We propose a definition of cycle representation for Quantum Markov Semigroups (qms) and Quantum Entropy Production Rate (QEPR) in terms of the ρ-adjoint. We introduce the class of circulant qms, which admit non-equilibrium steady states but exhibit symmetries that allow us to compute explicitly the QEPR, gain a deeper insight into the notion of cycle decomposition and prove that quantum detailed balance holds if and only if the QEPR equals zero.
We introduce the notion of Θ-KMS adjoint of a quantum Markov semigroup, which is identified with the time reversed semigroup. The break of Θ-KMS symmetry, or Θ-standard quantum detailed balance in the sense of Fagnola–Umanità,11 is measured by means of the von Neumann relative entropy of states associated with the semigroup and its Θ-KMS adjoint.
We propose a definition of infinite dimensional Choi-Jamio lkowski state associated with a completely positive trace preserving map. We introduce the notion of Θ-KMS adjoint of a quantum Markov semigroup, which is identified with the time reversed semigroup. The break down of Θ-KMS symmetry (or Θ-standard quantum detailed balance in the sense of Fagnola-Umanità[10]) is measured by means of the von Neumann relative entropy of the Choi-Jamio lkowski states associated with the semigroup and its Θ-KMS adjoint.
We use a natural generalization of the discrete Fourier transform to define transition maps between Hilbert subspaces and the global transport operator Z. By using these transition maps as Kraus (or noise) operators, an extension of the quantum energy transport model of describing the dynamics of an open quantum system of N-levels is presented. We deduce the structure of the invariant states which can be recovered by transporting states supported on the first level.
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