Critical Behaviors of Asymmetric Granular Maxwell’s Demon Phenomenon

We theoretically derived the critical behaviors of the asymmetric granular Maxwell's demon phenomenon by introducing a symmetry-breaking parameter. This symmetry breaking can be realized experimentally by forming an angle between the vibration and vertical directions. The values of the conventional critical exponents beta, gamma, and delta were determined, and they satisfied Widom's scaling relation. In addition, the scaling function was calculated using asymptotic expansion, which was consistent with the numerical simulation.