Demystifying Arrow of Time

Scientific discussions of the arrow of time often get quite confusing due to highly complex systems they deal with. Popular literature then often coveys messages that tend to get lost in translation. The purpose of this note is to demystify the arrow of time by stripping off the unnecessary complexities and thereby simplifying the discussion. We do this by providing examples that are exactly solvable and make it easy to see the root cause of the apparent "time-irreversibility". We also discuss "time-reversal" solutions, where the initial state evolves such that it reaches the state which is the same as the initial state moving backward in time. These solutions are simple enough to be comprehensible to a highschooler. We discuss the arrow of time both in the classical and quantum settings, including in the cosmological context.