Fluctuation reversals and one over root N
Signed entropy-production bars marching along the time axis. At 16k a few run backwards and light up as anomalies; switch to 64k and watch them vanish.
The relation on screen
Reversals are not forbidden, only exponentially rare, exactly as the Crooks relation states.
Symbols
- entropy change over a window
- forward and reverse probabilities
what to look for · Negative excursions exist and shrink with system size. The second law is statistical here, as it is in the lab.
Consensus to physics
- 01entropy production per step is a fluctuating quantity
- 02the integral fluctuation identity forces <e^-s> = 1 exactly
- 03Jensen then gives <s> >= 0, the second law, while leaving individual negative events possible
- 04those events are visible at small N and vanish at large N
In standard physics
Crooks and Jarzynski, the Brownian ratchet
The panel that shows the second law is statistical. At 16k patches three cycles run entropy backwards; at 64k there are none. They vanish because relative fluctuations fall like one over root N, which is why the second law looks absolute at everyday scale.
boundary · Zero reversals at 64k is not the second law being exact. It is fluctuations shrinking with N.