Any adequate account of how micro-causality and quantum coherence can explain the emergent-property of spacetime and how the Wheeler-DeWitt problem of time can be solved must incorporate a theory of how the Lindblad master equation solves the Markov quantum fluctuation problem as well as showing how the quantum Jarzynski-Hatano-Sasa relation can be homologically defined globally for both, Minkowski space and Friedmann-Robertson-Walker generalized Cartan space-times. This is a step towards those goals. Consider a wave-function and the entropic quantum entanglement relation of the total system consisting of ‘S’, ‘m’ and the quantum-time measuring clock ‘c’ subject to Heisenberg’s UP. It follows then that the probability that any given initial state evolves for a time that undergoes jumps during intervals centered at times is given by:

So, the master equation:

is valid iff the Markovian approximation is faithful and valid only on time-scales longer than , hence the jump occurs during an interval centered on . Therefore, with the Hamiltonian:

where are the lowering/raising operators for the system and output mode respectively, it follows that the total system satisfies the master equation:

where the Pauli operator acts on the output mode and is the Liouville superoperator. Given that it is a linear equation, it has a solution given as:

and so the evolution of the density matrix is given by the Lindblad master equation: