Johnson noise

Johnson noise (also Johnson–Nyquist or thermal noise) is the random electrical voltage that appears across any resistor in thermal equilibrium, caused by the thermal agitation of its charge carriers. Its mean-square open-circuit value over a bandwidth Δf is V² = 4k_BTRΔf, rising linearly with temperature, resistance and bandwidth. The noise is white over a wide range of frequencies and is present whether or not any current flows.

Its most striking feature is universality: the noise depends only on resistance, temperature and bandwidth, never on the resistor's material, geometry or construction. This material-independence is the signature of a thermodynamic result and is what allowed Nyquist to derive the formula from equilibrium thermodynamics alone, without any model of the electrons.

Johnson noise sets the fundamental sensitivity limit of electronic measurement: no amplifier can be quieter than the thermal hiss of its own input resistance. It is the reason sensitive detectors — from radio telescopes to gravitational-wave interferometers — cool their front ends to cryogenic temperatures, since lowering T is the only way to lower the floor.

Discovered experimentally by John B. Johnson at Bell Labs in 1927 and explained thermodynamically by his colleague Harry Nyquist in 1928, making it one of the first quantitative confirmations of the connection between thermal fluctuations and dissipation.