There is No Quantum Regression Theorem

The Onsager regression hypothesis states that the regression of fluctuations is governed by macroscopic equations describing the approach to equilibrium. It is here asserted that this hypothesis fails in the quantum case. This is shown first by explicit calculation for the example of quantum Brownian motion of an oscillator and then in general from the fluctuation-dissipation theorem. It is asserted that the correct generalization of the Onsager hypothesis is the fluctuation-dissipation theorem.