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Résumé |
In general, the difficulty to characterise non-equilibrium systems lies in the
fact that there is no analogue of the Boltzmann-distribution to describe
thermodynamic variables and their fluctuations. Over the last 20 years, however,
it was observed that there is a class of classical non-equilibrium systems with
diffusive transport in which the statistics of particle density and particle
current show universal properties that do not depend on the microscopic details of
the model. The general framework to characterise these systems from a macroscopic
point of view is today called the “Macroscopic Fluctuation Theory”. A natural
question is whether this framework can be extended to quantum mechanics to
describe the statistics of purely quantum mechanical effects such as entanglement
in diffusive out-of-equilibrium systems. With this aim in mind, I will introduce
the Quantum Simple Symmetric Exclusion Process (Q-SSEP), a microscopic toy model,
from which we hope to gain inside in possible universal features of these quantum
mechanical effects. I will present the results obtained so far and comment shortly
on the recent observation that free cumulants, a tool from free probability
theory, seems to play a role in the mathematical structure of the model. |
