The question of why we cannot reverse the flow of time is often linked to the second law of thermodynamics, which asserts that entropy within an isolated system—like our Universe—cannot decrease.

But what exactly is entropy? Simply put, it refers to the number of possible microscopic arrangements that a collection of elements can form when they come together to create a macroscopic entity.

The total number of configurations is dependent on both the quantity of elements and the various ways they can be arranged. This principle applies universally, whether the elements are atoms, playing cards, or data. It fundamentally relates to the degree of order (or disorder) within a system.

For instance, if we have an automatic mechanism that randomly places three coins into three boxes, how many distinct arrangements can it produce? By conducting a few tests, we find that there are exactly ten ways to distribute them: three where all coins are in one box (A, B, or C); two with two coins in one box and one in another; and one where each box contains one coin. In total, this results in 3 + 2 + 2 + 2 + 1 = 10.

Now, if we increase the number of coins to 30, the possible arrangements skyrocket to 496. Out of these, only three configurations place all coins in a single box. Hence, with just three coins, the configuration where one box is full while the others are empty has a 30% chance of happening. In contrast, with 30 coins, this configuration’s probability plummets to only 0.6%.

What if we instead have 20 coins in one box and distribute the remaining 10 among the other two? To find all combinations, we consider the following possibilities:

1. A 20, B 10, C 0
2. A 20, B 9, C 1
3. A 20, B 8, C 2
4. A 20, B 7, C 3
5. A 20, B 6, C 4
6. A 20, B 5, C 5
7. A 20, B 4, C 6
8. A 20, B 3, C 7
9. A 20, B 2, C 8
10. A 20, B 1, C 9
11. A 20, B 0, C 10

This results in 11 combinations, which triples when accounting for the three possible boxes that can hold the 20 coins. Thus, the probability of selecting a configuration with 20 coins in one box and 10 in the others is 6.7%, which is over ten times more likely than the previous 0.6% chance for a single box with all 30 coins.

Now, let’s consider a case where there are 10 coins in one box and 20 to distribute in the other two:

1. A 10, B 20, C 0
2. A 10, B 19, C 1
3. A 10, B 18, C 2
4. A 10, B 17, C 3
5. A 10, B 16, C 4
6. A 10, B 15, C 5
7. A 10, B 14, C 6
8. A 10, B 13, C 7
9. A 10, B 12, C 8
10. A 10, B 11, C 9
11. A 10, B 10, C 10
12. A 10, B 9, C 11
13. A 10, B 8, C 12
14. A 10, B 7, C 13
15. A 10, B 6, C 14
16. A 10, B 5, C 15
17. A 10, B 4, C 16
18. A 10, B 3, C 17
19. A 10, B 2, C 18
20. A 10, B 1, C 19
21. A 10, B 0, C 20

This results in 21 configurations per box, leading to a total of 63 combinations. The probability of having 10 coins in one box and 20 in the others is 12.7%, making it over 20 times more likely than the scenario with all 30 coins in one box.

Summarizing the examples, we can see that the least likely configuration occurs when all coins are concentrated in one box. As distributions become more balanced, their likelihood increases. This principle becomes even more pronounced as the number of coins increases. For three coins, the probability of an extremely unbalanced distribution is 30%, but it drops to just 0.6% for 30 coins. Essentially, the more items in play, the less probable extreme configurations are.

This statistical fact, applicable not only to coins and boxes but any random distribution of particles and energies, has significant implications for physical systems. In any closed system, particles and energies tend to distribute themselves to achieve the most likely configuration, which has the least variation.

While extreme distributions are theoretically possible, they are extremely rare in practice. The frequency of such occurrences depends on the number of items being distributed and the total possible configurations.

This leads us to consider that we, along with everything around us, are made up of countless atoms and molecules. For example, a single ice cube contains approximately 10²? water molecules. When energy exchanges occur between liquid water, ice, and the surrounding air, the resulting balanced temperature distribution is far more likely than retaining the temperature difference. Consequently, as energy is exchanged, the ice melts, increasing the total entropy of the system.

In summary, due to statistical probability, it is nearly impossible for an ice cube to remain intact at room temperature. The appearance of an ice cube emerging from a glass of water is something only achievable in reverse, as in a movie, not in reality. While it’s not physically impossible for individual frozen water molecules to transfer energy to liquid water molecules, experimental evidence shows that the second law of thermodynamics can indeed be violated on a microscopic scale.

However, the total entropy of a macroscopic system can only increase due to the overwhelming influence of large numbers. Our human experience occurs at this macroscopic level, where we interact with objects composed of trillions of atoms and molecules. This leads to events having an irreversible trajectory; as transformations occur, total entropy increases along with disorder. The localized order we create as intelligent beings comes at the expense of greater disorder in the overall Universe, often manifested as heat released into space.

This statistical principle, which indicates that transformations involving macroscopic objects lead to an inevitable rise in entropy, provides time with its irreversibility. It’s impossible for shattered glass pieces on the ground to spontaneously reassemble into a whole glass, even though such an event wouldn't contradict any physical laws. Similarly, time travel remains highly improbable. To travel back in time would mean reverting the universe, or a part of it, to a macroscopic state of lower entropy. For instance, envision traveling back to when a twig was still unburned before being tossed into a fire, requiring a decrease in the universe's total entropy.

The law of large numbers as it applies to us and our surroundings seems to categorically prevent us from rewinding the "tape" of events. Since we cannot reduce total entropy, we are equally unable to reverse the arrow of time.