Basis of the generalized irreversible Carnot engine model and the generalized heat transfer law Q alpha (Delta T-m)(n), the exergy loss methodology and the entransy loss methodology are employed to investigate the irreversibility of the generalized irreversible Carnot engine system (GICES). The mathematical expression of entransy loss and the exergy loss for different types of the GICES are derived. Additionally, two novel physical variables defined as potential entransy loss and entransy degeneration are proposed. Then, the entransy loss equilibrium and the entransy loss equation are derived. Moreover, with the Newton's heat transfer law and the generalized heat transfer law, the characteristics of entransy loss, exergy loss and entransy degeneration for the GICES are investigated. Finally, with the entransy degeneration, the entransy loss coefficient (phi) is defined, which can synthesize the entransy loss for the GICES and the entransy dissipation for the heat transfer system. (C) 2016 Elsevier Ltd. All rights reserved.