Non-local origin and correlations in the Johnson noise at nonuniform temperatures (2401.10960v3)

Abstract: We propose an alternative scenario for the propagation of thermal noise in a conductor. In this scenario, the noise in the emf (electromotive force) between two terminals cannot be described as a sum of contributions from uncorrelated regions, each in local thermal equilibrium. We review previous studies of thermal noise in circuits with nonuniform temperature. We suggest experiments that could distinguish between different scenarios. We build 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 enunciate definitions of current, voltage, and emf, appropriate to a wire with limited number of particles. For uniform temperature, within appropriate length and temperature ranges, our simulations comply with Nyquist's result. Analytic results can be obtained in the limit of strong interparticle interaction. The simulations indicate that (1) thermal noise in a resistor at uniform temperature within an electric circuit can be larger (smaller) than predicted by Nyquist due to the presence of a resistor with higher (lower) temperature 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; (3) if the resistors differ in temperature, their emf can be correlated, even if they are detached. The long-range repulsion between charges in electrically connected resistors may have conceptual and technological impact in nanodevices.