A quantum generalization of the thermal viscous friction law

TL;DR

This paper introduces a quantum extension of the classical viscous friction law for Langevin equations, ensuring consistency with quantum principles and resolving anomalies in quantum fluctuation-dissipation relations.

Contribution

It proposes a quantum generalization of the viscous friction law based on energy balance equivalence, valid without zero-point contributions, and consistent with the quantum regression theorem.

Findings

Recovers classical law as Planck's constant approaches zero

Resolves anomalies in quantum fluctuation-dissipation theorem

Satisfies the quantum regression theorem

Abstract

On the basis of the equivalence of the energy balance deacription at micro- and macro-level we propose a quantum generalization of the viscous friction law for a macroscopic Langevin equation describing thermal fluctuations without the zero point contribution. This equation recovers the classical case in the limit h -> 0. In particular it satisfies the quantum regression theorem and resolves several anomalies appearing in the quantum extension of the fluctuation dissipation theorem.