A Fluctuation-Dissipation Structure of Quantum Dynamical Semigroups Reveals a Unique Internal Hamiltonian

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 principle for objectively distinguishing coherent from incoherent parts of the dynamics, enabling an unambiguous determination of a system's inherent energy structure.