Violating the Second Law of Thermodynamics

"Modified Feynman ratchet with velocity-dependent fluctuations"
"Such randomness-breaking can spontaneously obtain via interaction between Brownian-motional Doppler effects --- which manifest the required velocity-dependence --- and system geometrical asymmetry"
"Uncompensated decreases in total entropy,
challenging the second law of thermodynamics, are thereby implied."    mdpi.com/1099-4300/6/1/76/pdf

Gedanken;
An adiabatic (non-convective) volume of gas has a temperature gradient - the lapse dT/dz=-g/Cp is gas specific -- the gas can have temperature less than convective, and conduction downward will be toward ~adiabatic. (radiation tends to isothermal, and gravity which tends to adiabatic)

A radiator feeding into a light pipe on the bottom -- The temperature of the bottom can be transferred to the top (photons lapse only a little due to gravity) -- run a heat engine between the difference

Converting thermal energy to mechanical,
through gravitational asymmetry

Prove it.


Good f'ing luck.