One-directional quantum mechanical dynamics and an application to decision making

In recent works we have used quantum tools in the analysis of the time evolution of several macroscopic systems. The main ingredient in our approach is the self-adjoint Hamiltonian $H$ of the system $\text{Sc}$. This Hamiltonian quite often, and in particular for systems with a finite number of degrees of freedom, gives rise to reversible and oscillatory dynamics. Sometimes this is not what physical reasons suggest. We discuss here how to use non self-adjoint Hamiltonians to overcome this difficulty: the time evolution we obtain out of them show a preferable arrow of time, and it is not reversible. Several applications are constructed, in particular in connection to information dynamics.