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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.
Stationary non-equilibrium states describe steady flows through macroscopic systems. Although they represent the simplest generalization of equilibrium states, they exhibit a variety of new phenomena. Within a statistical mechanics approach, these st
We will discuss the link between scientific explanations and probabilities, specially in relationship with statistical mechanics and the derivation of macroscopic laws from microscopic ones.
A stochastic dynamics has a natural decomposition into a drift capturing mean rate of change and a martingale increment capturing randomness. They are two statistically uncorrelated, but not necessarily independent mechanisms contributing to the over
We examine the Hall conductivity of macroscopic two-dimensional quantum system, and show that the observed quantities can sometimes violate the fluctuation dissipation theorem (FDT), even in the linear response (LR) regime infinitesimally close to eq
Stochastic entropy production, which quantifies the difference between the probabilities of trajectories of a stochastic dynamics and its time reversals, has a central role in nonequilibrium thermodynamics. In the theory of probability, the change in