Maxwell's demon

Simulation of the Maxwell's demon thought experiment with a two-dimensional ideal gas based on Hamiltonian physics and soft sphere potentials.

:: Maxwell's demon ::
Maxwell's demon challenges the second law of thermodynamics by systematically decreasing the entropy of a closed system without introducing external work or forces.
This is achieved by the demon deciding which particles are to penetrate the potential barrier dividing high energy (left) and low energy particles (right.
The original proposal of Maxwell's demon depicted the demon opening and closing a hatch, but is here depicted with a glow of the eligible particles. Either process requires only infinitesimal work by the demon, as the hatch may be regarded as massless.

:: Technical ::
The entire video covers only one single simulation, which was performed and rendered in real time.

The simulation involves 256 soft sphere particles that act upon any other object with a compactly supported soft sphere potential, allowing the simulation to be performed in O(N*log(N)). The demon decides which particles can penetrate the center potential barrier, based on their velocity. The decision is always made before the particles enter the center potential. A penetrating particle may encounter a second potential barrier near the center in case the particle was struck just as it was about to enter. This particularly prevents particles from achieving high energy just as they are about to enter the right side.

The simulation was made using explicit higher order symplectic integrators. Consequently, the energy is conserved at any time regardless of the decisions made by the demon.

All graphs have an origo offset. The entropy decreases only by a few percent.

The entropy was calculated using a two-dimensional variant of the Sackur-Tetrode equation.

The system is (arguably) not time reversible
The system is (arguably) violating Liouville's theorem
The system is (arguably) violating the second law of thermodynamics
None of the statements are to be associated with or attributed to numerical errors or the accuracy of the used symplectic integrators.

[NANO]

Unfair, you didn't count the entropy of the demon 😉

[bogdan_ostaficiuc]

That demon really is a demon if entropy decreseases.

[ixqyumo]

That’s how air conditioning works. You get more heat blown out from condenser than removed by evaporator.