Nonlocal origin and correlations in the Johnson noise at nonuniform temperature

The conventional description of thermal noise in conductors (the Nyquist scenario) assumes that this noise has local origin and, therefore, the noise in the emf (electromotive force) in a conductor with nonuniform temperature can be described as a sum of contributions from uncorrelated regions, each in local thermal equilibrium. Here we propose an alternative scenario for the propagation of thermal noise in a conductor and suggest experiments that could distinguish between different scenarios. To explore the proposed scenario, we introduce a workable 1D model for a gas of particles that undergo stochastic collisions with the lattice and exert distance-dependent forces on each other. We define current, voltage, and emf in a manner appropriate to a wire with limited number of particles. For uniform temperature and within appropriate length and temperature ranges, we verify that our simulations comply with Nyquist's result. Our numerical simulations indicate that (1) thermal noise in a resistor at uniform local temperature is influenced not only by its own temperature but also by the temperatures of other resistors in the circuit; (2) for sufficiently long circuits, the deviation from the Nyquist prediction is inversely proportional to the distance between the centers of the resistors; and (3) if the resistors differ in temperature, their emf can be correlated, even if they are detached. Analytic results can be obtained in the limit of strong interparticle interaction. The long-range repulsion between charges in electrically connected resistors may have conceptual and technological impact on nanodevices.