, but as you say, the microphysics there are much easier to understand, and you can sorta explain it as a bunch of billiard balls banging around. So I thought it wasn’t a great example of something that really demands an entropic explanation. The rubber band is much less tractable and pretty tough to explain in any other way.