Open Quantum Theory of Shot Noise in Dissipative Chiral Transport

We develop an open quantum theory for shot-noise dynamics in dissipative chiral transport. By mapping a system under consideration onto a quantum circuit, we show that current noise is governed by two competing factors: the average occupancy distribution and particle-number fluctuations. With energy fully relaxed, shot noise is strongly suppressed, reflecting the stacking of electrons into lower energy states due to dissipation. This process quenches the partition noise from partially occupied levels, and finally isolates the residual noise protected by strong $U(1)$ symmetry. Moreover, selectively heating the source against the bath uncovers the underlying competition between the noise contributions from the occupancy distribution and those from the particle-number fluctuations. It triggers a sign reversal in inter-channel correlation noise, a signature masked by seemingly identical single-channel thermal noises. We propose an inversion scheme to experimentally reconstruct the hidden occupancy distribution directly from measurable noise cumulants.