How do we explain the motion of a time-reversed emptying balloon in vacuum? Imagine a balloon filled with air, let loose in outer space. There is an imbalance of pressure pushing to the insides of the balloon, and this imbalance is the motor of motion. There is no pressure in the area of the open mouth, and the balloon moves in the direction of the opposite closed side.
Now we inverse all motion. It's quite complicated in practice, I would say even impossible (to say the least!) but it can be done in the mind. Of course it's impossible to reverse all motion in the universe but locally it can be done, though it can be questioned then where the reversed system "ends". Note that this problem touches upon the problem of time, irreversibility, begin conditions, etc. Entropic time, irreversible processes, have begin conditions, while the reversed processes have not (well, at infinity, which is the same). A time reversed universe conspires towards a very specific end state. I don't want to discuss the nature of time though, but merely posit the balloon grows in size while air flows in. Its speed is reduced until it stops where it started when time went forward. How do we describe this motion? With differences in pressure, just as in the forward case?
 A: To time reverse that scenario, you would reverse the direction of every atom. You would be very precise about it so that as all the atoms in the escaping air precisely follow their trajectory in reverse as they bounce off atom after atom. Even the slightest error in direction or speed would mean the next collision would bounce at a different angle, and the one after that wouldn't happen.
The initial condition you would reverse would be the atoms flying away from the balloon to the left and the empty balloon flying away to the right. You would reverse them so they are flying toward each other.
If you did that reversal, you would have arranged everything just right for an astonishing "coincidence". Atom after atom would wind up flying into the opening of the balloon at high speed until none were left outside. They would have enough momentum to slow the balloon and themselves to a stop as they filled it, and enough energy to stretch the balloon.
If you did a less precise reversal, the odds are overwhelming that you would see something different that you might explain with ordinary fluid dynamics. A cloud of atoms would fly into a balloon. A few would fly into the opening, but most would bounce off each other into an expanding and increasingly dilute ball of gas. The pressure would rapidly approach $0$. Those atoms that did hit the balloon would slow it. This could be explained with pressure and velocity of the gas.
A: A cloud of gas and an empty baloon move towards each other, they collide in a way that particles go against the pressure gradient in the baloon's opening, which is very unlikely statistically. Gas cloud gets warmer as it is getting more dense inside the baloon, as more gas particle collision happen per time. At the end all the gas molecules appear inside the baloon, and momentum of the gas cloud and baloon are cancelled out, both objects appear to be not moving, in the center of their mass.
It cant be explained with things like pressure, as it relies on the forward motion of time. To explain this in time reverse you will need to get down to motion of separate particles - that this cloud of gas consist of particles that just so happen to be directed in a way to hit the baloon's opening.
Emergent properties of many particles such as pressure, heat, require forward moving time to work. Without it only physics that works is the one on a scale of separate particles.
A: It's simple: since you reversed the motion of all the atoms of escaped gas, they are now converging at the mouth of the balloon. This creates an area of high-pressure gas, which inflates the balloon.
There is one thing about this that looks strange. The pressure inside the balloon is higher than the pressure just outside it, yet the gas is flowing into the balloon, not the other way. But this can be explained too. It's because the incoming gas has a high kinetic energy - it's already flowing rapidly towards the balloon when it arrives. The pressure gradient is slowing it down, but it isn't quite enough to overcome the inertia of the incoming gas, not until the very moment when the balloon is fully inflated. (In forward time, this corresponds to the moment when the mouth was first opened.)
Generally, in reversed time, the second law of thermodynamics is reversed, but the laws of mechanics are exactly the same. This means that quantities like pressure (in the sense of force per unit area) are perfectly meaningful and behave exactly as they do in forward time, despite what another answer says.
If the example had included an entropic process like heat flow or diffusion then it wouldn't have been possible to tell a consistent story in the same way. If you were to let two fluids diffuse into each other and then reverse time, you would observe them spontaneously separating, and it wouldn't be possible to explain that thermodynamically.
A: One has to take into account the interaction between pressure and the rate of change of momentum and density of the gas. Consider a different scenario with similar properties that perhaps will not invoke the ire of those who worry about the increase in entropy.
A cylinder is filled with a uniform gas such that the molecules have a local mean velocity toward one end of the cylinder. One can expect that the momentum of the molecules will be gradually exchanged for pressure as the molecules move toward one end of the cylinder. This is not entirely distinct from the situation of a horizontal cylinder of gas being rotated to the vertical in a gravitational field.
But, it can also be achieved in practice by observing, in the frame of the car, a cylinder of gas that is in a car that briefly accelerates. The molecules of the gas in the cylinder have a momentum now. They will push toward the end of the cylinder, and eventually the extra energy in that reference frame will be converted into heat and the cylinder will move back to a uniform pressure.
Ignoring the practical improbability of setting up the reversed balloon scenario, the description - including the mathematics of the fluid flow - simply takes into account the initial momentum distribution of the molecules, density, and pressure, and the result will be a full balloon. At which point, if you keep playing the simulation - the balloon will exhale.
A: This question is closely related to the so-called Feynman sprinkler problem, but with the complication that, in vacuum, the experiment is impossible.
In the sprinkler problem, some number of L-shaped pipes are connected to a hose at a joint which is allowed to swivel.  If water runs out the hose and out the pipes, the momentum of the escaping jets causes the assembly to spin.  This type of water-powered motor is commonly used to irrigate lawns and amuse children.  The question associate with Feynman (but going back at least to Mach) is what happens if you put the sprinkler head underwater and run it backwards.  Does time reversal symmetry make it run the other way?  Or does the impact of the incoming water against the corners of the L-shaped pipes mean the sprinkler turns the same way regardless of the direction of water flow?
The experimental result of the reversed-sprinkler problem seems to be that the effects cancel out.  Apparently the head undergoes a “tremor” when the flow begins, but does not experience steady-state rotation in either direction.
There’s a long tradition in physics of impractical thought experiments.  But your thought experiment here is impossible.  A low-pressure chamber containing a high-pressure balloon has less entropy than a medium-pressure chamber containing an empty balloon, so the balloon-emptying transition happens spontaneously.  The balloon-filling transition does not happen spontaneously, and any question you have about its momentum exchange is going to be sensitive the mechanism you’ve used to deal with the second-law violation.
If you start with a movie of a balloon emptying and just run it backwards, time-reversibility demands that momentum is still conserved, which you can verify by examining every gas-molecule collision.  But in your reversed movie, you can still confirm the pressure inside the balloon is higher than the pressure outside the balloon.  Pressure-driven flows are fundamentally entropy-driven flows.  When a real balloon is filled, it’s because the pressure on the inside is lower than the pressure on the outside.
If you are a human person, you have almost certainly filled and emptied a balloon several times while reading this:  your lung system, using the muscles in your torso.  (“That’s not a high-pressure balloon!” you protest.  But if you can fill a balloon, it’s because you temporarily made the pressure in your lungs higher than the pressure in the balloon.  Puff out your cheeks: ta-da, your internal high pressure has overwhelmed the strength of your facial musculature.)  You can certainly propel yourself by blowing out, even though that propulsion is much less dramatic than a low-mass rubber balloon without a high-mass human body attached to it.  Do you also propel yourself in the opposite direction by breathing in?
In the realm of Youtube physics debates, the question of whether air intake has any associated thrust, and how that intake thrust compares to the more obvious thrust from an exhaust jet, takes the form of debates about

*

*whether you can power a skateboard with a leaf blower (almost certainly),


*whether you can reverse the thrust direction by pointing the leaf blower at an umbrella (probably not as pictured, but)


*whether the leaf-blower-plus-umbrella is conceptually different from the thrust reversers on jet aircraft.
