Non-equilibrium, weak-field induced magnetism: a mechanism for magnetobiology

There is a long-time quest for understanding physical mechanisms of weak magnetic field interaction with biological matter. Two factors impeded the development of such mechanisms: first, a high (room) temperature of a cellular environment, where a weak, static magnetic field induces a (classically) zero equilibrium response. Second, the friction in the cellular environment is large, preventing a weak field to alter non-equilibrium processes such as a free diffusion of charges. Here we study a class of non-equilibrium steady states of a cellular ion in a confining potential, where the response to a (weak, homogeneous, static) magnetic field survives strong friction and thermal fluctuations. The magnetic field induces a rotational motion of the ion that proceeds with the cyclotron frequency. Such non-equilibrium states are generated by a white noise acting on the ion additionally to the non-local (memory-containing) friction and noise generated by an equilibrium thermal bath. The intensity of this white noise can be weak, i.e. much smaller than the thermal noise intensity.