How do we physically reverse a classical wavepacket? Imagine a classical dispersive Gaussian wavepacket (GW). In a wonderful answer by @Qmechanic, to this question (who seems to do much tagging these days, with an occasional well-aimed-and-hit answer), it is shown that the time-reversed GW in quantum mechanics is both forward and backward dispersing in time, if I understand him correctly (though I don't believe this is the case if we take hidden variables into account). A classical GW will get narrower in reversed time though.
Can we compare this situation with a gas spreading out when released in a vacuum? In other words, is it physically impossible to reverse the evolving classical GW in time? Is this a case of entropic time asymmetry?
 A: You prepare a wave packet in an initial state by setting initial conditions. To prepare a time reversed wave packet, choose different initial conditions.
For example a photon in a laser. You set up an excited medium in a cavity bounded by mirrors and let whatever photons get emitted bounce back and forth. Those that happen to match the cavity's modes get bounced back through the excited medium and stimulate more photons to be emitted in that same cavity-matching state. One of the mirrors is mostly reflective, but slightly transparent, so a small fraction of the photons escape. If all goes well, you have prepared a nice Gaussian Beam, say pointed to the right.
To prepare a time reversed packet, you get another laser and point it to the left. You get another ordinary laser beam traveling forward in time, but it looks just like the first would if it were traveling backwards.
It gets harder for an ordinary macroscopic object. You might mean a wave packet that describes a single atom, or perhaps a wave function that describes the entire object. Either way, you have a lot of work to do.
Say you blow up a balloon,  and let it fly around the room. Most wave packets don't follow trajectories that look normal when time reversed. Typically they start from states that are very unlikely to be arrived at by atoms flying around at random. They start in a more ordered state than they end up in. Atoms don't just fly into a balloon. They have to be put there. The odds are overwhelming that they will fly out of the balloon and mix with the room air when the balloon is released. There are a huge number of ways they can mix.
To prepare a time reversed wave packet that follows the trajectory requires choosing an instant and finding the position and velocity of all the atoms from the balloon and the room. You need to set up initial conditions where  they are all are aimed exactly backwards along their trajectories at exactly the right speeds. Atoms got to their current position by bouncing off atom after atom after atom. A time reversed packet would follow its trajectory backward through bounce after bounce until all of the balloon air was back in the balloon and all of the room air was outside.
You have to be extremely precise. The slightest error means that the first bounce would be at a different angle and the second bounce wouldn't happen. The uncertainty principal prevents you from aiming so precisely, so you can't really do it.

A time reversed object brings up deep questions about the nature of time.
For a macroscopic object, causes come before effects, and not the other way around. For microscopic objects, atoms look the same bouncing off each other forward or time-reversed. How does the asymmetric macroscopic world emerge from the symmetric microscopic world? Is the flow of time really just determined by probability?
It appears that it is.
For a balloon flying normally, the nozzle jerks around randomly, which causes the balloon to fly around in a complicated way. In a time-reversed balloon, these former causes are now in the future from their former effects. How does that work?
For a time-reversed balloon, the jerks of the nozzle are effects caused by precisely arranging the trajectories of lots of atoms so they arrive just when the nozzle does at just the right speed and direction to give it just the right reverse jerk.
It doesn't violate any law of physics for all these atoms to follow a reverse trajectory and wind up in a low probability final state. But the odds are so far against it happening by chance that you will never see it. We are safe in treating a low probability ordered state as the cause of whatever disordered state they wind up in. The vast majority of these disordered states look the same to us. So the odds are overwhelming that cause will proceed to effect, and time will flow forward.
