1 Proof of zero Johnson noise at zero temperature Laszlo B. Kish 1 , Gunnar Niklasson 2 , Claes-Goran Granqvist 2 1 Department of Electrical and Computer Engineering, Texas A&M University, College Station, TX 778943-3128, USA 2 Department of Engineering Sciences, The Ångström Laboratory, Uppsala University, P.O. Box 534, SE-75121 Uppsala, Sweden Abstract. The Callen-Welton formula (fluctuation-dissipation theorem) of voltage and current noise of a resistance are the sum of Nyquist's classical Johnson noise equations and a (quantum) zero-point term with power density spectrum proportional to frequency and independent of temperature. At zero temperature, the classical Nyquist term vanishes however the zero-point term produces non-zero noise voltage and current. We show that the claim of zero-point noise directly contradicts to the Fermi-Dirac distribution, which defines the thermodynamics of electrons according to quantum-statistical physics. As a consequence, the Johnson noise must be zero at zero temperature, which is in accordance with Nyquist's original formula. Further investigation shows that Callen-Welton disregarded the Pauli principle during calculating the transition probabilities and, in this way, they produced the zero-point noise artifact. 1. Introduction: The Johnson noise and the second law In this paper, we prove that the zero-point term in the Johnson noise of resistors is non- existent. The Johnson (-Nyquist) noise [1,2] of resistors and impedances is a spontaneous voltage and current fluctuation due to the stochastic motion of charge carriers (electrons) in the conductor material at thermal equilibrium. The second law of thermodynamics requires that, in thermal equilibrium, the time average of the instantaneous power flow between two parallel resistors is zero: P a⇔b (t , T ) t = 0 , (1) where P a⇔b (t , T ) is the instantaneous power flow between resistors R a and R b , see Figure 1, and Equation 1 holds in any frequency band. Versions: June 1, 2; 2015