Non-Markovian dynamics under time-translation symmetry

A dynamical symmetry is employed to determine the structure of quantum non-Markovian time-local master equation. Such a composed from two components: scalar kinetic coefficients and standard Markovian operator form. The are generally time-dependent incorporate information on kinematics memory effects, while operators manifest symmetry. Specifically, we focus time-translation symmetric dynamics, where Lindblad jump constitute eigenoperators free dynamics. This motivated by thermodynamic microscopic considerations, strict energy conservation between system environment imposes construction generalized other symmetries, driven systems. formalism illustrated three exactly solvable models, exact reduced description exhibits structure. formal equation leads first principle calculation coefficients. opens possibility simulate in modular fashion