In this work, we numerically investigate linear thermal noise in a four-terminal system with a finite Berry curvature dipole (BCD) using the nonequilibrium Green's function formalism. By comparing with the semiclassical results for bulk systems, we establish a one-to-one correspondence between terminal-resolved linear noise in multiterminal systems and direction-resolved noise in bulk transport. Specifically, the autocorrelation function scales as $2k_{B}T$ when the driving field is perpendicular to the BCD and vanishes when they are parallel, whereas the cross-correlation scales as $k_{B}T$. Both the autocorrelation and cross-correlation functions exhibit pronounced peaks near the band edges, consistent with BCD-induced features. In addition, the linear thermal noise increases approximately linearly with $T$ at low temperatures and is suppressed by the dephasing effect at high temperatures. Our work bridges semiclassical bulk theory and quantum multiterminal theory for linear thermal noise, highlighting the symmetry (geometry)-selection rule in quantum transport.

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• Quantum fluctuations & noise
• Quantum geometry
• Transport phenomena
• 2-dimensional systems
• Nonequilibrium Green's function