Arrow of Time

Entropy increase and the thermodynamic direction of time — why the past is different from the future

1.0 (maximum)
1.0×
Phase Space

The Past Hypothesis (David Albert, 2000)

The second law says entropy increases. But microscopic laws are time-reversible — there is no built-in "arrow." The resolution: the universe started in an extraordinarily low-entropy state (the Big Bang). This "Past Hypothesis" selects a special initial condition that breaks time symmetry.

Phase space volume occupied by ordered states is exponentially tiny. Almost every trajectory from any state leads toward higher entropy — because there are vastly more disordered states to go to.

dS/dt ≥ 0 (Second Law) — holds overwhelmingly but not absolutely