Can quantum regression theorem be reconciled with quantum fluctuation dissipation theorem ?

TL;DR

This paper investigates whether a conventional quantum fluctuation dissipation theorem (QFDT) exists and demonstrates that the perceived conflict with the quantum regression theorem can be resolved by interpreting QFDT as a condition of energetic balance.

Contribution

The paper offers a new interpretation of QFDT as a condition of energetic balance, reconciling it with the quantum regression theorem.

Findings

QFDT is equivalent to detailed energetic balance.

The conflict between QFDT and the regression theorem is resolved under this interpretation.

The conventional QFDT can be valid in quantum systems when viewed as an energetic balance condition.

Abstract

In the attempt to derive the regression theorem from the fluctuation dissipation theorem several authors claim the violation of the former theorem in the quantum case. Here we pose the question: does it exists a quantum fluctuation dissipation theorem (QFDT) in its conventional interpretation? It is shown that the relation usually called as the QFDT is the condition of detailed macroscopic energetic balance. Following this interpretation the existing conflict between the two theorems in the quantum case is removed.