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We review the description of the Johnson noise as a particular case ofBrownian motion and compare it with Nyquist's description. Motivated by theanalysis of a simple circuit with two resistors, we hypothesize that theelectric field that generates the Johnson noise originates from all theconducting material that makes up the circuit. We build a workable onedimensional model for a gas of particles that undergo stochastic collisionswith the lattice and distance-dependent inter-particle interaction. Simulationswith this model predict that in the case of a circuit with nonuniformtemperature, the strength of the Johnson noise at a segment of the circuit isinfluenced by the temperature at other parts of the circuit in an essentiallynon-local way.

Non-local origin and correlations in the Johnson noise at nonuniform temperatures