Noncanonical statistics of a finite quantum system with non-negligible system-bath coupling

The canonical statistics describes the statistical properties of an open system by assuming its coupling with the heat bath is infinitesimal in comparison with the total energy in thermodynamic limit. In this paper, we generally derive a noncanonical density matrix for the open system with a finite coupling to the heat bath, which deforms the energy shell to effectively modify the conventional canonical way. The obtained noncanonical distribution reflects the back action of system on the bath and thus depicts the statistical correlations between two subsystems by the mutual information as a result of energy conservation.