Fluctuation Theorem

The ratio of probability of entropy-producing to entropy-consuming trajectories is exponential in entropy production

F = 1.5
kT = 1.0
N = 2000

The Theorem

The Crooks Fluctuation Theorem (Evans-Searles, Gallavotti-Cohen) states that the probability ratio of observing entropy production +σ vs −σ is exactly:

P(+σ) / P(−σ) = eσ

This means entropy-consuming trajectories are exponentially rare but never exactly zero. The log-ratio plot (green line) should have slope exactly 1 if the theorem holds — watch how well it fits even for small samples.