Jarza

Jarza pulls a molecular rope again and again. Some pulls cost less than the free energy. Average them the right way and the answer comes out exact.

The Physics

Pulling a small system out of equilibrium, the work W varies from run to run. The Jarzynski equality says the exponential average of that work gives the equilibrium free-energy difference exactly. Individual pulls can come in below ΔF; on average W ≥ ΔF still holds.

⟨e^(−βW)⟩ = e^(−βΔF), β = 1/(k_B T)

• W: work done in one run (J)
• ΔF: free-energy difference (J)
• β: inverse thermal energy (1/J)
• k_B: Boltzmann constant (J/K)
• T: temperature (K)
• ⟨ ⟩: average over many runs

C. Jarzynski published it in 1997, G. Crooks generalised it in 1999, and Liphardt et al. tested it by pulling single RNA molecules (Science, 2002).

Honest caveat: It is not a second-law violation, and it needs the system to start in equilibrium.

On the shirt

Front: Jarza, the pixel-art character, with the title. Back: the equality, the Crooks relation, the below-ΔF note and the 1997, 1999 and 2002 sources. Printed on a unisex tee.