Microscopic irreversibility in the neutral kaon system and the thermodynamical arrow of time I. CPT symmetric case

The master equation for the reduced density matrix of the neutral kaon system interacting with a (low temperature) boson gas is derived. The equation is transformed under time reversal (assuming CPT conservation) and the equations of motion in the direct and inverted time schemes are compared. The equations of motion are solved, in a perturbation method, and the explicit approach to thermodynamical equilibrium is described. The entropy production function for the kaonic decaying system is defined and calculated. It is shown that although the equilibrium state and the total entropy change during the approach to it are the same in both time schemes, the details of the entropy time dependence of a coherent initial state are different, thus suggesting a relation between microscopic and macroscopic arrows of time.