Can the Macroscopic Fluctuation Theory be Quantized?

Abstract: The Macroscopic Fluctuation Theory is an effective framework to describe transports and their fluctuations in classical out-of-equilibrium diffusive systems. Whether the Macroscopic Fluctuation Theory 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 Macroscopic Fluctuation Theory could address and how analysing Quantum Simple Exclusion Processes yields pieces of answers to these questions.