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.

28 pages plus references, 5 figures. Prepared as a contribution to a special volume of Journal of Physics A on "Hydrodynamics of Low-Dimensional Quantum Systems"

References in corpus (5)

• Non equilibrium steady states: fluctuations and large deviations of the density and of the current
• Nonequilibrium Steady States of Matrix Product Form: A Solver's Guide
• Progressive field-state collapse and quantum non-demolition photon counting
• Bethe Ansatz Solution of the Asymmetric Exclusion Process with Open Boundaries
• The Exclusion Process: A paradigm for non-equilibrium behaviour