Can the macroscopic fluctuation theory be quantized?

@article{Bernard2021CanTM,
  title={Can the macroscopic fluctuation theory be quantized?},
  author={Denis Bernard},
  journal={Journal of Physics A: Mathematical and Theoretical},
  year={2021},
  volume={54}
}
  • D. Bernard
  • Published 9 July 2021
  • Physics
  • Journal of Physics A: Mathematical and Theoretical
The macroscopic fluctuation theory (MFT) is an effective framework to describe transports and their fluctuations in classical out-of-equilibrium diffusive systems. Whether the MFT 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 MFT could address and how analysing quantum simple exclusion processes yields pieces of answers to… 
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References

SHOWING 1-10 OF 116 REFERENCES
Macroscopic fluctuation theory
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
Stochastic dissipative quantum spin chains (I) : Quantum fluctuating discrete hydrodynamics
Motivated by the search for a quantum analogue of the macroscopic fluctuation theory, we study quantum spin chains dissipatively coupled to quantum noise. The dynamical processes are encoded in
Current fluctuations in stochastic lattice gases.
TLDR
A large deviation theory is established for the space-time fluctuations of the empirical current for lattice gases in the macroscopic limit extending the dynamic approach for density fluctuations developed in previous articles.
Crossover between ballistic and diffusive transport: the quantum exclusion process
We study the evolution of a system of free fermions in one dimension under the simultaneous effects of coherent tunneling and stochastic Markovian noise. We identify a class of noise terms where a
Open Quantum Symmetric Simple Exclusion Process.
TLDR
The approach gives a solution of the classical symmetric simple exclusion process based on fermion technology and opens the route towards the extension of the macroscopic fluctuation theory to many-body quantum systems.
Equilibrium fluctuations in maximally noisy extended quantum systems
We introduce and study a class of models of free fermions hopping between neighbouring sites with random Brownian amplitudes. These simple models describe stochastic, diffusive, quantum, unitary
Current fluctuations in nonequilibrium diffusive systems: an additivity principle.
We formulate a simple additivity principle allowing one to calculate the whole distribution of current fluctuations through a large one dimensional system in contact with two reservoirs at unequal
Dynamics of fluctuations in quantum simple exclusion processes
We consider the dynamics of fluctuations in the quantum asymmetric simple exclusion process (Q-ASEP) with periodic boundary conditions. The Q-ASEP describes a chain of spinless fermions with random
From Stochastic Spin Chains to Quantum Kardar-Parisi-Zhang Dynamics.
TLDR
The asymmetric extension of the quantum symmetric simple exclusion process which is a stochastic model of fermions on a lattice hopping with random amplitudes is introduced and the discrete Cole-Hopf (or Gärtner) transform of the height field that satisfies a quantum version of the Stochastic heat equation is introduced.
Quench dynamics and relaxation in isolated integrable quantum spin chains
We review the dynamics after quantum quenches in integrable quantum spin chains. We give a pedagogical introduction to relaxation in isolated quantum systems, and discuss the description of the
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