Abstract
Applying monochromatic filters to the ends of a one-dimensional nonlinear medium, we find an exact identity relating the nonreciprocity—the difference in transmission from the left or right—to the power flowing with equal sources on both sides. Thus, nonreciprocity has an unanticipated link to an apparent violation of the second law of thermodynamics; this violation is only apparent because of a subtle dependence on the (arbitrarily small) filter bandwidth. At high intensities, a nonperturbative transition to a noisy state destroys the identity. Apart from the theoretical insight provided by filters, not contaminating other frequency channels has obvious advantages in communications.
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