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.

arXiv comment28 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"

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Cited by in corpus (16)

• Ballistic macroscopic fluctuation theory
• Generalized hydrodynamics: a perspective
• Coherent Fluctuations in Noisy Mesoscopic Systems, the Open Quantum SSEP and Free Probability
• A Dyson Brownian motion model for weak measurements in chaotic quantum systems
• Bernoulli variables, classical exclusion processes and free probability
• Universal out-of-equilibrium dynamics of 1D critical quantum systems perturbed by noise coupled to energy
• Ballistic Modes as a Source of Anomalous Charge Noise
• Large deviations of density fluctuations in the boundary driven Quantum Symmetric Simple Inclusion Process
• Measurement-Induced Phase Transition in State Estimation of Chaotic Systems and the Directed Polymer
• Symmetry shapes thermodynamics of macroscopic quantum systems
• Large deviations of current for the symmetric simple exclusion process on a semi-infinite line, and on an infinite line with a slow bond
• Correlation functions of the Bjorken flow in the holographic Schwinger-Keldysh approach
• Dynamics of entanglement fluctuations and quantum Mpemba effect in the $\nu =1$ QSSEP model
• $\nu$-QSSEP: A toy model for entanglement spreading in stochastic diffusive quantum systems
• Nonequilibrium phases and quantum correlations in synthetic transport models
• Inhomogeneous quenches and GHD in the $\nu =1$ QSSEP model