Equipartition laws of thermal noise

Classically, the thermal noise in electrical circuits and series circuits is governed by the equipartition law , where is the noise voltage developed across . When quantum effects are taken into account, the equipartition law no longer holds for circuits, although an equipartition law can be deemed for the measured mean square noise voltage under certain conditions. In series circuits the equipartition law , changes into for high- tuned circuits, where is the average energy of a harmonic oscillator tuned at the tuning frequency of the tuned circuit.