Fluctuation-dissipation structure of quantum-dynamical semigroups revealing a unique internal Hamiltonian
Phys. Rev. A 114, 042412 – Published 8 October, 2026
DOI: https://doi.org/10.1103/d7ns-vcxn
Abstract
We refine a fluctuation-dissipation framework for quantum-dynamical semigroups to resolve a long-standing ambiguity in Markovian master equations. For finite-dimensional systems, we prove that the underlying diffusion-dissipation structure—rooted in a classical Markov process analogy—is invariant under Lindblad generator symmetries. This invariance uniquely identifies the internal Hamiltonian. Our framework provides a universal classification of quantum-dynamical semigroups where the coherent and incoherent parts of the dynamics are uniquely determined, thus enabling an unambiguous determination of a system's inherent energy structure.
