This paper develops simplifying entropic models of irreversible closed cycles. The entropic models involve the irreversible connections between external and internal main operational parameters with finite physical dimensions. The external parameters are the mean temperatures of external heat reservoirs, the heat transfers thermal conductance, and the heat transfer mean log temperatures differences. The internal involved parameters are the reference entropy of the cycle and the internal irreversibility number. The cycle’s design might use four possible operational constraints in order to find out the reference entropy. The internal irreversibility number allows the evaluation of the reversible heat output function of the reversible heat input. Thus the cycle entropy balance equation to design the trigeneration cycles only through external operational parameters might be involved. In designing trigeneration systems, they must know the requirements of all consumers of the useful energies delivered by the trigeneration system. The conclusions emphasize the complexity in designing and/or optimizing the irreversible trigeneration systems.