Definition
The arrow of time is the observed asymmetry between past and future: we remember the past but not the future, ordered systems decay into disordered ones, and the universe expands.
The fundamental laws of physics are nearly time-symmetric — they look the same run forward or backward. The arrow of time is the puzzle of where one-way behavior comes from in a world built from two-way equations.
Why it matters
How it works
The thermodynamic arrow comes from the second law of thermodynamics: the entropy of an isolated system never decreases. Shuffle a deck and it almost surely becomes more disordered, never less. The arrow points from low-entropy past to high-entropy future.
The psychological arrow — our subjective sense that time flows from past to future — is widely believed to track the thermodynamic one. Memory formation requires recording information in the brain, which is itself an entropy-increasing process. We remember the past because the past was lower-entropy and could be encoded; we cannot remember the future because that record has not yet been written.
The cosmological arrow is the direction in which the universe expands. The very early universe was extremely smooth and hot but in a special, low-gravitational-entropy state (matter and energy spread out evenly rather than clumped into black holes). As the universe evolved, gravitational clumping increased entropy enormously.
Hawking's no-boundary proposal supplies a possible reason all three arrows coincide: the universe begins in a low-entropy state by construction, and the thermodynamic arrow inherits its direction from that initial condition. Time's apparent flow is the universe rolling away from that boundary.