Is Einstein's relation D = kTU always true?

TL;DR

This paper examines the conditions under which Einstein's fluctuation-dissipation relation holds, proposing alternative models for adiabatic fluctuations and extending the analysis to quantum systems, challenging the universality of the classical formula.

Contribution

It introduces a new approach to quantum relaxation, showing that Einstein's relation may not always be valid and that adiabatic models are more appropriate in quantum Brownian motion.

Findings

Einstein's relation holds under isothermic fluctuations

Adiabatic fluctuations lead to a different diffusion-mobility relation

Quantum systems are better described by adiabatic models

Abstract

The validity of Einstein's fluctuation-dissipation relation is discussed in respect to the type of relaxation in an isothermal system. The first model, presuming isothermic fluctuations, leads to the Einstein formula. The second model supposes adiabatic fluctuations and yields another relation between the diffusion coefficient and mobility of a Brownian particle. A new approach to relaxations in quantum systems is also proposed that demonstrates applicability only of the adiabatic model for description of the quantum Brownian dynamics.