An Analog of the 2-Wasserstein Metric in Non-Commutative Probability Under Which the Fermionic Fokker–Planck Equation is Gradient Flow for the Entropy

@article{Carlen2012AnAO,
  title={An Analog of the 2-Wasserstein Metric in Non-Commutative Probability Under Which the Fermionic Fokker–Planck Equation is Gradient Flow for the Entropy},
  author={Eric A. Carlen and Jan Maas},
  journal={Communications in Mathematical Physics},
  year={2012},
  volume={331},
  pages={887-926}
}
  • Eric A. Carlen, Jan Maas
  • Published 2012
  • Mathematics, Physics
  • Communications in Mathematical Physics
  • Let $${\mathfrak{C}}$$C denote the Clifford algebra over $${\mathbb{R}^n}$$Rn, which is the von Neumann algebra generated by n self-adjoint operators Qj, j = 1,…,n satisfying the canonical anticommutation relations, QiQj + QjQi =  2δijI, and let τ denote the normalized trace on $${\mathfrak{C}}$$C. This algebra arises in quantum mechanics as the algebra of observables generated by n fermionic degrees of freedom. Let $${\mathfrak{P}}$$P denote the set of all positive operators $${\rho\in… CONTINUE READING

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