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We extend the finite-temperature Keldysh non-equilibrium coupled clustertheory (Keldysh-CC) [{\it J. Chem. Theory Comput.} \textbf{2019}, 15,6137-6253] to include a time-dependent orbital basis. When chosen to minimizethe action, such a basis restores local and global conservation laws(Ehrenfest's theorem) for all one-particle properties, while remaining energyconserving for time-independent Hamiltonians. We present the time-dependentorbital-optimized coupled cluster doubles method (Keldysh-OCCD) in analogy withthe formalism for zero-temperature dynamics, extended to finite temperaturesthrough the time-dependent action on the Keldysh contour. To demonstrate theconservation property and understand the numerical performance of the method,we apply it to several problems of non-equilibrium finite-temperature dynamics:a 1D Hubbard model with a time-dependent Peierls phase, laser driving ofmolecular H$_2$, driven dynamics in warm-dense silicon, and transport in thesingle impurity Anderson model.

Conservation laws in coupled cluster dynamics at finite-temperature