Johnson–Nyquist noise

Johnson–Nyquist noise (thermal noise, Johnson noise, or Nyquist noise) is the electronic noise generated by the thermal agitation of the charge carriers (usually the electrons) inside an electrical conductor at equilibrium, which happens regardless of any applied voltage. Thermal noise is present in all electrical circuits, and in sensitive electronic equipment (such as radio receivers) can drown out weak signals, and can be the limiting factor on sensitivity of electrical measuring instruments. Thermal noise increases with temperature. Some sensitive electronic equipment such as radio telescope receivers are cooled to cryogenic temperatures to reduce thermal noise in their circuits. The generic, statistical physical derivation of this noise is called the fluctuation-dissipation theorem, where generalized impedance or generalized susceptibility is used to characterize the medium. Thermal noise in an ideal resistor is approximately white, meaning that the power spectral density is nearly constant throughout the frequency spectrum, but does decay to zero at extremely high frequencies (terahertz for room temperature). When limited to a finite bandwidth, thermal noise has a nearly Gaussian amplitude distribution. This type of noise was discovered and first measured by John B. Johnson at Bell Labs in 1926. He described his findings to Harry Nyquist, also at Bell Labs, who was able to explain the results. As Nyquist stated in his 1928 paper, the sum of the energy in the normal modes of electrical oscillation would determine the amplitude of the noise. Nyquist used the equipartition law of Boltzmann and Maxwell. Using the concept potential energy and harmonic oscillators of the equipartition law, where is the noise power density in (W/Hz), is the Boltzmann constant and is the temperature. Multiplying the equation by bandwidth gives the result as noise power. where N is the noise power and Δf is the bandwidth. Thermal noise is distinct from shot noise, which consists of additional current fluctuations that occur when a voltage is applied and a macroscopic current starts to flow.

The Privacy Power of Correlated Noise in Decentralized Learning

The Privacy Power of Correlated Noise in Decentralized Learning