Anomalous transport phenomenon of a charged Brownian particle under a thermal gradient and a magnetic field

There is a growing interest in the stochastic processes of nonequilibrium systems subject to nonconserved forces, such as the magnetic forces acting on charged particles and the chiral self-propelled force acting on active particles. In this paper, we consider the stationary transport of noninteracting Brownian particles under a constant magnetic field in a position-dependent temperature background. We demonstrate the existence of the Nernst-like stationary density current perpendicular to both the temperature gradient and magnetic field, induced by the intricate coupling between the nonconserved force and the multiplicative noises due to the position-dependent temperature.