Synchronicity is Improbable
This is a different way of describing Roger Vadim's answer, but hopefully it will help. Imagine a billiard table. With a single ball, it is easy to imagine typical scenarios of motion, and their reversals. With two balls, it is also fairly easy to imagine that time-reversal is effectively impossible to detect (especially if the table is infinitely large). However, once there are 3 balls on the table, something special happens: there are now a large number of typical, common scenarios whose time-reversal is manifestly unlikely. The simplest one to imagine is when two balls are sitting at a location touching, and a third ball strikes them at the same time, coming to a stop and transferring all its momentum to the targets, which fly off at angles away from each other. There is nothing special about this scenario, until you try to run it in reverse. The reason you will suspect that the inverse scenario is backwards-time is because it is extremely easy to push one ball into two, but it is extremely difficult to time two balls to collide with a single ball, transferring all their momentum to it. This requires exquisitely precise timing and positioning. While any regular at your local pool hall can set up the forward scenario with ease, the reverse may be nearly impossible even if you get two professional billiards players to cooperate on it.
Improbability Grows Exponentially
As the number of objects in the system increases, the number of these improbable sequences goes up exponentially, because each new object can multiply the number of existing improbable sequences. Thus, when we are talking about "microscopic" vs "macroscopic" scales, really, we are talking about fundamental particle number. And once you get to 3, you are basically already in the "macroscopic" realm.
Now, you may not have noticed it, but the 3-billiard ball example above is a simplified model of the sliding wood-block example. The initially moving ball is the wood block, and the initially static balls are the desk. Their final motion is "heat". If we increase the number of target balls to a standard 15 ball pool rack, the number of possible outcomes quickly becomes intractable. And yet, they are all consistent with a general idea of: "moving object dissipates kinetic energy into heat via friction". But what should we make of the time-reversal of these traces? Technically speaking, they are possible! A universe in which one of them occurs does not automatically invalidate QM. But if all possible traces are equally likely, then it is easy to see why we don't observe blocks of wood spontaneously sliding around desks from a concentration of local thermal energy. Obviously, the number of ways for the collision to go forwards is much larger than the number of ways for it to run backwards...or is it? After all, we can just reverse all the momentum arrows, so the forward and backward traces should be equal in number, right?
Instead of the block sliding on wood, imagine that it is in space, and drifts into a gas cloud. If the cloud is big enough (or the momentum is small enough), the block will eventually dissipate all its KE into the cloud as heat (it will raise the temperature of the gas cloud). Now, the time-reversal would be for a gas cloud to have a block of wood, then spontaneously eject it in some direction, while simultaneously cooling.
To pinpoint exactly why the forward scenario is boring, and the backwards is magical, we just need to look at two states: one where the block is outside the cloud with momentum, and one where the block is inside the cloud with no momentum. These are the macrostates of interest. If we are told that these states are causally connected and asked which comes first, our intuition will tell us that the block moves from outside in. But does the math tell us that?
Yes. Yes, it does. As the block moves towards the gas cloud, the cloud just sits there being warm: its constituent particles are bouncing around randomly, not changing the temperature of the gas by a meaningful amount (we presume that in both states the gas is in thermal equilibrium, or close enough). Once the block hits the gas, there are many, many ways for the gas to absorb its momentum and convert it to heat (convert the unified momentum of the block into the randomized momentum of the gas molecules). However, there are only a few ways for the thermal motion of the gas molecules to conspire to push a static block out of the gas.
Again, we need to start small. If we just consider a single gas molecule that hits the block, the probability that it will push the block towards the external end state instead of away from it is 50%. But if we look at two molecules which hit the block, there are several possibilities:
- Both molecules push the block towards the external state
- Both molecules push the block away from the external state
- The molecules tend to cancel each other out
Because of the high-dimensional nature of the momentum space, it is not trivial to give the precise probabilities for each outcome, but hopefully it is clear that even with just two gas molecules, there are more ways for the external state to not happen than there are for it to happen. And each additional molecule that we add to the computation reduces the probability of case 1 and increases the probability of case 3.
So even though every microstate which leads from the external moving block to the internal static block is individually reversible, there simply aren't enough of the reversed states for this outcome to be likely. The vast majority of microstates correspond to the gas molecules hitting the block randomly with a near net-zero force. These swamp the comparatively tiny number of states in which the gas molecules are synchronized in their momentum to push the block out of the cloud.
Low-Entropy States are Few
Ultimately, the improbability of time-reversed processes doesn't really depend on much physics at all. It can all be deduced mathematically using statistics. If we take a finite sequence of integers, and permute it randomly, what are the odds that all the numbers in the first half will be smaller than all the numbers in the second half? It's not large, but also not absurdly tiny. It only requires a fairly coarse-grained sorting function to achieve this (gravity operating on rocks in a gently-shaken bucket will suffice). But what is the probability that the sequence will become strictly ascending? Well, there is only one way for that state to occur, no matter how big the list is. Which means that the bigger the list, the more improbable this state becomes. This would correspond to a minimum-entropy state in a physical system. The probability of the system entering this state from a random walk becomes inconceivably small as the size of the list gets large (especially if the transition function is not a global permutation, but rather a bunch of local permutations, so that it takes a while for a number to move from one end of the list to the other).
Now, what is the probability of a state in which the largest number occurs after the smallest number? It's easy to see that virtually every microstate occurs in this distribution, making this macrostate very high-entropy.
The macrostate in which the thermal motions of gas molecules produce a consistent net force on a block is extremely low-entropy, because there are only a tiny number of microstates which can produce this macrostate. The vast majority of macrostates will produce a net zero force, for the same reason that most random shuffles of a card deck will not deal you a straight flush in a game of poker.
All we need to know to obtain this statistical result is that thermal motion is effectively random. Since random walks toward a low-entropy state are highly improbable, the shape of the state transition space itself effectively defines the arrow of time. Random processes tend to push systems towards the most heavily populated macrostates, not the least-populated. And those macrostates are the ones which look like "boring thermal equilibrium", not "objects shooting spontaneously out of a static cloud".