Zero-point term and quantum effects in the Johnson noise of resistors: a critical appraisal

Abstract

Abstract. There is a longstanding debate about the zero-point term in the Johnson noise voltage of a resistor. This term originates from a quantum-theoretical treatment of the Fluctuation-Dissipation Theorem (FDT). Is the zero-point term really there, or is it only an experimental artefact, due to the uncertainty principle, for phase-sensitive amplifiers? Could it be removed by renormalization of theories? We discuss some historical measurement schemes that do not lead to the effect predicted by the FDT, and we analyse new features that emerge when the consequences of the zero-point term are measured via the mean energy and force in a capacitor shunting the resistor. If these measurements verify the existence of a zero-point term in the noise, then two types of perpetual motion machines can be constructed. Further investigation with the same approach shows that, in the quantum limit, the Johnson-Nyquist formula is also invalid under general conditions even though it is valid for a resistor-antenna system. Therefore we conclude that and a satisfactory quantum theory of the Johnson noise, the Fluctuation-Dissipation Theorem, must, as a minimum, include also the measurement system used to evaluate the observed quantities. Issues concerning the zero-point term may also have implications for phenomena in advanced nanotechnology.

Information entropy and thermal entropy: apples and oranges

“…z) If the measurement is done by measuring the force between the plates of the C s shunt capacitor in the cicuitry in Figure 4, then the observed thermal noise is again zero, otherwise the Second Law is violated [27].…”

Second Law based definition of passivity/activity of devices

“…where Equation 2 is the Johnson-Nyquist formula; k is the Boltzmann constant; and T is the absolute temperature of the free-standing impedance in thermal equilibrium. Even though there are current discussions [3,4] about the FDT's prediction in the quantum region (at very low temperatures and/or very high frequencies), in the classical physical limit Equation 2 is verified by both careful experiments and everyday electrical engineering practice.…”

Does a Standalone, “Cold” (Low-Thermal-Noise), Linear Resistor Exist Without Cooling?

“…The thermal noise (Johnson-Nyquist noise) of resistors is due to the thermal motion of charge carriers in the sample, and it is the manifestation of Boltzmann's energy equipartition theorem. Its general existence in the quantum (high-frequency/low-temperature) limit is debated [1,2]. However the present paper is about its classical (low-frequency/high-temperature) limit, where there is a common agreement that the power density spectrum S u ( f ) of the thermal noise voltage of a resistor of resistance R is correctly given by the Johnson-Nyquist formula used in electrical engineering [3]:…”