  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 $\Sc$. 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.
