It’s true that entropy does explain the arrow of time for a number of phenomena, including why coffee and milk mix but don’t unmix, why ice melts into a warm drink but never spontaneously arises along with a warm beverage from a cool drink, and why a cooked scrambled egg never resolves back into an uncooked, separated albumen and yolk. In all of these cases, an initially lower-entropy state (with more available, capable-of-doing-work energy) has moved into a higher-entropy (and lower available energy) state as time has moved forwards. There are plenty of examples of this in nature, including of a room filled with molecules: one side full of cold, slow-moving molecules and the other full of hot, fast-moving ones. Simply give it time, and the room will be fully mixed with intermediate-energy particles, representing a large increase in entropy and an irreversible reaction.
Except, it isn’t irreversible completely. You see, there’s a caveat that most people forget when it comes to the second law of thermodynamics and entropy increase: it only refers to the entropy of a closed system, or a system where no external energy or changes in entropy are added or taken away. A way to reverse this reaction was first thought up by the great physicist James Clerk Maxwell way back in the 1870s: simply have an external entity that opens a divide between the two sides of the room when it allows the “cold” molecules to flow onto one side and the “hot” molecules to flow onto the other. This idea became known as Maxwell’s demon, and it enables you to decrease the entropy of the system after all!