Reversa

Reversa flips every molecule's velocity, and the gas should un-mix. So why does time only run one way?

The Physics

Newton's laws run equally well backwards, yet Boltzmann's H-theorem says a gas always heads toward equilibrium. Reverse every velocity and the gas would retrace its steps, so the arrow of time cannot come from the dynamics alone. The H-theorem rests on the molecular-chaos assumption.

H = ∫ f ln f d³v, dH/dt ≤ 0

• H: Boltzmann's H function (dimensionless, per volume)
• f: velocity distribution (s³/m⁶)
• d³v: velocity-space volume element (m³/s³)
• t: time (s)

Josef Loschmidt raised the objection in 1876.

Honest caveat: This does not break the second law. Why the past had low entropy is still debated.

On the shirt

Front: Reversa, the pixel-art character, with the title. Back: the reversibility of Newton's laws, Boltzmann's H-theorem, the molecular-chaos note and the 1876 objection. Printed on a unisex tee.