  For sound waves impinging on a one-dimensional medium, we show that
nonlinearity can lead to nonreciprocal transmission, without dissipation or
broken time reversal invariance. Placing quasi-monochromatic filters at the
ends of the nonlinear medium, nonreciprocity can be obtained without the
generation of higher harmonics outside the medium. Remarkably, in this
configuration the nonreciprocity is found to be proportional to the net energy
flow when monochromatic sources of equal strength (at the filter frequency) are
simultaneously turned on at both ends. This result is conjectured to be general
for one dimensional scattering. It is also shown that although simultaneous
monochromatic sources lead to net energy flow, with sources of small but
non-zero bandwidth there is no net energy transport, in accordance with the
second law of thermodynamics.
