Asymmetric stochastic localization in geometry controlled kinetics.

We consider the motion of Brownian particles confined in a two-dimensional symmetric bilobal enclosure with uneven cross section. Varying cross section of the confinement results in an effective entropic potential in reduced dimension. By employing two external noise forces, one additive and another multiplicative along x direction, we demonstrate that a correlation between them causes a symmetry breaking of entropic stability, i.e., a difference in relative stability of two lobes. This leads to an asymmetric localization of population in the stationary state. A two-state model is proposed to explain the asymmetric localization of population due to entropic diffusion.