Can the macroscopic fluctuation theory be quantized?

Abstract

The macroscopic fluctuation theory (MFT) is an effective framework to describe transports and their fluctuations in classical out-of-equilibrium diffusive systems. Whether the MFT may be extended to the quantum realm and which form this extension may take is yet terra incognita but is a timely question. In this short introductory review, I discuss possible questions that a quantum version of the MFT could address and how analysing quantum simple exclusion processes yields pieces of answers to these questions.