In a description of physical systems with Langevin equations, interacting degrees of freedom are usually coupled through symmetric parameter matrices. This coupling symmetry is a consequence of time-reversal symmetry of the involved conservative forces. If coupling parameters fluctuate randomly, the resulting noise is called multiplicative. For example, mechanical oscillators can be coupled through a fluctuating, symmetric matrix of spring constants. Such systems exhibit well-studied instabilities. In this note, we study the complementary case of antisymmetric, time-reversal symmetry breaking coupling that can be realized with Lorentz forces or various gyrators. We consider the case that these antisymmetric couplings fluctuate. This type of multiplicative noise does not lead to instabilities in the stationary state but renormalizes the effective non-equilibrium friction. Fluctuating Lorentz-force-like couplings also allow to control and rectify heat transfer. A noteworthy property of this mechanism of producing asymmetric heat flux is that the controlling couplings do not exchange energy with the system..
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