Can the Macroscopic Fluctuation Theory be Quantized?

TL;DR

This paper explores the potential for extending the classical Macroscopic Fluctuation Theory to quantum systems, using Quantum Simple Exclusion Processes to investigate possible formulations and implications.

Contribution

It provides an introductory discussion on how a quantum version of the Macroscopic Fluctuation Theory could be developed and what questions it might address.

Findings

Quantum Simple Exclusion Processes offer insights into quantum extensions

Potential formulations for quantum Macroscopic Fluctuation Theory

Identifies open questions and future directions

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.