*3.5. Calculating the Diagrams*

The main reason why the time evolution of entropy in Equation (21) has been diagrammatically represented is that, due to the multiplicity in time ordering interactions, these extended Keldysh diagrams can help to correctly determine all possible symmetries that may simplify the problem. We need to express all 'single-world' interactions that carry the highest order perturbation as well as all 'cross-world' terms with lower orders of perturbation.

We assume the interaction Hamiltonian does not implicitly depend on time through its parameters; instead, the time dependence is globally assigned in the rotating frame and state evolutions. The explicit formulation of quantum dynamics and keeping track of symmetries between different diagrams have resulted in the following rules for the evaluations of the diagrams:

	- (a) Every interaction on a ket contour will be (*i*/¯*h*) *HI* (*t* ) and will be (−*i*/¯*h*) *HI* (*t* ) on a bra contour.
	- (b) After passing an interaction, the states must change. The new states remain the same until a new interaction is encountered, or if the initial time or the final time is reached.
	- (c) A contour arriving at the initial time will capture the initial density matrix in the interaction picture *R*0.
