The dual property of number and velocity fluctuations of charge carriers in a macroscopic conductor under thermodynamic equilibrium conditions

Fluctuation-dissipation relations are complemented by relating the macrovariables conductance and resistance, that describe dissipation, to the microvariables variance of carrier number and drift velocity fluctuations, that are the noise sources for constant voltage and constant current operation conditions, respectively. Thermal equilibrium implies a relationship between these two noise sources which follows from the reciprocity property of conductance and resistance. The boundary conditions of the measurement select the proper microscopic source of fluctuations to be related to the dissipation. An important consequence is that the source of shot noise, being associated with fluctuations of the carrier number inside the sample, is already present under equilibrium conditions, while the time scale of the source changes from an effective transport time to a current transit time when going from equilibrium to nonequilibrium conditions.