Johnson–Nyquist noise in the context of "Spectral density"

The Boltzmann constant (k_B or k) is the proportionality factor that relates the average relative thermal energy of particles in a gas with the thermodynamic temperature of the gas. It occurs in the definitions of the kelvin (K) and the molar gas constant, in Planck's law of black-body radiation and Boltzmann's entropy formula, and is used in calculating thermal noise in resistors. The Boltzmann constant has dimensions of energy divided by temperature, the same as entropy and heat capacity. It is named after the Austrian scientist Ludwig Boltzmann.

As part of the 2019 revision of the SI, the Boltzmann constant is one of the seven "defining constants" that have been defined so as to have exact finite decimal values in SI units. They are used in various combinations to define the seven SI base units. The Boltzmann constant is defined to be exactly 1.380649×10 joules per kelvin, with the effect of defining the SI unit kelvin.

John Erik Bertrand Johnson (born Johan Erik Bertrand; October 2, 1887 – November 27, 1970) was a Swedish-born American electrical engineer and physicist. He created the first cathode-ray tube oscilloscope and detailed a fundamental source of random interference with information traveling on wires, now called Johnson–Nyquist noise.

The fluctuation–dissipation theorem (FDT) or fluctuation–dissipation relation (FDR) is a powerful tool in statistical physics for predicting the behavior of systems that obey detailed balance. Given that a system obeys detailed balance, the theorem is a proof that thermodynamic fluctuations in a physical variable predict the response quantified by the admittance or impedance (in their general sense, not only in electromagnetic terms) of the same physical variable (like voltage, temperature difference, etc.), and vice versa. The fluctuation–dissipation theorem applies both to classical and quantum mechanical systems.

The fluctuation–dissipation theorem was proven by Herbert Callen and Theodore Welton in 1951and expanded by Ryogo Kubo. There are antecedents to the general theorem, including Einstein's explanation of Brownian motionduring his annus mirabilis and Harry Nyquist's explanation in 1928 of Johnson noise in electrical resistors.