Irreversibility

Macroscopic time-asymmetry emerging from time-reversible microscopic dynamics

N = 120
T = 2.0
40%

The Puzzle of Irreversibility

Newton's laws (and quantum mechanics) are time-reversible: if you flip all velocities, the system retraces its path. Yet macroscopically, gas never spontaneously unmixes. The "reverse" movie looks wrong.

The resolution lies in initial conditions and phase space volume: states that look "ordered" occupy an exponentially tiny fraction of phase space. A randomly chosen microstate from a "mixed" macrostate will almost never be one that leads to unmixing.

S = k ln W (Boltzmann) — entropy counts accessible microstates